The World's future
Innovations and New Technologies (v.2)
By Alexander Bolonkin
Dr.Sci., Professor of Russian and American Universities,
Former Senior Researcher of NASA, USA Air Force and Russian Aerospace Industry

New York, Lulu, 2013

The World's future

Innovations and New Technologies (v.2)
By Alexander Bolonkin
Dr.Sci., Professor of Russian and American Universities,
Former Senior Researcher of NASA,USA Air Force and Russian Aerospace Industry

Lulu, New Your, 2013

Book 5 Innovations and New Technologies 7 9 13

Contents:
About author 4
Abstract 5
Preface 6
Part 1. New Ideas and Innovations in Aerospace 7
1. Air Catapult Transportation 7
2. Hypersonic Ground Electric AB Engine 26
3. Protection of the Earth from Asteroids 42
4. Re-Entry Space Craft to Earth Atmosphere 49
5. Energy Transfers from Airborne Wind Turbines.
Review and Comparison of Airborne Turbines 61
6. Delivery of Asteroids to the Earth 88
7. Non Turbo Electric Wind Generator 102
8. Electron Air Hypersonic Propulsion 114
9. Long Distance Artillery 121
10. New Self-Propelled Penetration Bomb 134
11. Inexpensive Mini Thermonuclear Reactor 151
12.Hypersonic Space Aircraft 175
13. Method for Interstellar Flight 195

Part 2. New Ideas and Innovation in Space Sciences and Earth Technologies. 206
1. Universe. Relations between Time, Matter, Volume, Distance, and Energy.
Rolling of Space (Volume, Distance), Time, and Matter into a Point. 206
2. Underground Explosion Nuclear Energy. 215
3. Protection of Environment from Damaged Nuclear Station and Transparant Inflatable
Blanket for Cities (Protection from Radioactive Dust and Ghimical, Biological Weapons) 234
4. Electron Hydro Electric Generator 258
5. Hydro Propulsion for High Speed Submarines 266
6. Stability and Artificial Distraction of Tornado 273
7. Femtotechnology: Stability and Production Super-Strong AB Matter 283
8. Universe (Part 3). Relations between Charge, Time, Matter, Volume, Distance, and Energy 302
9. Electrostatic Generator and Electrostatic Transfomer 311
10. Jet Generator 322
11. Terroformatic of Planets and Space Objects 338

Appendix (Data) 362
General Reference 378

About the Author

Bolonkin, Alexander Alexandrovich (1933-)

Alexander A. Bolonkin was born in the former USSR. He holds doctoral degree in aviation engineering from Moscow Aviation Institute and a post-doctoral degree in aerospace engineering from Leningrad Polytechnic University. He has held the positions of senior engineer in the Antonov Aircraft Design Company and Chairman of the Reliability Department in the Clushko Rocket Design Company. He has also lectured at the Moscow Aviation Universities. Following his arrival in the United States in 1988, he lectured at the New Jersey Institute of Technology and worked as a Senior Researcher at NASA and the US Air Force Research Laboratories.

Bolonkin is the author of more than 250 scientific articles and books and has 17 inventions to his credit. His most notable books include The Development of Soviet Rocket Engines (Delphic Ass., Inc., Washington , 1991); Non-Rocket Space Launch and Flight (Elsevier, 2006); New Concepts, Ideas, Innovation in Aerospace, Technology and Human Life (NOVA, 2007); Macro-Projects: Environment and Technology (NOVA, 2008); Femtoyechnologies and Revolutionary Projects, (Lambert, 2009); Human Immortality and Electronic Civilization, 3-rd Edition, (Lulu, 2007; Publish America, 2010); Universe, Human Immortality and Future Human Evaluation. Elsevier. 2011г., 124 pages, 4.8 Mb.; LIFE. SCIENCE. FUTURE (Biography notes, researches and innovations). Publish America, Baltimore, USA, 2010, 208 pgs.

Abstract

In recent years of the 21^st Century the author of this book and other scientists as well, have instigated and described many new ideas, researches, theories, macro-projects, USA and other countries patented concepts, speculative macro-engineering ideas, projects and other general innovations in technology and environment change. These all hold the enticing promise for a true revolution in the lives of humans everywhere in the Solar System.
In aerospace these include air catapult transportation, hypersonic ground electric AB engine, protection of the Earth from asteroids and delivery of asteroids to the Earth, re-entry space apparatus to Earth, airborne wind turbines, electronic wind generator and propulsion, long distance shells, new self-propelled penetration bomb, inexpensive mini thermonuclear reactor, etc.

In technology these include new ideas and innovation in space sciences and Earth technologies: Relations between time, matter, volume, distance, and energy in the Universe; Rolling of Space (volume, distance), time, and matter into a point; Underground explosion nuclear energy; Protection of environment from damaged nuclear station; Electron hydro electric generator; Electron super speed hydro propulsion; Electric theory of tornado; Protection from tornado; and so on.

Author succinctly summarizes some of these revolutionary macro-projects, concepts, ideas, innovations, and methods for scientists, engineers, technical students, and the world public. Every Chapter has three main sections: At first section the author describes the new idea in an easily comprehensible way acceptable for the general public (no equations), the second section contains the scientific proof of the innovation acceptable for technical students, engineers and scientists, and the third section contains the applications of innovation. And, naturally, he fervently hopes the popular news media, various governments and the large international aerospace and other engineering-focused corporations will, as well, increase their respective observation, R&D activity in the technologies for living and the surrounding human environment.

Key words: Universe, transportation, energy, nuclear energy, aerospace, non-rocket space launch and flight, environment.

Preface

New macro-projects, concepts, ideas, methods, and innovations are explored here, but hardly developed. There remain many problems that must be researched, modeled, and tested before these summarized research ideas can be practically designed, built, and utilized--that is, fully developed and utilized.

Most ideas in our book are described in the following way: 1) Description of current state in a given field of endeavor. A brief explanation of the idea researched, including its advantages and short comings; 2) Then methods, estimation and computations of the main system parameters are listed, and 3) A brief description of possible applications--candidate macro-projects, including estimations of the main physical parameters of such economic developmental undertakings.

The first and third parts are in a popular form accessible to the wider reading public, the second part of this book will require some mathematical and scientific knowledge, such as may be found amongst technical school graduate students.
The book gives the main physical data and technical equations in attachments which will help researchers, engineers, dedicated students and enthusiastic readers make estimations for their own macro-projects. Also, inventors will find an extensive field of inventions and innovations revealed in our book.

The author have published many new ideas and articles and proposed macro-projects in recent years (see: General References). This book is useful as an archive of material from the authors' own articles published during the last few years.

The book mainly contains material from the author's articles published in the last few years.

Every chapter is independent. Than why some figures are repited.

Acknowledgement

1. Some data in this work is garnered from Wikipedia under the Creative Commons License.
2. The author wish to acknowledge Professor Shmuel Neumann and Jorseph Friedlander for help in editing of
this book.

Part 1.
New Ideas and Innovations in Aerospace

Chapter 1.

Air Catapult Transportation

Abstract

The current flight passenger-transport and cargo systems have reached the peak of their development. In the last 30 years there has been no increase in speed or reductions in trip costs. The transportation industry needs a revolutionary idea, which allows jumps in speed and delivery capability, and dramatic drops in trip price. The author offers a new idea in transportation in which trip (flight) time practically does not depend on distance, and vehicle load capability doubles and which has a driving engine that is located on the ground and can use any cheap source of energy.

The author develops the theory and provides computations for a project containing five subprojects united by the common idea: acceleration the air vehicle on the ground and continuation of flight by inertia (high speed catapulting). The initial speed is 290 - 6000 m/s, the range is 50 -10000 km (short, average, and long distances). Short transport system has a range on the order of 50-70 km, for example: city - sub-city, strait and air bridges such as across the Straits of Gibraltar 16 km, the English Channel 40 km, Bering Straits 100 km (Russia-America), Sakhalin-Asia 20 km, Russia-Japan, etc. The long distance has range up 10000 km such as New York-Paris 5838 km, Washington-London 7373 km, San-Francisco - Tokyo 8277 km, San-Francisco - Vladivostok (Russia) 8377 km, New York - Moscow 7519 km, Moscow - Beijing 5800 km, Moscow - Tokyo 7487 km, New York - Berlin 6392 km, and so on.

The offered catapult system having a length of 400 km can be used as a space launch system which decreases the space launch cost by hundreds of times. This also may be used as a new conventional high speed (up 1000 km/h) transport system between cities. That will be significantly cheaper then used MagLev (Magnetic Levitation) systems, because for levitation of the vehicle we employ conventional wings. The offered system may be also used for the mass launch of bombs (projectiles) in war.

-------------------
Key word: air catapult transport, air kinetic transport, new passenger and cargo transport, catapult aviation, new space launch system, new suspending high speed ground system, cattran, skimplane.

Introduction

Current takeoff mass of a long distance aircraft is made up of approximately 1/3 aircraft body, 1/3 fuel, and 1/3 payload. The aircraft engine needs expensive aviation fuel. The passenger-transport aircraft cannot exceed the speed of sound. The history of "Concorde" shows that the conventional passenger supersonic aircraft is unprofitable [1]. The hypersonic aircraft, which is under development by the USA, will be more unprofitable still as a passenger long distance aircraft because it will use very expensive hydrogen fuel, it is very complex and it has a high production cost. The hypersonic engine problems have not been solved in spite of spending large multiples of millions of dollars in research and testing. Space launch by the current rocket space system is very expensive. The current high speed (up to 580 km/h) MagLev (Magnetic Levitation) transport systems are also very expensive.

Transport, space launch systems and aviation all need new ideas that increase speed, and load capability, and reduce delivery cost. Some of these ideas have been published by the current author [1-11].

The initial author's idea is the acceleration (catapulting) of a cargo glider (vehicle), winged cargo box (non-engine aircraft), or space ship to high speed by using a cable engine. It was offered in 2002 [2] - [7], in particularly, it was presented in [1] and published in [8]. The current research is different because it uses a linear electric engine located on the ground. The vehicle will then use its kinetic energy for flight. The computation shows that a catapulted/kinetic aircraft accelerated to subsonic speed of 270-300 m/s can fly up to 60-80 km until its speed decreases to a landing speed of 50-60 m/s. This is far enough for suburban transport or for air bridges across the Straits of Gibraltar, English Channel, Bering Straits (Russia-America), Sakhalin-Asia, Russia-Japan, etc. For acceleration to this speed at a rate that is acceptable to passengers (overload of 3g) the runway length must be 1.5 km (current runways for large aircraft are 1.5 - 3 km long). For the middle range (200 - 1600 km) the runway must have a length of 4 - 67 km. For the long-distance flight (6000-8000 km), the air vehicle must be accelerated to a speed of 4-6 km/s. For acceleration of no more than 3g the required runway length would then be 270 - 400 km. This runway can be also used for a space launch. One author method and design are described in References [5, 8]. Rather than being a conventional runway, it is an air cable acceleration system [5] - [8] for the acceleration of space vehicles and it is located in atmosphere.

The offered method is different from conventional MagLev because for levitation of the vehicle we employ the conventional wing (no magnetic levitation!). That is significantly cheaper. The offered system has also smaller financial risk because it is uses conventional technologies and in any case one may be used in the place of a conventional ground high-speed transport system between big cities, opening a large market.

Brief description of the innovation

The system for catapult/kinetic vehicles (CV/KV) includes Figure (1) a runway having the linear electric engine (LEE) [1], [9]. The runway may be located on ground or over columns. The LEE can be located under the runway cover. In this case the runway may be used as a conventional aircraft take-off way (runway) or a car highway (quite straight) and may double as a launcher. At speeds over 50 m/s (180 km/s) the catapult vehicle supported by its wings and does not have friction with ground. As computations show, the length of runway is 1400 m for the subsonic vehicles having range 50-70 km; 4 - 67 km for the supersonic vehicle having range 200 - 1600 km; and 270 - 600 km for hypersonic vehicles having range up 10,000 km (and more) for acceptable (for conventional passengers) acceleration 3g. Trained astronauts/cosmonauts can tolerate a "G" overload of up to 9g and their starting runway can be 400 km for a final speed of 8 km/s. For cargo space ships the runway will be significantly lower (because of higher G tolerance). The part of runway, where vehicle has supersonic or over Mach 1 speed may need reflectors, which will reflect the shock wave (sound boom). The system has a starting trolley where the catapulted vehicle is supported during launch. After release this trolley brakes at high deceleration and the additional braking distance is small. This part of spent energy is retuned back into the system.

This system is significantly cheaper than MagLev because it does not need the expensive magnetic suspension system. Rather than expensive liquid fuels, it uses cheaper electric energy. The vehicles save greatly on expensive engines.

The system works in the following way. The catapult vehicle (aircraft without engines, wing container) located on the start trolley, accelerates (overload n = 3g), separates from trolley, climbs to the needed altitude (one may has the vertical overload n = 3g), flies (using its kinetic energy, gradually loses speed and increases its attack angle or/and wing area), glides and lands as a conventional aircraft.

Figure (1). Trajectories of the catapult vehicles (kinetic/ballistic vehicle, aircraft). (a) Short distance (up 70 km) subsonic vehicle (city - sub-city. Strait, mountain); (b) Middle distance (up 1500 km) supersonic vehicle (between cities); (c) Long distance (intercontinental, outer space) hypersonic vehicle, (space ship, satellites, probes). (d) Hypersonic vehicle with rebound from atmosphere. Notations: 1 - start, acceleration station; 2 - Climb to altitude; 3 - flight into atmosphere (subsonic and supersonic vehicles), or outer space (hypersonic vehicle; 3a - flight with rebound from atmosphere; 4 - gliding in atmosphere; 5 - trajectory, 6 - surface, 7 - boundary of atmosphere (- 80 - 100 km).

The range strongly depends upon the ratio K = lift/drag. The subsonic civil aircraft has K - 12 - 20 (gliders have K up 70). For example, Boeing-747 has K = 17 [19]. The supersonic aircraft in the range Max number M = 1.5 - 4 has K - 6 - 8. For example, Concord has K = 7.14 [8]. The hypersonic aircraft has K - 4 - 4.5. Approximately K = 4(1+3/M) for M > 1.5, where M is Mach number. The special catapult aircraft will have K of (1 - 3) more because one does not have the motor gondolas (drag inducing engine mounts). A good trajectory is a trajectory when aircraft climbs to high altitude and glides. The hypersonic CV may reach rarefied heights or out of atmosphere and significantly increase the range. It is very useful if the aircraft has the variable swept and wing area. Many current supersonic aircraft have these properties (B-1, Tu-160) [8].

The subsonic CV starts from a conventional aerodrome equipped by LEE, and is accelerated (with 3g) up to a speed of 270-300 m/s (Mach number 0.9) by the linear electric engine into the runway which is 1500-1800 m long Figure (1). The aircraft takes off, flies (50-70 km, Fig. (1a)), gradually loses speed and increases its attack angle and extend the flaps. When the speed drops so it is close to landing speed, the aircraft extends the landing gear and lands. At first modified old aircraft (without engines and engine nacelles) can be used for early versions of the offered transport system.

The range of the high-speed aircraft may reach 200-10,000 km (or more) see Figure (3). The aircraft can make a full circle and return to its base. The flight data are drastically improved if the vehicle has variable wing area or variable swept wings [5]. Other similar ideas and useful points for kinetic aviation are presented in References [5 - 8]. The flight altitude does not its influence range because the energy spent in climbing will be returned in gliding.

This new type of -+transportation the author names as Cattran (Catapult transportation).

Theory of catapult transport (Cattran) and a general estimation of flight data

(In metric system)

(1)

where R is range [m]; R₀ = 6,378^.10⁶ is the Earth's radius [m]; K is the average aerodynamic efficiency (K = 10 - 22 for subsonic air vehicles and K = 5-8 for supersonic air vehicles. For example: the subsonic Boeing-747 has maximum K = 17; Tu-104 K=18; B-1, Tu-160 K > 19 (in subsonic regime); Boeing 47E K = 20; Boeing B-52G K = 21.5; Rutan Voyager K = 27, Lockheed U-2 K = 28; M-17 (high altitude aircraft) K = 30; gliders have K = 40 - 70; the supersonic "Concorde" has maximum K = 7,5, supersonic aircraft XB-70 and YF-12 have K = 7, and Boeing 2707-300 has K = 7.8 ); g_o = 9.81 m/s² is gravity [8]; V₁ is initial (after acceleration) speed [m/s]; V₀ < V₁ is final (near landing) speed [m/s] (V₀ = 50-60 m/s); V is variable speed, V₀ < V < V₁ [m/s]. For estimation average V = 0.5(V₁+V₀); mg/K = D is air drag [N]; m is vehicle mass [kg]. For V < 2000 m/s, variable gravity g - g_o. Last equation in (1) is obtained from the first equation using integration.

The ratio K approximately equals:

(2)

Here M is Mach number; L is wing span, m; S is wing area, m²; a is sound speed, at H = 0, T = 0^oC a = 330 m/s; for T = 20^oC a = 342 m/s. For H > 11 km a - 295 m/s; C_d,0 - 0.008 - 0.012 is the vehicle drag coefficient for attack angle = 0.

Results of computations for subsonic (V < 300 m/s, M < 0.9, M is Mach number) and supersonic vehicles are presented in Figures (2&3). The range of a subsonic vehicle is 45 - 90 km for V₁ = 300 m/s Figure (2); the range of a supersonic vehicle can reach 4000 - 8200 km for V₁ = 4500 m/s (figure.3).

2. Maximum acceleration sub-distance 1 (S) Figure (1) and required energy (E) (only for acceleration - that is main part of common energy) can be calculated using the equation

(3)

where n is overload, g; m is vehicle mass, kg.

Results of computations for subsonic and supersonic aircraft are presented in Figures (4 & 5).

Figure (2). Range of the subsonic catapult (kinetic) vehicle versus initial speed for different aerodynamic efficiency K = 10 12 14 16 18 20.

Figure (3). Range of the supersonic catapult vehicle versus initial speed for different aerodynamic
efficiency K = 4 5 6 7 8.

Figure (4). Acceleration distance of subsonic catapult vehicle versus initial speed and different overloads.

Acceleration (3g) distance is 1500 m for a speed of 300 m/s for the subsonic vehicle and 340 km for a speed of 4.5 km/s for the supersonic vehicle.

Figure (5). Acceleration distance of supersonic catapult aircraft versus initial speed and different overload.

3. Average speed, V_a, and flight time, T, are

(4)

The results of computation of eq.(4) are presented in Figures (6 &7). The subsonic vehicle has an average speed 1.5 times greater than conventional aircraft (because the catapult vehicle has high subsonic speed of the beginning), and the average speed of the supersonic (hypersonic) vehicle is more than 6-9 times that of a conventional subsonic vehicle. The flight time is less for both cases.

Figure (6). Average speed of the kinetic/catapult and conventional vehicle versus range for differentaerodynamic efficiency K = 4 5 6 7 8.

Figure (7). Average flight time of the kinetic/catapult vehicle and conventional aircraft versus range.

4. The trajectory of horizontal turn can be found from the following differential equations

(5)

where L₁ is the projection of the vehicle lift force to a horizontal plane (vertical overload is n = 3g); t is time [seconds]; ? is turn angle [rad].

Results of computations for different overloads show that the vehicle can turn back and return to its original aerodrome (for example, the transport/passenger vehicle in emergency case or a bomber after a flight into enemy territory) (see [1], [8] p.366, figs. A.2.8-9).

5. Computation of the complex trajectory used for high altitude and outer space.

Accurate equations of ballistic trajectory are:

(6)
For subsonic speed (M < 0.9)

L = 0.5C_L ?V²S, D =0.5C_L ?V²S , g = g_o ,
For supersonic (M > 1.5) and hypersonic speed

L = 0.5C_L ?aVS, D = 0.5C_D ?aVS, g = g_o(R_o/R)²,

where r is range of ship flight, m; R₀ = 6,378,000 is radius of Earth, m; R is radius of ship flight from Earth's center, m. R = R_o+H; V is ship speed, m/s; H is ship altitude, m; ? is trajectory angle, radians; D is ship drag, N; m is ship mass, kg; g is gravity at altitude H, m/s²; L is ship lift force, N; ?_E = 7.27^.10^-5 is angle Earth speed, rad/sec; ?_E = 0 is lesser angle between perpendicular to flight plate and Earth polar axis; t is flight time, sec.; C_L is lift force coefficient, for subsonic speed C_L = 0 - 3.5 , for supersonic speed C_L - 4? , where ? is the wing attack angle, rad; C_D is air drag coefficient. For supersonic wing C_D - ?²; a - 295 m/s for H > 11 km is sonic speed in atmosphere; S is wing area, m²; ? is the air density, for H = 0 ?_o = 1.225 kg/m³. For H = 0 - 100 km ? - ?_o exp(-1.4^.10^-4).

6. Estimation of range: The computation of equation (5) requests the complex numerical integration. For estimation of climb range (sub-distance 2 in Figure (1) can be used the simpler equation

(7)
where g - 10 m/s² Earth gravitation; n = 3 - 9 vehicle overload; K = L/D is the ratio lift/drag. For subsonic speed (M < 0.9) K - 17 - 22, for supersonic speed (M >1.5) K - 4(1+3/M), where M = V/a is Mach number. The ratio K for subsonic aircraft is significantly more than K for supersonic aircraft. The way for large range at the start is to get a high altitude and glide from it (fig.1b). For the same reason after entering to atmosphere from vacuum it may be useful to bounce off the atmosphere and return to vacuum Figure (1d). It is also useful for cooling of vehicle.

Sub-distance 3 (flight out Earth atmosphere, H >- 80 -100 km) can be computed by equations:

(8)
where L₃ is sub-distance 3 (fig.1) (flight out Earth atmosphere, H >- 80 -100 km), m; ? is Earth angle, rad; V_a is vehicle speed at the exit from atmosphere, m/s; ?_a is trajectory angle at the exit from atmosphere; ?_a,opt is optimal trajectory angle (maximal range of sub-distance 3) at the exit from atmosphere.

7. Estimation of heating: The magnitudes in equations (5)-(6) for hypersonic speed compute as:

(9)

where: g₀ = 9.81 m/s² is gravity at Earth surface; ? is air density, kg/m³; Q is heat flow in 1 m²/s of leading sharp, J/s^.m²; S is wing area, m²; ?_SL= 1.225 kg/m³ is air density at sea level; V_CO = 7950 m/s is circle orbit speed; T₁ is temperature of leading edge (tip) in stagnation point in Kelvin, ^oK; T is temperature of leading edge in stagnation point in centigrade, ^oC; T₂ is temperature of the standard atmosphere at given altitude, ^oK; D is vehicle drag, N; L is vehicle lift force, N; C_D is drag coefficient; a = 295 m/s is sound speed; C_S = 5.67 W/(m^2.K⁴) is coefficient radiation of black body; ? is coefficient of a black (? - 0.03 - 0.99).

For speed less than M = 3 (V < 900 m/s) the heating of the leading edge from a shock wave is small. For example, for Concord and Ty-144 it is about 127^oC [8]. The aluminum alloys can resist 175^oC. But for hypersonic vehicle that heat may reach 1500^oC. But for the offered vehicle that is not a problem. The current material can keep up to 2500^oC, the leading edge is under this temperature a shot time (about only 40 seconds), that can require only a small cooling. The problem of heating for re-entry apparatus such as Shuttle and Apollo and the catapult vehicle is opposite. The re-entry apparatus must SPEND its gigantic kinetic energy as soon as possible (to brake). That way Shuttle has a BLUNT (obtuse) fuselage and wing edge, which give a high air drag. That gives a very high heat flow. Our vehicle must CONSERVE the kinetic energy. One has a sharp fuselage and wing edge, which has a small air drag and small heat flow [9, Chapter8].

The Shuttle must decrease speed from 8000 m/s to zero (Apollo must lose 11 km/s). Our vehicle loses only 500 -1000 m/s during lifting (climbing) in atmosphere. That means one get a specific heat (in 1m²) of 500 - 4000 times less than Shuttle. The flight time of Shuttle in dense atmosphere is tens of minutes, our vehicle - only 40 sec. [17, Chapter 4].

8. Linear electric engine: Linear electric (magnetic) engines (LEE) exist in various forms. They are widely used for subsonic Maglev. The record speed of MagLev is 581 km/h (2011), the railroad is 575 km/h. Some hypersonic LEEs are offered and researched by author in [10] Chapter 8, [11], [14-16]. The new linear electrostatic engine was offered by author in [17].

9. Levitation of vehicle. The current railroad wheels cannot support high-speed vehicles because the centrifugal force of wheels is very large. For supporting vehicle was suggested magnetic force (as Maglev) or an air cushion (as hovercraft). Author offers the new method of the ground vehicle levitation by lift from wings. That is very simple. The ratio K = L/D can be up 100 and more. The specific feature of offered apparatus from flarecraft, sea skimmer, ekranoplan, is next: ekranoplan and others has engine located in apparatus and they can fly anywhere. The offered apparatus has engine located at ground level and moves only over a special track. One version has the ability to run only on special flat, smooth way (as Maglev) with very high K. Therefore I name that version the Skimplane.

Advantages

The offered method has the following advantages:

The load capability of catapult vehicle increases as a factor of two in comparison with
conventional aircraft (no fuel or engine in the catapult vehicle. Fuel mass reaches 30 - 40%, engine mass is about 10% of total conventional aircraft mass).

The catapult vehicle (cattran) is significantly cheaper than conventional aircraft (no aviation engines, which are very expensive and have limited engine life: 2000-9000 hours. The aircraft body has a lifetime of 20-30 years). In with ground transport, we don't need expensive bridges, tunnels, roads.

The linear electric engine located on the ground can work on cheaper electric energy.

The average speed for long-distance travel is increased by 6-9 times see Figure (6).

The maximum flight time is about 34 min for a distance at 10,000 km (see Table 3 and Figure (7)).

The flight article production cost is dramatically reduced.

One installation can have a very large capability and can serve many airlines, for example, most airlines from the USA to Europe (New York to London, Paris, Berlin, Madrid, Brussels, Fan Francisco - Tokyo, Shanghais, etc). The load capability is also increased greatly.

The installation can be used to launch outer space passenger and cargo ships, satellites and probes (some accelerator projects currently offered use conventional airplanes as a Stage 0 booster but they have a maximum speed of only 270 m/s).

The installation can be used for space tourism and flights along high altitude ballistic trajectories.

The installation can be used as conventional very high-speed ground transport between big cities (skimplane).

The installation can be used for mass launch of military projectiles in wartime.

Projects (Cattran, Skimplane)

The offered project contains only the well-known technologies. The risk is small. The full project contains the 4 subprojects. The realization of this project is best to start from the cheapest subproject 1, which allows getting the experience for more complex subprojects.

Subproject 1. Subsonic speed sort distance (50 -70 km) catapult passenger vehicle (for city and sub city, straits, mountains, and etc.).

There are a lot of islands in the world, located close to one another or located close to a continent, which have large transportation flows. For example:

Assume the mass of the passenger vehicle is m = 15 tons (100 passengers and 4 members of crew); the start acceleration is a = 3g - 60 m/s² (this acceleration is acceptable for conventional people). The range is approximately 67 km (see Fig. 2) or calculate using R - KV²/2g = 67.3 km for a final acceleration speed of 290 m/s and K = 16, g = 9.81 m/s².

The required acceleration distance is about S = V²/2a =1400 m. The time of horizontal acceleration is t = V/a = 9.7 seconds. The energy required for acceleration of the aircraft is E = mV²/2. This is about E=0.63^.10⁹ Giga joules (1 Giga joules = 10⁹ J) if V = 290 m/s. A power is about P = E/t = 0.63^.10⁹/ 9.7- 65,000 kW. If the engine efficiency is ? = 0.95, the energy consumption will be F = E/? = 0.63^.10⁹/0.95 = 0.66 GJ per flight or 6.6 MJ per one passenger. As it is shown below the 1 MJ of electric energy cost 0.00877$. Therefore the energy spent by 1 passenger will be cost 6.6^.0.00877 = 0.0578$ or about 6 cents.
Flight time is about 394 sec or 6.57 minutes. In present time the car or train requires at distance 67 km about 1 hour and in traffic it is requires significantly more time.

Summary of the main results: For the start speed - 300 m/s, landing speed - 50 m/s, maximal range 70 km, average speed 175 m/s = 630 km/h, flight time - 400 sec = 6.7 min, acceleration distance for overload 3g is 1500 m, acceleration time is 10 sec.

Subproject 2. Supersonic speed catapult passenger vehicle for distance 200 - 1500 km.

Distance between main cities are: New York - Washington 329 km, London-Paris 344 km, Berlin-Warsaw 517 km, Moscow-St.-Petersburg 653 km, Moscow-Kiev 756 km, Berlin-Paris 878 km, Paris-Madrid 1054 km, Tokyo-Vladivostok 1157 km, Tokyo-Seoul 1157 km, Rome-Berlin 1185 km, Rome-Madrid 1365 km.

Assume the mass of the passenger vehicle is m = 15 tons (100 passengers and 4 members of crew); the start acceleration is a = 3g. The result of computations in the trajectory #2 (climbing of altitude up speed 270 m/s and gliding with ratio lift/drag K = 20) are presented in Table 1. Used equations are (7).

Table 1. Computations of supersonic catapult passenger vehicle for range 200 - 1500 km. Overload is n = 3g.

Subproject 3. Catapulted hypersonic speed passenger vehicle for distance 4000 - 10000 km.

The distance between main cities are (aircraft great circle courses are not straight lines): New York-Paris 5838 km, Washington-London 7373 km, San-Francisco - Tokyo 8277 km, San-Francisco - Vladivostok (Russia) 8377 km, New York - Moscow 7519 km, Moscow - Beijing 5800 km, Moscow - Tokyo 7487 km, New York - Berlin 6392 km.

Assume the mass of the space vehicle is m = 15 tons (100 passengers and 4 members of crew); the acceleration is a = 3g (this acceleration is acceptable for conventional people). Results of computation in Trajectory 3 (climbing of altitude 100 km, ballistic flight in space and gliding with ratio lift/drag K₁ = 4.5 up V = 290 m/s and K = 20 for V < 290 m/s) are presented in Table 2. Equations are (6) - (7).

Table 2. Computations the hypersonic catapult passenger vehicle
for range 4000 - 10,000 km. Overload n = 3g.

Flight time (NY - Paris, range 5838 km) is about 25 minutes. In present time the trip NY - Paris takes about 7 hours. The required acceleration distance is S = 340 km. The time of horizontal acceleration is t = V/a =V/3g = 150 seconds = 2.5 minutes (see also Reference [7]).
As you see for acceleration up to hypersonic speed requires a special launch track having a linear electric engine and the special trolley (cart) where the catapult vehicle is located. A small additional way is required for braking this cart at high G. This launch track may be used:
1) For very high speed transportation between cities.
2) As cheap space launcher.

Subproject 4. A high speed (up 1000 km/h) ground transport system between cities (skimplane).

There are a lot of conventional projects for high speed transportation between cities. For our case are suitable city pairs: New York - Washington 329 km, Berlin-Warsaw 517 km, Moscow-St.-Petersburg 653 km, etc.

Economical efficiency

The conventional railroad costs about 0.8 - 1.3 M$/km (in permafrost (Siberia) - 11M$/km), highway system (8 lanes) 30 M$/km (USA), sea bridge 50- 80 M$/km, underground tunnel about 200 M$/km (English-France $12B, 50 km, 240 M$/km), Maglev about 25 M$/km.

Our system does not have a magnetic suspending system and one will be cheaper than MagLev. In present time the significant part of the passenger ticket cost is the cost of fuel. In aviation, car and bus this fuel percentage of cost reaches up 50%. For comparison of different transport systems we compute the cost of energy receiving from dissimilar types of fuel and the cost of delivery of one passenger to one kilometer by different types of transportation.

In Table 3 the reader will find the approximate costs of the different form of energy converted to mechanical energy.

Table 3. Average cost of mechanical energy for different fuels.

Quote sources: Internet, Cost of fuel, December 2011.

Notes: 1. Price of the wholesale aviation (turbojet) fuel and an average retail price of gas/diesel fuel for car/bus in the USA.
2. Average wholesale price in the USA. Retail price is $0.065/kWh.
3. Russia sells natural gas to Europe $400/1000 m³ (2011).

As you see the cost of a unit of the electric energy in 9 times is less than aviation liquid fuel. The aviation, cars, buses, and most military vehicles can work only by liquid fuel, but the electric power plant can be hydro, wind, and nuclear power installations. This is an advantage for countries wishing to cut oil imports.

Method estimation of the cost of fuel for moving one passenger (100 kg) per the distance 1 km by the conventional transport (aviation, bus, railroad, sea ship) and cattran, skimplane.

1. Energy required for moving one passenger (100kg) per the distance 1 km by conventional transport and skimplane

(10 )
where E_v is energy requested for moving 100 kg of the loaded vehicle per 1 km = 1000 m [J/km]; m is mass of vehicle, 100 kg; g = 9.81m/s²; D = 1 km = 1000 m is distance; K = L/D_r is ratio of lift force to drag of the vehicle; E_p is energy required for moving one passenger per 1 km, J/man^.km; b = m_p/m is ratio of total mass passengers to total mass of vehicle (load coefficient); C is cost of fuel for moving one passenger to distance 1 km; c is cost of energy.

2. Energy required for moving one passenger (100kg) per the distance 1 km by catapult transport (cattran)

(11 )

where V_m is the maximal speed of catapulting, m/s; D_f is distance of full flight, km.

For the sea ship the equations in (10) are

(12 )

Here N is power of engine, W; V is ship speed, m/s; W is displacement of the sea ship, kg.
The results of computation are presented in Table 4.

Table 4. Average cost of fuel for moving one passenger (100 kg) per distance 1 km by conventional,
catapult transport (cattran) and skimplane

Notes: 1. Bus has 60 passengers; total mass of bus is 28 tons.
2. Wagon has 54 sleeping places; total mass of the empty wagon is 23 tons.
3. Sea ship has displacement 14660 tons, engine 6252 kW, passengers 1078.

As you see the fuel cost of delivery of one passenger to one kilometer by cattran is 5.5 times less than long distance aviation and in 14 times less than by middle range aviation. The fuel cost of the delivery passengers from a sub-city to city by the subsonic cattran is 24 times less than a bus.

At the present time the fuel cost is 20 - 50% of a ticket cost in aviation, bus and ship. The real consumption of fuel for Boeing-747 (M = 0.9) is 0.031 liter/passenger.km, for supersonic (M = 2) and for Concord the fuel consumption is 0.166 liter/passenger.km [8] which explains why the Concord is not profitable. Fuel prices change with time, but in any case the cost of delivery will be some times less than delivery by conventional aircraft. Critics must remember that the main content of this article is not economic estimations, but the new idea for transportation, aviation and space launch.

Discussion of Problems

If speed is less than 5-7 Mach, the catapult vehicles (the leading edges) can be made from heat-resistant material. If the speed is more than Mach 7, the hypersonic CV may need to have a cooling system. However, this problem is not as difficult for catapult vehicles as it is for the Space Shuttle. The problems of the Space Shuttle and the CV are different. The Space Shuttle has much greater speed (about 8000 m/s) and kinetic energy, and needs to reduce this speed and energy by air drag. For this the Space Shuttle has an obtuse (blunt) nose and leading edges of the wings. The CV must conserve its speed and energy for the long flight. The CV has a sharp nose and leading edges of the wings. The Shuttle must lose 8 km/s of speed, the CV loses in atmosphere only about 1 km/s. That means CV gets heated about (8³) 300-500 times less than the Space Shuttle. This problem can be solved by a light knockout ceramic cover (as on the Space Shuttle) or a cooling system. If it uses water for cooling, the vapor can be used for additional thrust. Lithium as a cooler (in place of water, not in conjunction with it) has 5 times the capability of water, 0.9 kg of lithium is enough to cooling a 5-ton projectile launched from the ground at a speed of 8 km/s. However, this method needs more research and computation.

Some other ideas of the author the reader find in the References [5-17]. Cost of projects may be calculated using [18]. Some patents are in [19]-[33].

Conclusion
Author offers and researches new transportation forms, which increase speed by 2 - 9 times, decreases fuel consumption (and trip cost) and allows cheaper launch to outer space.

Current and Future Developments: A good progress is in Maglev Train and records:

And R&D of the RailGun (NAVY projects) makes possible the creating of the offered transportation system. This system makes possible rapid progress in high-speed ground, air and space transportation. In air transportation the offered system increases speed and decreases cost several times, in aerospace decreases cost of outer space launch over a hundred times.

References

[1]. A.A. Bolonkin, "High Speed Catapult Aviation", AIAA-2005-6221, presented to Atmospheric Flight Mechanic Conference - 2005. 15-18 August, USA.[2]. A.A. Bolonkin, "Air Cable Transport System", Journal of Aircraft, Vol. 40, No. 2, July-August 2003, pp. 265-269.

[3]. A.A. Bolonkin, "Bolonkin's Method Movement of Vehicles and Installation for It", US Patent 6,494,143 B1, Priority is on 28 June 2001.

[4]. A.A. Bolonkin, "Air Cable Transport and Bridges", TN 7567, International Air & Space Symposium - The Next 100 Years, 14-17 July 2002, Dayton, Ohio, USA

[5]. A.A. Bolonkin, "Non-Rocket Missile Rope Launcher", IAC-02-IAA.S.P.14, 53rd International Astronautical Congress, The World Space Congress - 2002, 10-19 Oct 2002, Houston, Texas, USA.

[6]. A.A. Bolonkin, "Inexpensive Cable Space Launcher of High Capability", IAC-02-V.P.07, 53^rd International Astronautical Congress. The World Space Congress - 2002, 10-19 Oct. 2002. Houston, Texas, USA.

[7]. A.A. Bolonkin, "Non-Rocket Space Rope Launcher for People", IAC-02-V.P.06, 53rd International Astronautical Congress. The World Space Congress - 2002, 10-19 Oct 2002, Houston, Texas, USA.

[8]. A.A. Bolonkin, "Non-Rocket Space Launch and Flight", Elsevier, 2005, 468 pgs. Attachment 2: High speed catapult aviation, pp.359-369.
http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182

[9]. A.A. Bolonkin, "New Concepts, Ideas, Innovations in Aerospace, Technology and the Human
Sciences", NOVA, 2006, 510 pgs. http://www.scribd.com/doc/24057071 ,
http://www.archive.org/details/NewConceptsIfeasAndInnovationsInAerospaceTechnologyAndHumanSciences

[10]. A.A. Bolonkin, R. Cathcart, "Macro-Projects: Environments and Technologies", NOVA, 2007,
536 pgs. http://www.scribd.com/doc/24057930 .
http://www.archive.org/details/Macro-projectsEnvironmentsAndTechnologies .

[11]. A.A. Bolonkin, Femtotechnologies and Revolutionary Projects. Lambert, USA, 2011. 538 p.
16 Mb. http://www.scribd.com/doc/75519828/
http://www.archive.org/details/FemtotechnologiesAndRevolutionaryProjects
[12]. A.A. Bolonkin, LIFE. SCIENCE. FUTURE (Biography notes, researches and innovations). Scribd,
2010, 208 pgs. 16 Mb. http://www.scribd.com/doc/48229884,
http://www.archive.org/details/Life.Science.Future.biographyNotesResearchesAndInnovations
[13]. A.A. Bolonkin, Universe, Human Immortality and Future Human Evaluation. Scribd. 2010г.,
4.8 Mb. http://www.archive.org/details/UniverseHumanImmortalityAndFutureHumanEvaluation,
http://www.scribd.com/doc/52969933/

[14]. A.A.Bolonkin, "Magnetic Space Launcher" has been published online 15 December 2010, in the
ASCE, Journal of Aerospace Engineering (Vol.24, No.1, 2011, pp.124-134).
http://www.scribd.com/doc/24051286/

[15]. A.A.Bolonkin, Universe. Relations between Time, Matter, Volume, Distance, and Energy
(part 1) http://viXra.org/abs/1207.0075, http://www.scribd.com/doc/100541327/ ,
http://archive.org/details/Universe.RelationsBetweenTimeMatterVolumeDistanceAndEnergy

[16]. A.A.Bolonkin, Lower Current and Plasma Magnetic Railguns. Internet, 2008.
http://www.scribd.com/doc/31090728 ; http://Bolonkin.narod.ru/p65.htm .

[17] A.A.Bolonkin, Electrostatic Climber for Space Elevator and Launcher. Paper AIAA-2007-5838
for 43 Joint Propulsion Conference. Chincinnati, Ohio, USA, 9 - 11 July,2007. See also [10],
Ch.4, pp. 65-82.
[18] Koell D.E., Handbook of Cost Engineering, TCS, Germany, 2000.
Patents having relation to this topic:
[19] A.A. Bolonkin, Installation for Open Electrostatic Field. Patent Application #3467270/21
116676, 9 July, 1982 (in Russian), Russion PTO.
[20] A.A. Bolonkin, Light Pressure Engine. USSR, Patent, # 1183421, 1985.
[21] A.A. Bolonkin, Rotor Hydra-machine. USSR, Patent, # 1184973, 1985.

[22] A.A.Bolonkin, Bolonkin Rotor Engine. Patent application US PTO 09/290,465 of April 12,
1999. Patent US 6,248,921 of October 9, 2001.

[23] A.A.Bolonkin, Hypersonic Space Launcher (Method and Installation) Patent
application US PTO 09/13,08 of 1/26/1998; 09/344,235 of 06/25/1999; 1/057,819 of 01/18/2002.
[24] A.A.Bolonkin, Eccentric Engine. Patent application US PTO 09/575,256 of 05/22/2000.
Patent US 6,526,937 B1 of March 4, 2003.
[25] A.A.Bolonkin, Method and Installation for Space Trip. Patent application US PTO 09/789,959
of February 23, 2001.
[26] A.A.Bolonkin, Method and Installation for Space Launch. Patent application US PTO 09/873,985
of June 4, 2001.
[27] A.A.Bolonkin, "Method Transportation of Vehicles and Installations for It". Patent application
US PTO 09/893,060 of June 28, 2001. Patent US 6,434,143 B1 of December 16, 2002.
[28] A.A. Bolonkin, Method and Installation for getting of Energy. Patent application US PTO
09/945,497 of September 6, 2001.
[29] A.A. Bolonkin, "Method for Gas and Payload Transportation at Long Distance and
Installations for It", Patent Application US PTO # 09/978,507 of October 18, 2001.
[30] A.A. Bolonkin, , Cable Launcher. Patent application US PTO 09/974,670 of October 11, 2001.
[31] A.A. Bolonkin, Uniblade Air Rotor and Flight Vehicles with Its, Patent Application 09/203,130 of
February 1, 1998. Patent US PTO, #6,234,422 B1, May 22, 2001.
[32] A.A. Bolonkin, Bolonkin's Method Movements of Vehicles and Installation for It. Patent US PTO
6,494,143 B1, Priority is on 28 June 2001.
[33] A.A. Bolonkin, Economical Eccentric Internal Combustion Engine, Patent Application 09/5675,256
of May 22, 2000. Patent US PTO 6,526,937 B1, March 4, 2003

17 January, 2012.

Chapter 2

Hypersonic Ground Electric AB Engine

Abstract

At the present time, rocket launch systems, flight passenger-transport and ground passenger systems have reached their peak of development. In the last 30 years there has been no increase in speed or reductions in trip costs and space launch. The space launch and air and ground transportation industry needs revolutionary ideas, which allow a jump in speed and delivery capability, and a dramatic drop in space launch and trip price. This idea (kinetic aviation and space launch) was offered and developed in a series of the author researches [1]-[4], but an important facet of this method - the ground electric hypersonic engine - was insufficiently developed. Rail Gun idea was unfit for low acceleration and long rails. All energy is spent into creating a powerful magnetic field produces a strong flash when the apparatus is disconnected from rails. When the rail length is increased, the efficiency of low speed railgun engine approaches zero.

The main idea of the offered ground hypersonic electric engine is segmentation of the acceleration track on small special closed-loop sections (12.5 - 100 m) and a system of special switches which allow return of the magnetic energy to the system transferring it to apparatus movement. This increases the efficiency of hypersonic engine up 0.9, avoids the burning of rails and using the engine for long periods of time. The same idea may be used in a conventional Rail Gun.

Author designed and computed the feasibility and practability of this invention which he designed for the purpose of using it as a space launcher for astronauts and space load, as method for hypersonic long distance aviation and as method for supersonic passenger ground rail transportation. The offered system will be significantly cheaper than the currently used MagLev (Magnetic Levitation) systems, because the vehicle employs conventional wings for levitation and the hypersonic engine is very simple. The offered system may be also used for mass launch of projectiles in war.

Key word: hypersonic ground engine, space launcher, air catapult transport, kinetic aviation, air kinetic system, new high speed ground system.

Introduction

Kinetic aviation. Current takeoff mass of a long distance aircraft is made up of approximately 1/3 aircraft body, 1/3 fuel, and 1/3 payload. The aircraft engine needs expensive aviation fuel. The passenger-transport aircraft cannot exceed the speed of sound. The history of "Concorde" shows that the conventional passenger supersonic aircraft is unprofitable [1]. The hypersonic aircraft, which is under development by the USA, will be more unprofitable still as a passenger long distance aircraft because it will use very expensive hydrogen fuel, it is very complex and it has a high production cost. The hypersonic engine problems have not been solved in spite of spending large multiples of millions of dollars in research and testing. Space launch by the current rocket space system is very expensive. The current high speed (record is up to 580 km/h) MagLev (Magnetic Levitation) transport systems are also very expensive.

Transport, space launch systems and aviation all need new ideas that increase speed, and load capability, and reduce delivery cost. Some of these ideas have been published by the current author [1-16]. The initial author's idea is the acceleration (catapulting) of a cargo glider (vehicle), winged cargo box (non-engine aircraft), or space ship to high speed by using a cable engine. It was offered in 2001 [2] - [7], in particularly, it was presented in [1] and published in [1 -20]. The current research is different because it uses a linear electric engine located on the ground. The vehicle will then use its kinetic energy for flight. The computation shows that a catapulted/kinetic aircraft accelerated to subsonic speed of 270-300 m/s can fly up to 60-80 km until its speed decreases to a landing speed of 50-60 m/s. This is far enough for suburban transport or for air bridges across the Straits of Gibraltar, English Channel, Bering Straits (Russia-America), Sakhalin-Asia, Russia-Japan, etc. For acceleration to this speed at a rate that is acceptable to passengers (overload of 3g) the runway length must be 1.5 km (current runways for large aircraft are 1.5 - 3 km long). For the middle range (200 - 1600 km) the runway must have a length of 4 - 67 km. For the long-distance flight (6000-8000 km), the air vehicle must be accelerated to a speed of 4-6 km/s. For acceleration of no more than 3g the required runway length would then be 270 - 400 km. This runway can be also used for a space launch. One author method and design are described in References [5, 8]. Rather than being a conventional runway, it is an air cable acceleration system [6] - [9] for the acceleration of space vehicles and it is located in atmosphere.

The offered method is different from conventional MagLev because for levitation of the vehicle we employ the conventional wing (no magnetic levitation!). That is significantly cheaper. The offered system has also smaller financial risk because it is uses conventional technologies and in any case one may be used in the place of a conventional ground high-speed transport system between big cities, opening a large market transport, new passenger and cargo transport, catapult aviation, new space launch.

Fig.1. Catapult for aircraft. Credit NASA.

Brief history. In the World Space Congress-2002, Houston, USA, and series of other works [1]-[20] the author offered and researched many new non-rocket space launchers and space flights apparatus, aviation and high speed ground systems. At that conference, the author of this paper offered and researched the total combined transportation system which can be used as a high speed aviation and space launcher. [6] In one paper [16] he offered and researched the electrostatic high speed engine for a space elevator and space accelerator. The new very simple magnetic engine for acceleration and moving vehicles proposed in that paper is analyzed by computation in this paper. This engine is similar to the rail gun as all magnetic engines uses the magnetic field but there is one significant difference to conventional railguns. Conventional rail guns are long; acceleration is low (more 25 - 50 m, a << 10g); has very low efficiency; and generates a very high plasma flash (fig. 1). Please notice in fig. 1 the gigantic cloud of plasma behind the projectile which is the result of an electric arc between the contacts. About 70 - 80% of electric energy is lost uselessly.

Fig. 2. Railgun. Credit NAVY. Naval Surface Warfare Center test firing in January 2008, leaving a plume of plasma behind the projectile. The Gun has a small shell and gigantic plasma flash. The 70 - 80% of energy lost in this flash overheats the rails and does not allow immediately making the next shot.

The offered Hypersonic Engine (HABE) is different from rail gun. It is segmented in special small sections and has a special system of the switches which allows using the magnetic energy stored into rails for moving of apparatus. That significantly (up to 90%) increases the system efficiently, saves the rails from burning, and allows using the rails for a long time.

Description and Innovations

The offered engine is presented in fig.3. One has two rails 1, 2, sliding jumper 3 and an electric current source 11. That part is same as conventional railguns. But unlike the railgun the path is divided into small sections which are only activated when the apparatus moves along in that section. In this design, the rails contain two special motionless jumpers 14, 15 and special three-position electric switches 8. Every part of the railway contains two sections 17 and 16. In the first section 17 the apparatus is accelerated by the outer electric source 11. And in the second section 16 the apparatus is accelerated by the internal inductive electric energy of that part. This operation significantly increases the efficiency coefficient, saves energy and saves the rails from thermal distraction which allows acceleration over any length which can therefore reach a very high speed. Another cost saving feature is that in this design, the railway can be conventional iron rails (not from expensive copper) and small cross-section area which allows using the conventional high voltage electric line for delivering electric energy along the long acceleration distance.

The suggested system works the following way. When the apparatus (jumper 3) located at point "a", the switch 8 turn on to contact 10 and connect the circuit "abcde" to the electric source 11 (transformer of the high voltage electric line 12). The electric current runs into circuit "abcde". As the result the moving force appears in jumper 3 and move the jumper and apparatus 5 in direction 6. Simultaneously the circuit "abcd" accumulates the electric energy into Magnetic field. The accumulated energy is large because the current is strong.

When the apparatus reaches point 13 the switch is disconnected from the contact 10 (from outer electric source 11) and one is connected to contact 9 and completes the electric circuit "abcd". The electric current will decrease, but an inductive magnetic field of "abcd" hinder it and at the same time produces the electric current into circuit "abcd" in the same direction.

In the next part the process is repeated.

Fig.3. Hypersonic AB Engine (HABE) for super high speed train, launcher for hypersonic aviation and space apparatus/ship. Notations: 1 - 2 - rails; 3 - (HABE) mobile jumper; 4 - sliding contact; 5 - train, or hypersonic aircraft, or space ship; 6 - direction of moving apparatus; 7 - electric current; 8 - three-position switch of electric current; 9 - contact for closed loop electric circuit; 10 - contact to outer electric circuit; 11 - electric transformer; 12 - high voltage outer line; 13 - moment of connection of switch 8 to contact 9; 14 - fixed jumper two; 15 - fixed jumper three; 16 - way "cf" of engine using internal inductive electric energy; 17 - way "dc" of engine using external electric energy; abcd - internal electric circuit.

The offered hypersonic liner electric engine (HABE) has the following advantages over the RailGun:

Theory of Hypersonic Engine.

The parameters of HABE may be computed/estimated by following equations:

1. Computation of uniformly accelerated motion:

(1)
where a = constant acceleration, m/s; V is speed, m/s; t is time, sec; S is way, m; F is force, N;
P is power, W; E is energy, J.

2. Computation of force and voltage when the conductor is moving perpendicular in a magnetic field:

(2)
where i is electric current, A; U is electric intensity in ends of conductor, V; B is intensity of magnetic field, T; d is length of the conductor, m; V is conductor speed, m/s.

3. Trust and current of HABE

(3)
where b is coefficient of given design HABE,
is magnetic constant, H/m; a is average radius of rail, m;

4. Required voltage, power and energy by HABE:

(4)
where
is requested voltage for overcoming the magnetic field, V;
is requested voltage for overcoming the ohmic resistance, V; r is electric ohmic resistance, ?; ? - specific electric resistance for given material, ?m,


l is length of conductor ; s is cross-section area of the conductor, m« ; ? is a outer current time, s ; P is average power, W; E is average energy, J .

5. Inductance of two-wire lines (HABE rails):

(5)

is design coefficient; L is inductance, Henry; Ф is magnetic flow, Weber;

6. Energy expended in the creation of a magnetic field

(6)

7. Self-induced voltage:

. (7)

8. Change electric current in turn on and turn off the electric voltage in a circuit line having
the inductance:

(8)

T is constant, sec, when current changed in e = 2.71 times. This change is presented in fig.4.
The current reaches the finish approximately in T seconds. T - 0.1 sec for HABE.
The capacitance of HABE is small and we neglect it.

9. Efficiency of conventional RailGun and HABE may be computed by equations:

(9)
Here
is the useful energy, which accelerates the apparatus, J; k is coefficient of transferring (returning) the inductive energy in the useful energy, k - 0.5 - 0.95 .

Fig.4. Change electric current via time in turn on and turn off the electric voltage in a circuit line having the inductance.

Drawing your attention to the coefficient of HABE efficiency has in numerator additional member
which increases the efficiency of HABE.

Substituting the second line in equation (9) to the first line of (9) we get

. (10)

As you see the HABE has more efficiency then RailGun in any case approximately in 25 - 30% plus less damage from flash. The computation for different
are presented in Fig. 5.

Fig.5. Comparison of efficiency the RailGan (dash line) and HABE (full line) via outer current time ? for different Ohm resistance
.

As you see for high efficiency the Ohm resistance and stay time in every section 17 (fig.3) must be small.

10. The repellant force of rails may be computed by equation:

. (11)

11. Safety heating of rails is

, (12)

where i/s is safety density of current, A/m«; ?T is change temperature of rail, C or K; t is time of heating, sec., ? is specific gravity of rail, kg/mЁ. For iron ? = 7900 kg/mЁ.
is heat capacity of rail, J/kg.K (for iron
= 0.45 kJ/kg.K, for copper
= 0.39 kJ/kg.K). Computation by equation (12) is presented in fig. 6.

Fig.6. Safety current density versus time of iron (dish line) and copper (full line) and for different safety rail temperature.

12. Computation of space ship/apparatus (SS) trajectory launched by offered Hypersonic Engine.
Equations for computation of the apparatus trajectory are:

(13)

where r is range of ship flight, m; R₀ = 6,378,000 is radius of the Earth, m; R is radius of ship flight from Earth's center, m; V is ship speed, m/s; H is ship altitude over Earth, m; ? is trajectory angle, radians; D is apparatus drag, N; m is apparatus mass, kg; g is gravity at altitude H, m/s²; L is apparatus lift force, N; ?_E is angle Earth speed; ?_E is lesser angle between perpendicular to flight plate and Earth polar axis; t is flight time, sec. (We take ?_E = 0).

The magnitudes in equations (13) compute as:

(14)

where g₀ = 9.81 m/s² is gravity at the Earth surface; ? is air density, kg/m³, ? = 1.225 at H = 0; C_D is apparatus drag coefficient; C_D,0 is apparatus drag coefficient when L = 0; C_i is coefficient of the inductive drag; C_D,F is fuselage drag coefficient;
is wing drag coefficient for ? = 0; ? is wing attack angle, rad; ? is wedge angle of fuselage, rad;
is fuselage cross-section area, sq.m; S is wing area; B(M) is induces coefficient; a is sound speed, at zero altitude. One is a = 330 m/s at H = 0.

13. The loss of energy for air drag in acceleration area (tube), in climb trajectory (flight with vertical
overload n) and lifting of apparatus at altitude H (H - 100 km) can be estimated the equations below:

(15)

where
is a loss of energy in acceleration area, J;
is a loss of energy in climbing trajectory, J;
is loss of energy from air drag
in distance
- lifting trajectory without vertical acceleration;
is a loss of energy for lifting the apparatus at altitude H;
is length of acceleration distance (tube) m; n is overload in "g"; K is ration L/D (K - 4 - 5 for hypersonic aircraft);
= 8440 m is thickness of the Earth atmosphere if one has constant air density, m;
is the final speed at altitude H,
is additional speed from Earth rotation (
= 463 m/s at equator); E is energy in end of acceleration distance.

14. Heating of apparatus in re-entry protected by conventional method.

(16)

where: Q is heat flow in 1 m²/s of apparatus, J/s^.m²; R_n is vehicle equivalent radius, m; S_n is cross-section fuselage area, ?_SL= 1.225 kg/m³ is air density at sea level; V_CO = 7950 m/s is circle orbit speed; T₁ is temperature of apparatus in Kelvin, ^oK; T is temperature of apparatus in centigrade, ^oC; T₂ is temperature of the standard atmosphere at given altitude, ^oK (T₂ = 288 ^oK at H = 0 km) ; C_S = 5.67 W/(m^2.K⁴) is coefficient radiation of black body; ? is coefficient of a black (? - 0.03 ¤ 0.99): K is ration L/D.

15. Cooling system and additional thrust.

The cooling system is heating, evaporates of cooling liquid, heating of the vapor up high temperature and emitted with high speed from reactive/rocket nozzle. As result we obtain additional thrust. The estimation can be made by equations for the vertical acceleration distance H = 0 - 20 km:

(17)
where Q is heat (energy) accepted by space ships, J; ? is transfer coefficient, for sharp edge fuselage and wing ? - 0,02 - 0.08;
is flight time in distance H = 0 - 20 km, sec;
is heat for heating 1 kg of given liquid, J;
is heat capacity of cool liquid, J/kg.K (for water
= 4.19 kJ/kg.K);
®C is change of temperature for boiling, K;
is coefficient of evaporation, KJ/kg (for water
= 2200 kJ/kg);;
is heat capacity of vapor, J/kg.K (for water
= 2.21 kJ/kg.K);
is temperature of vapor,
is mass of cooling liquid, kg; v is speed of gas/vipor from a rocket nuzzle, m/s (v - 2000 - 3000 m/s); I impulse, kg.m/s;
is trust of the rocket nozzle, N;
is work time of rocket nozzle, sec.;
is the additional speed, m/s; m is mass of the space ship, kg.

For the lifting distance
= 20 - 100 km the requested mass of the cooling liquid may be estimated by equation:

(18)

Where
is average air density in given diapason of altitude
, kg/mЁ;
is given region of the atmospheric altitude, m;
is air density in beginning (bottom) of the given diapason of the altitude
, kg/mЁ; ? is air density in an end (top) diapason of altitude
, kg/mЁ;
is distance of lifting, m;
is a need mass of cooling liquid, kg (small);
is heat from air, J;
is the flight time in distance
= 20 - 100 km.

16. Estimation of the energy loss and speed of SS in the flight time in the Earth atmosphere and additional speed from head rocket.

, (19)

where
is energy for curvature of trajectory;
is energy for air drag in diapason
= 20 - 100 km,
is energy for lifting the SS mass at altitude H = 0 - 100 km; K is ratio
;
is summary loss of the SS speed in Earth atmosphere in diapason H = 0 - 100 km;
is the SS additional speed from the rocked cooling system, m/s; v is the gas/vapor nozzle speed of rocket-cooling system, m/s;
is the mass of used cooling liquid, kg.

Project

From these computations we can estimate parameters of the operation of the offered hypersonic engine and space launcher. Suppose we want to estimate the system which uses as the supersonic ground transportation (speed up 4 km/s), continental hypersonic kinetic aviation (maximal speed up 5 km/s) and space launcher with speed up 8 km/s.

Space Launcher is most difficult in design, so for the sake of illustration, in this paper we estimate only one. The ground supersonic transport and kinetic air hypersonic transport are more simple in design and, if we get the acceptable space launcher for current technology, the installation may be used also as ground and air transportation system.

1) Acceleration track (tube) for space ship: Let us take the mass of space ship m = 10 tons = 10,000 kg, overload n = 6 (acceleration a = ng = 60 m/s«) and the final nozzle speed V = 8 km/s = 8000 m/s. The overload n = 6 is acceptable for trained people (astronauts can endure shortly time n up 9). The conventional people can endure n = 3, but in this case the acceleration track must be ~ two time longer.

For our data the acceleration track L and acceleration time t must be (all computation are in metric system):

.
(20)

Needed thrust, maximal power and total energy we increase in 10% for tube air drag (from primary computation). The needed force, maximal power and total acceleration energy are

(21)

2) Estimation of Hypersonic Engine. The railway track in Europe is d = 1.435 m, half of rail head is
= 0.036 m, cross-section area of rail is s =0.00613 m«, length of rail l = 12.5 m, iron rail has specific electric resistance
.

Need electric current, voltage, power, energy are:

(22)
Inductance L rail track for the rail length l = 12.5 m is:

H. (23)
Maximal energy of magnetic field time constant of inductance are

(24)

Average efficiency coefficient ? for l = 50 m, V = 4 km/s,
= 0.9, ? = 50/4000 = 0.0125 sec.

(25)
Repel force of rail and safety heating time t of for safety iron rail temperature
are:

(26)
Here ? is specific gravity of rail, kg/mЁ. For iron ? = 7900 kg/mЁ.

3) Trajectory into Earth atmosphere: We take the next trajectory after the acceleration (tube) distance. Curvature of trajectory to up by the lift force of the wing space ship (vertical acceleration with a = 6g = 60 m/s) from altitude H = 0 to H = 20 km and lifting of space ship with constant trajectory angle ? from H = 20 km to H = 100km.

(27)
where
is vertical speed of space ship (SS), m/s;
is horizontal distance, m/s.
The lifting distance from H = 20 km to H = 100 km is approximately:

(28)

The diagram of SS overload and trajectory is presented in fig. 7.

Fig.7. Launch trajectory of space ship (a) and diagram of overload (b).

4) Cooling system: We take the water-rocket cooling system. The data of this system in the vertical acceleration distance may be estimated by equations (17) for K = 5, ? = 0.04:

(29)

Here
is additional thrust from the air heating in distance 0 - 20 km and
is additional speed of SS.

The water-cooling in lifting distance (from H = 20 - 100 km) is small and expended water mass equals 2.8 kg. The total cooling water mass is 237 kg.

5) Estimation of loss the energy and speed of SS in Earth atmosphere: Curving of trajectory in distance H = 0 - 20 km

. (30)
Air drag in distance H = 20 - 100 km

. (31)

Lifting the SS mass in altitude H = 0 - 100 km

. (32)
Total loss of energy in moving the Earth atmosphere is

. (33)

The total speed loss is significantly less than SS speed. So we can use the equation (18)

(34)
The total additional speed from the cooling system is about 60 m/s. The maximal additional speed from the rotating Earth at equator is 463 m/s. We take 370 m/s for mid-latitude. In result we receive the final speed on the 100 km satellite orbit about 8 km/s: 8000 - 425 + 60 + 370 = 8005 m/s.

Discussion

The offered project of HABE engine uses conventional iron rails which are not only 28 times cheaper than copper or 7 times cheaper than aluminum rails, but iron rails have in 3 - 6 times more specific electric resistance. The road with these conventional iron rails may be used as a high speed conventional rail track. That means that in the worst case scenario the cost of construction will not be lost. The longest in World Beijing to Guangzhou high-speed line (China) will open Dec. 26, 2012. A 2,298-kilometer (1,428 mile) line links the nation's capital and the southern city will have average speed 300 km/hours. The speed record of rail train is about 580 km/hour.

The offered space launcher will need an initial acceleration up 100 m/s (360 km/hour) by a conventional locomotive because HABE has low efficiency in low speed. After initial acceleration the locomotive will be disconnected from launcher. The other features of the offered road (if one will be used also as a space and long distance aviation accelerator) are following: one must be strictly rectilinear and into a light (better partially transparent) tube. Sound waves from supersonic and hypersonic flight should not disturb the nearest population.

A conventional power electric station can produce sufficient energy to operate the offered HABE but the offered HABE engine needs a set of the electric transformers to produce a high ampere electric current.

For re-entry to the Earth atmosphere the Space Ship may be used the special brake parachute offered in [9] Ch. 8 and others.



Fig. 8. Magnetic catapult (Credit NASA)

Conclusion

In this article the author describes the new idea, theory, computations and design of the new hypersonic ground electric high efficiency engine (HABE) for space launch, hypersonic aviation, supersonic ground railroad transport and RailGun.
Important advantage of the offered engine is its very high inductive efficiency coefficient, close to 0.9 (compared to the efficiency of the current railgun equal to 20 - 40%). The suggested launcher is very simple, uses conventional iron rails, does not generate high heating and may be produced by present technology. The power of strong electric plant is enough for launching the space apparatus of some tens tons.

The offered magnetic space launcher is a thousand times cheaper than the well-known cable space elevator. NASA is spending hundreds of millions of dollars for research of space elevator. A small part of this sum is enough for R&D of the hypersonic launcher and to make a working model.

Small cheap prototypes would be easily tested.

The computed projects are not optimal. That is only illustration of an estimation method. The reader can recalculate the HABE-Launcher for his own scenarios (see also [1]-[23]).

References

(The reader may find some of these articles, at the author's web page: http://Bolonkin.narod.ru/p65.htm , in http://www.scribd.org , in the WEB of Cornel University http://arxiv.org , and in http://aiaa.org search term "Bolonkin")

http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182.

http://www.scribd.com/doc/24057930 . http://Bolonkin.narod.ru/p65.htm

http://www.scribd.com/doc/26270139, http://arxiv.org/ftp/arxiv/papers/1002/1002.2405.pdf

44th AIAA Aerospace Sciences Meeting and Exhibit, 2006, 10.2514/6.2006-222.

SpaceOps 2010 Conference, 2010, 10.2514/6.2010-2319.

http://NASA-NIAC.narod.ru , http://auditing-science.narod.ru

6 November, 2012

Article Defense from Asteroid for AJET 6 7 13 Short article

Chapter 3

Protection of the Earth from the Asteroids

Abstract

For Protection of the Earth from asteroid we need in methods for changing the asteroid trajectory and theory for an estimation or computation the impulse which produces these methods. Author develops some methods of this computation. There are: impact of the space apparatus to asteroid, explosion the conventional explosive having form of plate and ball on asteroid surface, explosion the small nuclear bomb on the asteroids surface, entry asteroid to Earth atmosphere, braking of asteroid by parachute.

Offered method may be also used for braking of apparatus reentering in the Earth from a space flight.
The offered theory also may be used for protection the Earth from impact of a big asteroid.
--------------------------------------
Key words: protection of the Earth from asteroids, asteroid delivery to Earth, impact to asteroid, nuclear explosion, atmospheric entry, Space Ships, thermal protection of asteroid and space apparatus, parachute braking of asteroid.

Introduction

There are many small solid objects in the Solar System called asteroids [1]. The vast majority are found in a swarm called the asteroid belt, located between the orbits of Mars and Jupiter at an average distance of 2.1 to 3.3 astronomical units (AU) from the Sun. Scientists know of approximately 6,000 large asteroids of a diameter of 1 kilometer or more, and of millions of small asteroids with a diameter of 3 meters or more.

Radar observations enable to discern of asteroids by measuring the distribution of echo power in time delay (range) and Doppler frequency. They allow a determination of the asteroid trajectory and spin and the creation of an asteroid image.

For Protection of the Earth and for delivery asteroid to the Earth author considers theory of three main methods: impact of the space apparatus to asteroid, explosion the conventional explosive on asteroid surface having form of plate and ball, explosion the small nuclear bomb on the asteroids surface, braking asteroid by parachute in Earth atmosphere.

The impact of a massive object, such as a spacecraft or another near-Earth object, is one possible solution to change the trajectory of the Near Earth asteroid or Object (NEO). Another object (for example, space apparatus) with a high mass close to the Earth could be forced into a collision with an asteroid, knocking it off course.

Fig.1. Asteroid belt.

Fig.2. Asteroids.

Kinetic impact.

When the asteroid is still far from the Earth, a means of deflecting the asteroid to Earh is to directly alter its momentum by colliding a spacecraft with the asteroid.
The European Space Agency is already studying the preliminary design of a space mission able to demonstrate this futuristic technology. The mission, named Don Quijote, is the first real asteroid deflection mission ever designed.
In the case of 99942 Apophis it has been demonstrated by ESA's Advanced Concepts Team that deflection could be achieved by sending a simple spacecraft weighing less than one ton to impact against the asteroid. During a trade-off study one of the leading researchers argued that a strategy called 'kinetic impactor deflection' was more efficient than others.

Nuclear bomb for deflection of asteroid.

Detonating a nuclear explosion above the surface (or on the surface or beneath it) of an NEO would be one option, with the blast vaporizing part of the surface of the object and nudging it off course with the reaction. This is a form of nuclear pulse propulsion. Even if not completely vaporized, the resulting reduction of mass from the blast combined with the radiation blast and rocket exhaust effect from eject could produce positive results.

Another proposed solution is to detonate a series of smaller nuclear bombs alongside the asteroid, far enough away as not to fracture the object. Providing this was done far enough in advance, the relatively small forces from any number of nuclear blasts could be enough to alter the object's trajectory enough to avoid an impact. The 1964 book Islands in Space, calculates that the nuclear megatonnage necessary for several deflection scenarios exists. In 1967, graduate students under Professor Paul Sandorff at the Massachusetts Institute of Technology designed a system using rockets and nuclear explosions to prevent a hypothetical impact on Earth by the asteroid 1566 Icarus. This design study was later published as Project Icarus which served as the inspiration for the 1979 film Meteor.

Theory of the asteroids movement and changing trajectory.

In Table 1 are computed the mass M of the ball asteroid, his energy E for speed V = 16 km/s and explosive power P of asteroids. One ton TNT has 4.184в10^9 joules of energy.
Table 1. Diameter D, mass M of ball asteroid having density 3500 kg/mЁ, energy E for speed V = 16 km/s and explosive power P of asteroids.

The Hiroshima nuclear bomb had power about 15 kilotons of TNT explosive. The small ball asteroid having diameter 10 m has energy in 4 times more for speed 16 km/s.

1. Equations for computation of trajectory in vacuum space near Earth.

These equations are following:

(1)

where r is radius from Earth center to point in trajectory, m; p is ellipse parament, m; e is ellipse eccentricity, e = 0 for circle trajectory, e < 1 for ellipse, e = 1 for parabola, e > 1 for hyperbola; ? is angle from perigee, K is Earth constant, v is speed, m/s; ? is angle between speed and tangent to circle; M = 5.976^.10²⁴ kg is mass of Earth; R = 6378 km is Earth radius; r_a is apogee, m; r_p is perigee, m; b is small semi axis of ellipse, m; a is small semi axis of ellipse, m; T is period of rotation, sec.

2. Change asteroid trajectory by impact of space apparatus.

Inelastic head-on collision space apparatus (SA) in the asteroid (As):

(2)

Where W is energy of system, J; Q is heat loss in impact, J;
is mass of space apparatus, kg;
is mass of asteroid, kg;
is speed of SA about center mass of the system asteroid-SA, m/s;
is speed of asteroid about center mass of system asteroid-SA,
is coefficient of efficiency.

Let us place the origin at the center of gravity of an asteroid. The speed of system asteroid-SA will be

(3)

Where ?V is change of asteroid speed, m/s; V is SA speed relative asteroid, m/s; ?I is additional impulse of system As+SA.

Example. Let us take the asteroid having diameter 10 m (
= 1830 tons) and SA having mass
= 10 tons and speed about asteroid V = 1 km/s. From equation (3)-(2) we find ?V = 5.43 m/s, ? = 0.00543.

3. Change trajectory by conventional plate explosive located on the asteroid surface.

In this case we get the impulse from the explosive gas.

The maximal speed of an explosion gas and asteroid speed received from explosion are

(4)
where
is speed of explosion gas, m/s; q is specific energy of the explosive, J/kg (q - 5.4 MJ/kg for TNT),
is asteroid speed received from explosion, m/s;
is mass of explosive, kg;
is mass of asteroid, kg.

Example. Let us take the asteroid having diameter 10 m (
= 1830 tons) and explosive having mass
= 10 tons and specific energy of the explosive q - 4.2 MJ/kg. From equation (4) we find the change of speed of asteroids
= ?V = 15.8 m/s.

If explosive is not plate (not optimum) and located in one point (ball) on the asteroid surface, the effect from the explosion will be less. Maximum speed is ?/4 = 0.785 from the plate explosion speed:

= ?V = 15.8в0.785 = 12.4 m/s.

4. Nuclear point explosion on the asteroid surface.

In this case the asteroid gets the impulse from evaporation part of asteroid. The asteroid rest can get the significant speed. If the energy of the nuclear bomb is E, bomb is located on asteroid surface, change the asteroid speed may be estimated by next equations

(6)
where
is speed of evaporation gas, m/s; ? is specific energy of the asteroid evaporation, J/kg (heating + melting + heating + evaporation), v is the volume of a sold evaporation mass, mЁ; ? is the asteroid density kg/ mЁ; I is impulse, kg m/s;
is change of the asteroid speed received from nuclear explosion, m/s;
is the asteroid evaporation mass in explosion, kg;
is initial mass of asteroid, kg; r is radius of explosion cavity, m.

For basalt the ? = heating + evaporation = 1191 + 3500 = 4691 kJ/kg, ? = 3500 kg/ mЁ. For iron

? - 8200 kJ/kg, ? = 7900 kg/ mЁ; for ice ? - 3000 kJ/kg, ? = 1000 kg/ mЁ..
Example. Let us take the iron asteroid having diameter 10 m (
= 1830 tons) and energy of a small nuclear bomb is E = 1 kton = 4.2 "
J. From equation (4) we find
= 2863 m/s;
=256 tons, the change of speed of asteroids
= ?V = 460 m/s.

The impact from nuclear explosion is very strong and aster0id may spell.

5. Computation of the asteroid trajectory when asteroid is towing by aircraft the Earth atmosphere.
Equations for computation of trajectory are (for the system of asteroid + space apparatus):

(7)

where r is range of ship flight, m; R₀ = 6,378,000 is radius of Earth, m; R is radius of ship flight from Earth's center, m; V is ship speed, m/s; H is ship altitude, m; ? is trajectory angle, radians; D is system drag (asteroid + apparatus), N; D_P is asteroid drag, N; m is system mass, kg; g is gravity at altitude H, m/s²; L is apparatus lift force, N; L_P is asteroid lift force, N; ?_E is angle Earth speed; ?_E = 0 is lesser angle between perpendicular to flight plate and Earth polar axis; t is flight time, sec.

The magnitudes in equations (4) compute as:

(8)

where: g₀ = 9.81 m/s² is gravity at Earth surface; ? is air density, kg/m³; Q is heat flow in 1 m²/s of parachute, J/s^.m²; R_n (or R_p) is asteroid radius, m; S_P (or S_m) is asteroid area, m²; ?_SL= 1.225 kg/m³ is air density at sea level; V_CO = 7950 m/s is circle orbit speed; T₁ is temperature of asteroid/apparatus in stagnation point in Kelvin, ^oK; T is temperature of parachute in stagnation point in centigrade, ^oC; T₂ is temperature of the standard atmosphere at given altitude, ^oK (T₂ = 253 ^oK at H = 60 km) ; D_P is asteroid drag, N.; L_P is asteroid lift force That is control from 0 to 0.4 D_p , N; D is ship drag, N; L is ship lift force, N; C_DP = 1 is asteroid drag coefficient; a = 295 m/s is sound speed at high altitude; ? = 40^o = 0.7 rad is apparatus attack angle. C_S = 5.67 W/(m^2.K⁴) is coefficient radiation of black body; ? is coefficient of a black (? - 0.03 ¤ 0.99), ?V is loss of speed in atmosphere on distance L.

The control is following: if T₁ is more the given safety temperature than the lift force L = maximum. In other case L = 0. If T₁ is less the given safety temperature than the lift force L = negative minimum.

Conclusion

For protection of the Earth from asteroids we need in methods for changing the asteroid trajectory and theory for an estimation or computation the impulse which produces these methods. Author develops some methods of this computation. There are: impact of the space apparatus to asteroid, explosion the conventional explosive on asteroid surface having form of plate and ball, explosion the small nuclear bomb on the asteroids surface.

The reader finds useful information about protection methods also in [1]-[10].

References

1. Asteroid Retrieval Feasibility,(2012) ESA ESTEC: March 14, 2012, Louis Friedman & Marco
Tantardini. http://www.kiss.caltech.edu/study/asteroid/20120314_ESA_ESTEC.pdf

2. Bolonkin A.A., (2005). Asteroids as propulsion system of space ship, Journal of The British
Interplanetary Society, Vol. 56, No.3/4, 2003 pp. 98-107. And Chapter 11 in book BolonkinA.A.,
Non-Rocket Space Launch and Flight, Elsevier, 2005, 488 pgs.
http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182
3. Bolonkin A.A., (2006). A New Method of Atmospheric Reentry for Space Ships. Presented
as Bolonkin's paper AIAA- 2006-6985 in Multidisciplinary Analyses and Optimization Conference,
6-8 September 2006, Fortsmouth. Virginia, USA. Or Chapter 8, in Bolonkin A.A., "New Concepts,
Ideas, Innovations in Aerospace, Technology and the Human Sciences", NOVA, 2006, 510 pgs.
http://www.scribd.com/doc/24057071 ,
http://www.archive.org/details/NewConceptsIfeasAndInnovationsInAerospaceTechnologyAndHumanSciences
4. Bolonkin A.A., (2006). "Non Rocket Space Launch and Flight". Elsevier, 2005. 488 pgs.
http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182 .
5. Bolonkin A.A., (2006). "New Concepts, Ideas, Innovations in Aerospace, Technology and the Human
Sciences", NOVA, 2006, 510 pgs. ISBN-13: 978-1-60021-787-6.
http://www.scribd.com/doc/24057071 ,
http://www.archive.org/details/NewConceptsIfeasAndInnovationsInAerospaceTechnologyAndHumanSciences
6. Bolonkin A.A., Cathcart R.B. (2006). "Macro-Projects: Environments and Technologies", NOVA,
2007, 536 pgs. http://www.scribd.com/doc/24057930 .
http://www.archive.org/details/Macro-projectsEnvironmentsAndTechnologies
7. Bolonkin A.A., (2006). Femtotechnologies and Revolutionary Projects. Scribd, USA, 2011. 538 p. 16
Mb. http://www.scribd.com/doc/75519828/
http://www.archive.org/details/FemtotechnologiesAndRevolutionaryProjects
8. Elvis, C. (2012) Let's mine asteroids--for science and profit. Nature 485: 549
9. Efrati, A. (24 April 2012) Start-Up Sees New Frontier In Mining: Asteroids in Space. The
Wall Street Journal CCLIX: B1.
10. Friedman, L., Tantardini, M. (2012) Asteroid Retrieval Feasibility, ESA ESTEC
http://www.kiss.caltech.edu/study/asteroid/20120314_ESA_ESTEC.pdf
20 October 201

Article Reentry of Space Ship after Shmuel 11 24 12

Chapter 4

Reentry of Space Craft To Earth Atmosphere

Abstract

Currently reentry of USA Space Shuttles and Command Module of Lunar Ships burns a great deal of fuel to reduce reentry speed because the temperatures are too high for atmospheric braking by conventional fiber parachutes. Recently high-temperature fiber and whiskers have been produced which could be employed in a new control rectangle parachute to create the negative lift force required. Though it is not large, a light parachute decreases Shuttle speed from 8 km/s (Shuttle) and 11 km/s (Apollo Command Module) up to 1 km/s and Space Ship heat flow by 3 - 4 times (not over the given temperature). The parachute surface is opened with backside so that it can emit the heat radiation efficiently to Earth-atmosphere. The temperature of parachute is about 600-1500^o C. The carbon fiber is able to keep its functionality up to a temperature of 1500-2000^o C. There is no conceivable problem to manufacture the parachute from carbon fiber. The proposed new method of braking may be applied to the old Space Ship as well as to newer spacecraft designs.
-------------------------------------------

Keywords: Atmospheric reentry, Space Shuttle, thermal protection of space craft, parachute braking.

Introduction

In 1969 author applied a new method of global optimization to the problem of atmospheric reentry of spaceships [1 p. 188]. The offered analysis presented an additional method to the well-known method of outer space to Earth-atmosphere reentry ("high-speed corridor"). In that approach, reentry is made in a low-speed corridor where total heat is less than conventional high-speed passage. At that time, in order to significantly decrease the speed of a spaceship, retro- and landing rocket engines which consumed a great deal of fuel were needed. With the new development by the textile industry of heat resistant fiber, parachute brake system can now be used in a high-temperature environment [2]-[4].

Main idea, Description of the parachute innovations and control

The greatest danger to spacecraft is the high temperatures generated upon reentry to Earth. The death of six astronauts in the Columbus catastrophe was the result of minor damage to the heat shield. Upon close examination, the danger of heat flow is only at altitudes of 50 - 60 km where the air has enough density so that space craft traveling at a high speed is met with air resistance which generates heat. It is not the ambient temperatures but the temperatures generated by air resistance which is a danger. At altitudes over 160 km the temperature of Earth atmosphere is more 1000®C, but because the air density is small there is no danger to space craft. In fact, a space ship can safely pass through space where space particles have temperature in millions degrees because their density is extremely small.

A space craft can avoid severe heating in reentry if it does not travel at high speed (lower than 2 -3 km/sec) when it is lower altitudes of 55 - 60 km. As such, the space craft speed may be decreased by back force of a rocket engine, but this method requires a great deal of fuel. Currently, space craft is designed with a blunt nose which by increasing air drag, decrease the craft's high speed but this generates high heat flow which means that space craft needs the protection by heavy ceramic shield which is vaporized upon reentry and largely requires replacement after every flight.

This paper proposes another method for braking the space craft in high altitude where the atmosphere is rarefied by a controlled hypersonic braked parachute for braking. The brake distance may be long. If the speed is significantly less than 8 km/s, the craft needs an additional lift force for supporting it. If the speed is radically more than 8 km/s, the centrifugal force is very large and the craft needs a significant NEGATIVE lift force for holding it into Earth atmosphere. That means the parachute must have a control. The proposed design for this rectangle control lift/drag parachute has the high ratio lift/drag (up Ђ4) and allows it to change the minimum/maximum drag 1:10.

The suggested method has significantly advantages over the current method (ceramic heat plates):

The parachute design is shown in fig.1. Parachute has the rectangle form and special control which allows it to change the length of cords (strops) (fig.2) and size of parachute entrance. The change of the cord length permits creating the lift force, the change of the direction of a lift force up to a negative lift force (fig.2, a, b), and creating the side force (fig.1, d). The cable control (fig.1, items 4-5) allows it to change the parachute aperture (fig.2 c, d) and the value of the parachute drag. The canopy and strops made from high temperature fiber, for example carbon filament. The parachute can have a rigid tin plate in forward edge.

Fig.1. The proposed design of a control mechanism for the high temperature parachute for braking space craft in the Earth high atmosphere. Notations: a -forward view (from space craft), b - side view, c -side view, d - creating of side force. 1 - parachute, 2 - brake force, 3 - direction of moving, 4 - 5 control cable (by changing the enter section), 6 - strops (cord, slings).

Fig. 2. Control of air drag, the positive and negative lift force (relative of horizontal moving) by offered parachute. Notations: a - producing the negative (direction down) lift force, b - producing the positive lift force, c - full drag of parachute, d - part drag of parachute; 1 - space craft, 2 - parachute, 4 - negative lift force, 5 - positive lift force, 6 - air drag, 7 - centrifugal force, 8 - direction of moving, 9 - weight (gravity) of craft, 10 - control of parachute entrance.

Another method is shown in fig. 3 which employs a folding fabric wing with variable area. This apparatus has high ratio lift/drag and can fly in the high rarified atmosphere for a long time.

Fig. 3. The fabric lift-brake wing. Notations: a - side view, b - forward view; 1 - wing-parachute, 2 - rigid plate, 3 - lift-drag force, 4 - cable connecting the first-back edge, 5 - strops, 6 - space craft, 7 - direction of moving.

Theory

The curves of altitude via speed for the given temperature H = H(V, T) and the longitudinal and vertical overloads can be computed by equations:

(1)

where: g is Earth gravity, m/s² , g₀ = 9.81 m/s² is gravity at Earth surface; ? is air density, kg/m³; Q is heat flow in 1 m²/s of parachute, J/s^.m²;
is constant for parachute area 1000 sq.m.; ?₀ = 1.225 kg/m³ is air density at sea level; V_O - 7950 m/s is circle orbit speed; T₁ is temperature of parachute in stagnation point in Kelvin, ^oK; T is temperature of parachute in stagnation point in centigrade, ^oC; T₂ is temperature of the standard atmosphere at a given altitude, ^oK, T₂ - 258 at H = 40 km; C_D = 1 is parachute drag coefficient; a - 295 m/s is sound speed;
is longitudinal overload;
is vertical overload; q is specific load on parachute surface, kg/sq/m; K is ratio
, ? is emissivity. Result of computation is presented in figs. 4 - 6. The limit altitude via speed for the given temperatures in the stagnation point is shown in fig. 4.

Fig. 4. Limit of altitude versus the speed for given stagnation temperature. Over this curve the temperature is less. Eps is emissivity. Safety temperature (less of given) is over appropriate curve.

As you see, we can reach a low temperature if the craft travels (losses speed) at high altitude. Although unimportant, the time of reentry is greater as the parachute lift force allows it to keep a needed altitude. The longitudinal overload versus speed for the different altitudes is shown in fig. 5.

Fig. 5. The longitudinal overload via speed in the different altitudes. q = 100 kg/sq.m.

As you see the overload is safe for manned space craft, but ideally suited for non-manned craft.

Fig. 6. Vertical overload via speed for the different altitudes, for ratio K= Lift/drag = Ђ1 and the special parachute load q = 100 kg/m2. K = -1 for V > 8 km/s.

As you see the positive (for speed V < 8 km/s) and negative (for V > 8 km/s) vertical load is also not large.

The reentry trajectory of craft may be computed by equations:

where r is range of ship flight, m; R₀ = 6,378,000 is radius of Earth, m; R is radius of ship flight from Earth's center, m; V is ship speed, m/s; H is ship altitude, m; ? is trajectory angle, radians; D is ship drag, N; D_P is parachute drag, N; m is ship mass, kg; g is gravity at altitude H, m/s²; L is ship lift force, N; L_P is parachute lift force, N; ?_E is angle Earth speed; ?_E = 0 is lesser angle between perpendicular to flight plate and Earth polar axis; t is flight time, sec. The magnitudes in equations (2) compute as in equations (1) or as below:

(3)

where: g₀ = 9.81 m/s² is gravity at Earth surface; ? is air density, kg/m³; Q is heat flow in 1 m²/s of parachute, J/s^.m²; R_n (or R_p) is parachute radius, m; S_P is parachute area, m²; ?_SL= 1.225 kg/m³ is air density at sea level; V_CO = 7950 m/s is circle orbit speed; T₁ is temperature of parachute in stagnation point in Kelvin, ^oK; T is temperature of parachute in stagnation point in centigrade, ^oC; T₂ is temperature of the standard atmosphere at given altitude, ^oK (T₂ = 253 ^oK at H = 60 km) ; D_P is parachute drag, N.; L_P is parachute lift force. That is control from 0 to 4 D_p , N; D is ship drag, N; L is ship lift force of craft, N; C_DP = 1 is parachute drag coefficient; a = 295 m/s is average sound speed at high altitude; ? = 40^o = 0.7 rad is craft attack angle. C_S = 5.67 W/(m^2.K⁴) is coefficient radiation of black body; ? is parachute coefficient of a black (? - 0.03 ¤ 0.99), ?V is loss of speed in atmosphere on distance L.

The control is computed as follows: if T₁ is more the given safety temperature than the lift force L_P = maximum = KD_p. If T₁ is less the given safety temperature than the lift force L_P = negative minimum = - - KD_p. When the speed is less the sound speed, the control parachute is also used for deliver in given point.

The proposed parachute area may be found by equations in lending study at sea level:

(4)
where C_L is lift coefficient of parachute, C_L - 2 ¤ 3; C_D is drag coefficient of parachute , C_D - 0.5 ¤ 1.2; ? = 1.225 kg/m³ is air density; V is speed system, m/s; S_p is parachute area, m²; K is ratio C_L/C_D; V_v is vertical speed, m/s.

For Example. Let us take the mass of system (craft + parachute) 100 tons = 10⁶ N, C_L = 2.5, safety V_v = 20 m/s, K = 4, V = 80 m/s. From equation (4) we receive the parachute aria is S_p = 100 m². The control rectangle parachute is 5.8 x 17.3 m.

Fig. 7 presents the loss of speed via altitude on distance L = 6378 km (radius of the Earth) for mass of a system 100 ton and parachute area 1000 m«, q = 100 kg/sq.m.

Fig.7. Loss of speed via altitude for distance L = 6378 km (radius of the Earth) for mass of system 100 ton and parachute area 1000 m«, q = 100 kg/sq.m..

For altitude of 80 km and distance of L = 6378 km, the loss is about 150 m/s. The parachute can keep this altitude by lift force. In this case the system losses about 2 km/s during two revolutions around Earth. This allows decreasing the safety altitude up 70 km and increase the speed loss up 1 km on distance L. Control parachute alloys a lift force (up and down) to decrease speed and to lend the system in need point of Earth surface.

Notes about current reenter craft.

Orbital Ship Shuttle

The main data of reentry of the Shuttle are: Empty weight is 78 tons; Full weight 104 tons; payload to LEO: 53,600 lb (24,310 kg), payload to GTO: 8,390 lb (3,806 kg); operational altitude 100 to 520 nmi (190 to 960 km; 120 to 600 mi); speed: 7,743 m/s (27,870 km/h; 17,320 mph).

The orbiter's maximum glide ratio/lift-to-drag ratio varies considerably with speed, ranging from 1:1 at hypersonic speeds, 2:1 at supersonic speeds and reaching 4.5:1 at subsonic speeds during approach and landing. In the lower atmosphere, the orbiter flies much like a conventional glider, except for a much higher descent rate, over 50 m/s (180 km/h; 110 mph) (9800 fpm). At approximately Mach 3, two air data probes, located on the left and right sides of the orbiter's forward lower fuselage, are deployed to sense air pressure related to the vehicle's movement in the atmosphere.

Fig. 8 . Endeavour deploys drag chute after touch-down the Shuttle.(Credit NASA)

The conventional system for protection of space craft is shown in fig. 9.

Fig. 9. Space Shuttle Thermal Protection System Constituent Materials.

When the approach and landing phase begins, the orbiter is at a 3,000 m (9,800 ft) altitude, 12 km (7.5 mi) from the runway. The pilots apply aerodynamic braking to help slow down the vehicle. The orbiter's speed is reduced from 682 to 346 km/h (424 to 215 mph), approximately, at touch-down (compared to 260 km/h (160 mph) for a jet airliner). The landing gear is deployed when the Orbiter is flying at 430 km/h (270 mph). To assist the speed brakes, a 12 m (39 ft) drag chute is deployed either after main gear or nose gear touchdown (depending on selected chute deploy mode) at about 343 km/h (213 mph). The chute is jettisoned once the orbiter slows to 110 km/h (68.4 mph) (fig. 8).
Computation with conventional brake chute.

The computation of the reentry orbital space ship Shuttle with only a brake chute is presented in [2]-[3]. The control is following: if d?/dt > 0 the all lift force L = L_P = 0. When the Shuttle riches the low speed the parachute area can be decreased or parachute can be detached. That case is not computed. Used control is not optimal.

The results of integration are presented in [3]. Used data: parachute area are S_P = 1000, 2000, 4000 m² (R_p = 17.8, 25.2, 35.7 m); m = 104,000 kg. The dash line is data of the Space Shuttle without a parachute. The parachute significantly decreases the shuttle speed from 8000 m/s to 350 - 2900 m/s after 550 sec of reentry flight (fig. 5 in [3]). Practically, the Space Shuttle overpasses the heat barrier (maximum of heat flow) near 200 sec into its reentry (see fig. 8 [3]). The heat flow depends on the power 3.15 from speed (see the second equation in (3)) and the speed strongly influences the heat flow. For example, the decreasing of speed in two times decreases the heat flows in 8.9 times!

At an altitude of 41 - 44 km the ship has speed 350 - 2900 m/s which is acceptable for high speed vehicle in short time of reentry (fig. 4).

The maximum temperature in a stagnation point of the parachute is 1000 - 1300^o C (fig. 7 [3]). The parachute can be made from carbon fiber that can keep the temperature 1500 - 2000^o C (carbon melting temperature is over 3000^o C). At present a carbon fiber composite matters uses by Shuttle for leader edges of Shuttle where temperature reaches 1550^o C.

Fig. 8 [3] shows the heat flow through 1 m²/s of Shuttle without or with a parachute. That is about 1.4 - 2.2 times less then without parachute. It means the future Space Shuttles can have a different system of heat protection and a modern design can be made lighter and cheaper.

Estimation Parachute System

The weight of the parachute system in comparison with current heat protection is the key for this innovative method. Industry has produced many metal and mineral fibers and whiskers having very high tensile stress at high temperatures. To estimate the mass of parachute system, assume the carbon fiber used for this parachute has the maximum tensile stress ? = 565 kg/mm² (? = 5.65в10⁹ N/m²) at temperature T = 1500 - 2000^o C. With a safety margin 2.3 - 3, ? = 150 kg/mm² for canopy and ? = 200 kg/mm² for cord. The fiber density is taken ? = 3000 kg/m³. The results of this computation are presented in Table 1.

Currently, the mass of the heat protection shield of the Shuttle is 9575 kg. By decreasing the heat flow by 2 - 3 times, the heat shield can be reduced proportionally saving 4 - 6 tons of Shuttle mass.

At the present time, changing of hundreds of hull protection tiles after every flight takes two weeks and is very costly to do. The new method requires only a few tile replacements (maximum temperature is less) or allows using a protective cooling method. The Command Module of spacecraft "Apollo" had a heat protection of approximately 1/2 of the total take-off/touchdown weight. The gain to be had from a new method reentering may be significantly more.

Table 1. Parachute data

Apollo Command Module

Earth Landing System Of Lunar Command Module.

The components of the ELS are housed around the forward docking tunnel. The forward compartment is separated from the central by a bulkhead and is divided into four 90-degree wedges. The ELS consists of three main parachutes, three pilot parachutes, two drogue parachute motors, three upright bags, a sea recovery cable, a dye marker, and a swimmer umbilical.

The Command Module's center of mass is offset a foot or so from the center of pressure (along the symmetry axis). This provides a rotational moment during reentry, angling the capsule and providing some lift (a lift to drag ratio of about 0.368). The capsule is then steered by rotating the capsule using thrusters; when no steering is required, the capsule is spun slowly, and the lift effects cancelled out. This system greatly reduces the g-force experienced by the astronauts, permits a reasonable amount of directional control and allows the capsule's splashdown point to be targeted within a few miles.

At 24,000 feet (7.3 km) the forward heat shield is jettisoned using four pressurized-gas compression springs. The drogue parachutes are then deployed, slowing the spacecraft to 125 miles per hour (201 km/h). At 10,700 feet (3.3 km) the drogues are jettisoned and the pilot parachutes, which pulls out the mains, are deployed. These slow the CM to 22 miles per hour (35 km/h) for splashdown. The portion of the capsule which first contacts the water surface is built with crushable ribs to further mitigate the force of impact. The Apollo Command Module could safely parachute to an ocean landing with at least two parachutes (as occurred on Apollo 15), the third parachute being a safety precaution.

Data of Apollo Command Module:

Fig.10. Apollo Command Module.

The method proposed in this paper (with control lift/drag force) can considerably decrease the required mass of the heat protection system. The Command Module of spacecraft "Apollo" has a heat protection of approximately 1/2 of the total take-off/touchdown weight. The gain to be had from a new method reentering may be significantly more.

Conclusion

The widespread production of high temperature fibers and whiskers allows us to design high-temperature tolerant control lift/drag parachutes, which may be used by space craft of all types for braking in a rarified planet atmosphere. The parachute has open backside surface that rapidly emits the heat radiation to outer space thereby quickly decreasing the parachute temperature. The proposed new method significantly decreases the maximum temperature and heat flow to main space craft. That decreases the heat protection mass and increases the useful load of the spacecraft. The method may be also used during an emergency reentering when spaceship heat protection is damaged (as in horrific instance of the Space Shuttle "Columbia").

RИfИrences

(Reader can find part of these articles in WEBs: http://Bolonkin.narod.ru/p65.htm, http://arxiv.org, search: Bolonkin, and in the book "Non-Rocket Space Launch and Flight", Elsevier, London, 2006, 488 pgs.)

http://aiaa.org search "Bolonkin".

http://www.scribd.com/doc/24057071 ,
http://www.archive.org/details/NewConceptsIfeasAndInnovationsInAerospaceTechnologyAndHumanSciences

http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182

October 2012

Article Airborne Wind Turbines 4 24 13 after Shmuel

Chapter 5
Energy Transfers from Airborne Wind Turbine:
Review and Comparison of Airborne Turbines.

Abstract

Ground based, wind energy extraction systems have reached their maximum capability. The limitations of current designs are wind instability and high cost of installations. The wind energy industry is in need of revolutionary ideas to increase the capabilities of wind systems. This article suggests a revolutionary innovation which produces a dramatic increase in power per unit at a lower cost per unit of energy extracted and is independent of prevailing weather. The main innovation consists of large free-flying air rotors positioned at high altitude for power and stable air stream, and two types (mechanical and electrical) of an energy cable transmission system between the air rotor and a ground system. The air rotor system flies at high altitude up to 10 km. Stability and control systems is provided which also enable changing altitude.

This chapter includes the theory of airborne wind systems and provides the analysis of four examples having a high unit power output (up to 50 MW). The proposed examples provide the following main advantages: 1) Large power production capacity per unit - up to ten - hundred times more than conventional ground-based small rotor designs; 2) The rotor operates at high altitude of 0.5 - 10 km where the wind flow is strong and steady; 3) Installation cost per unit energy is low and 4) The installation is environmentally friendly (no propeller noise).

Author also provides a brief review of other main wind systems/turbines describing their advantages and disadvantages.
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Keywords: wind energy, cable energy transmission, electric airborne transmission, utilization of wind energy at high altitude, air rotor, airborne wind turbines, windmills, Bolonkin.

Introduction
High Altitude Winds.

Power generation from winds usually comes from winds very close to the surface of the earth. Winds at higher altitudes are stronger and more consistent, and may have a global capacity of 380 TW. Recent years have seen significant advances in technologies meant to generate electricity from high altitude winds. Worldwide there are now over two hundred thousand wind turbines operating, with a total nameplate capacity of 282,482 MW as of end 2012. The European Union alone passed some 100,000 MW nameplate capacities in September 2012, while the United States surpassed 50,000 MW in August 2012 and China passed 50,000 MW the same month.

Some Information about Wind Energy.

The power of wind engine strongly depends on wind speed (to the third power). Low altitude wind (H = 10 m) has the standard average speed of V = 6 m/s. High altitude wind is powerful and practically everywhere is stable and constant. Wind in the troposphere and stratosphere are powerful and permanent. For example, at an altitude of 5 km, the average wind speed is about 20 M/s, at an altitude 10 - 12 km the wind may reach 40 m/s (at latitude of about 20 - 35⁰ N).
There are permanent jet streams at high altitude. For example, at H = 12-13 km and about 25⁰ N latitude, the average wind speed at its core is about 148 km/h (41 m/s). The most intensive portion has a maximum speed of 185 km/h (51 m/s) latitude 22⁰, and 151 km/h (42 m/s) at latitude 35⁰ in North America. On a given winter day, speeds in the jet core may exceed 370 km/h (103 m/s) for a distance of several hundred miles along the direction of the wind. Lateral wind shears in the direction normal to the jet stream may be 185 km/h per 556 km to right and 185 km/h per 185 km to the left.
The wind speed of V = 40 m/s at an altitude H = 13 km provides 64 times more energy than surface wind speeds of 6 m/s at an altitude of 10 m.
This is an enormous renewable and free energy source. (See reference: Science and Technology, v.2, p.265).

High altitude jet stream.

Jet streams are fast flowing, narrow air currents found in the atmospheres of some planets, including Earth. The main jet streams are located near the tropopause, the transition between the troposphere (where temperature decreases with altitude) and the stratosphere (where temperature increases with altitude). The major jet streams on Earth are westerly winds (flowing west to east). Their paths typically have a meandering shape; jet streams may start, stop, split into two or more parts, combine into one stream, or flow in various directions including the opposite direction of most of the jet. The strongest jet streams are the polar jets, at around 7-12 km (23,000-39,000 ft.) above sea level, and the higher and somewhat weaker subtropical jets at around 10-16 km (33,000-52,000 ft.). The Northern Hemisphere and the Southern Hemisphere each have both a polar jet and a subtropical jet. The northern hemisphere polar jet flows over the middle to northern latitudes of North America, Europe, and Asia and their intervening oceans. The southern hemisphere polar jet mostly circles Antarctica all year round.
Jet streams are caused by a combination of a planet's rotation on its axis and atmospheric heating (by solar radiation and, on some planets other than Earth, internal heat). Jet streams form near boundaries of adjacent air masses with significant differences in temperature, such as the polar region and the warmer air towards the equator.

Figure 1. General configuration of the polar and subtropical jet streams.

Other jet streams also exist. During the northern hemisphere summer, easterly jets can form in tropical regions, typically in a region where dry air encounters more humid air at high altitudes. Low-level jets also are typical of various regions such as the central United States.
Meteorologists use the location of some of the jet streams as an aid in weather forecasting. The main commercial relevance of the jet streams is in air travel, as flight time can be dramatically affected by either flying with the flow or against the flow of a jet stream. Clear-air turbulence, a potential hazard to aircraft passenger safety, is often found in a jet stream's vicinity but does not create a substantial alteration on flight times.

Economy of conventional utilization wind energy.

Wind power plants have low ongoing costs, but moderate capital cost. The marginal cost of wind energy once a plant is constructed is usually less than 1-cent per kW"h. As wind turbine technology improved this cost has been reduced. There are now longer and lighter wind turbine blades (up 75 m), improvements in turbine performance and increased power generation efficiency. Also, wind project capital and maintenance costs have continued to decline.
The estimated average cost per unit incorporates the cost of construction of the turbine and transmission facilities, borrowed funds, return to investors (including cost of risk), estimated annual production, and other components, averaged over the projected useful life of the equipment, which may be in excess of twenty years. Energy cost estimates are highly dependent on these assumptions so published cost figures can differ substantially. In 2004, wind energy cost a fifth of what it did in the 1980s, and a continued downward trend is expected as larger multi-megawatt turbines were mass-produced. As of 2012^[update] capital costs for wind turbines are substantially lower than 2008-2010 but are still above 2002 levels.http://en.wikipedia.org/wiki/Wind_Energy - cite_note-117 A 2011 report from the American Wind Energy Association stated, "Wind's costs have dropped over the past two years, in the range of 5 to 6 cents per kilowatt-hour recently.... about 2 cents cheaper than coal-fired electricity, and more projects were financed through debt arrangements than tax equity structures last year.... winning more mainstream acceptance from Wall Street's banks.... Equipment makers can also deliver products in the same year that they are ordered instead of waiting up to three years as was the case in previous cycles.... 5,600 MW of new installed capacity is under construction in the United States, more than double the number at this point in 2010. Thirty-five percent of all new power generation built in the United States since 2005 has come from wind, more than new gas and coal plants combined, as power providers are increasingly enticed to wind energy as a convenient hedge against unpredictable commodity price moves."

A British Wind Energy Association report gives an average generation cost of onshore wind power of around 3.2 pence (between US 5 and 6 cents) per kW"h (2005). Cost per unit of energy produced was estimated in 2006 to be comparable to the cost of new generating capacity in the US for coal and natural gas: wind cost was estimated at $55.80 per MW"h, coal at $53.10/MW"h and natural gas at $52.50. Similar comparative results with natural gas were obtained in a governmental study in the UK in 2011. A 2009 study on wind power in Spain by Gabriel Calzada Alvarez of King Juan Carlos University concluded that each installed MW of wind power led to the loss of 4.27 jobs, by raising energy costs and driving away electricity-intensive businesses. The U.S. Department of Energy found the study to be seriously flawed, and the conclusion unsupported. The presence of wind energy, even when subsidized, can reduce costs for consumers (€5 billion/yr in Germany) by reducing the marginal price, by minimizing the use of expensive peaking power plants.

In February 2013 Bloomberg New Energy Finance reported that the cost of generating electricity from new wind farms is cheaper than new coal or new baseload gas plants. In Australia, when including the current Australian federal government carbon pricing scheme their modeling gives costs (in Australian dollars) of $80/MWh for new wind farms, $143/MWh for new coal plants and $116/MWh for new baseload gas plants. The modeling also shows that "even without a carbon price (the most efficient way to reduce economy-wide emissions) wind energy is 14% cheaper than new coal and 18% cheaper than new gas." Part of the higher costs for new coal plants is due to high financial lending costs because of "the reputational damage of emissions-intensive investments". The expense of gas fired plants is partly due to "export market" effects on local prices. Costs of production from coal fired plants built in "the 1970s and 1980s" are cheaper than renewable energy sources because of depreciation.

High-altitude wind power (HAWP)

HAWP has been imagined as a source of useful energy since 1833 with John Etzler's vision of capturing the power of winds high in the sky by use of tether and cable technology. An atlas of the high-altitude wind power resource has been prepared for all points on Earth. A similar atlas of global assessment was developed at Joby Energy. The results were presented at the first annual Airborne Wind Energy Conference held at Stanford University by Airborne Wind Energy Consortium.

Various mechanisms are proposed for capturing the kinetic energy of winds such as kites, kytoons, aerostats, gliders, gliders with turbines for regenerative soaring, sailplanes with turbines, or other airfoils, including multiple-point building- or terrain-enabled holdings. Once the mechanical energy is derived from the wind's kinetic energy, then many options are available for using that mechanical energy: direct traction, conversion to electricity aloft or at ground station, conversion to laser or microwave for power beaming to other aircraft or ground receivers. Energy generated by a high-altitude system may be used aloft or sent to the ground surface by conducting cables, mechanical force through a tether, rotation of endless line loop, movement of changed chemicals, flow of high-pressure gases, flow of low-pressure gases, or laser or microwave power beams. There are two major scientific articles about jet stream power.

Programs for Developing Wind Energy

Wind is a clean and inexhaustible source of energy that has been used for many centuries to grind grain, pump water, propel sailing ships, and perform other work. Wind farm is the term used for a large number of wind machines clustered at a site with persistent favorable winds, generally near mountain passes. Wind farms have been erected in New Hampshire, in the Tehachapi Mountains. at Altamont Pass in California, at various sites in Hawaii, and may other locations. Machine capacities range from 10 to 500 kilowatts. In 1984 the total energy output of all wind farms in the United States exceeded 150 million kilowatt-hours.
A program of the United States Department of Energy encouraged the development of new machines, the construction of wind farms, and an evaluation of the economic effect of large-scale use of wind power.

The utilization of renewable energy (`green' energy) is currently on the increase. For example, numerous wind turbines are being installed along the British coast. In addition, the British government has plans to develop off-shore wind farms along their coast in an attempt to increase the use of renewable energy sources. A total of $2.4 billion was injected into renewable energy projects over the last three years in an attempt to meet the government's target of using renewable energy to generate 10% of the country's energy needs by 2010.
This British program saves the emission of almost a million tons of carbon dioxide. Denmark plans to get about 30% of their energy from wind sources.
Unfortunately, current ground wind energy systems have deficiencies which limit their commercial applications:

While there are many research programs and proposals for the wind driven power generation systems, all of them are ground or tower based. The system proposed in this article is located at high altitude (up to the stratosphere), where strong permanent and steady streams are located. This article also proposes a solution to the main technologist challenge of this system; the transfer of energy to the ground via a mechanical transmission made from closed loop, modern composite fiber cable.

The reader can find the information about this idea in [1]-[2], a detailed description of the innovation in [3]-[6], and the wind energy in references [7]-[8], new material used in the proposed innovation in [9]-[13]. The review of last airborne concepts in [14]-[17].

Description of Innovation

The main proposed high altitude wind system is presented in Figure 2. That includes: rotor (turbine) 1, support wing 2, cable mechanical transmission and keep system 3, electro-generator 4, and stabilizer 5. The transmission system has three cables (Figure 2e): main (central) cable, which keeps the rotor at a given altitude, and two transmission mobile cables, which transfer energy from the rotor to the ground electric generator. The device of Figure 2f allows changing a cable length and a rotor altitude. In calm weather the rotor can be support at altitude by dirigible 9 (Figure 2c) or that is turned in vertical position and support by rotation from the electric generator (Figure 2d). If the wind is less of a minimum speed for support of rotor at altitude the rotor may be supported by autogiro mode in position of Figure 2d. The probability of full wind calm at a high altitude is small and depends from an installation location.

Figure 3 shows other design of the proposed high altitude wind installation. This rotor has blades, 10, connected to closed-loop cables. The forward blades have a positive angle and lift force. When they are in a back position the lift force equals zero. The rotor is supported at the high altitude by the blades and the wing 2 and stabilizer 5. That design also has energy transmission 3 connected to the ground electric generator 4.

Figure 4 shows a parachute wind high altitude installation. Here the blades are changed by parachutes. The parachutes have a large air drag and rotate the cable rotor 1. The wind 2 supports the installation in high altitude. The cable transmission 3 passes the rotor rotation to the ground electric generator 4.

A system illustrated in Figure 5 uses a large Darries air turbine located at high altitude. This turbine has four blades.

The other components are same with previous projects.

Problems of Launch, Start, Guidance, Control, Stability, and Others

Launching. It is not difficult to launch the installations having support wing or blades as described in Figure 2 - 5. If the wind speed is more than the minimum required speed (>2-3 m/s), the support wing lifts the installation to the desired altitude.

Starting. All low-speed rotors are self-starting. All high-speed rotors require an initial starting rotation from the ground motor-generator 4 (figure 2).

Guidance and Control. The control of power, revolutions per minute, and torque moment are operated by the turning of blades around the blade longitudinal axis. The control of altitude may be manual or automatic when the wind speed is normal and over admissible minimum. Control is effected by wing flaps and stabilizer (elevator), fin, and ailerons (figs. 2, 3, 5).

Stability. Stability of altitude is produced by the length of the cable. Stability around the blade longitudinal axis is made by stabilizer (see figs.2, 3, 5). Rotor directional stability in line with the flow can be provided by fins (figs. 2). When the installation has the support wing rigidly connected to the rotor, the stability is also attained by the correct location of the center of gravity of the installation (system rotor-wing) and the point of connection of the main cable and the tension elements. The center-of-gravity and connection point must be located within a relatively narrow range 0.2 - 0.4 of the average aerodynamic chord of the support wing (for example, see Figure 2). There is the same requirement for the additional support wings such as Figures 3 - 5.

Figure 2. Propeller high altitude wind energy installation and cable energy transport system. Notation: a - side view; 1 - wind rotor; 2 - wing with ailerons; 3 - cable energy transport system; 4 - electric generator; 5 - stabilizer; b - front view; c - side view with a support dirigible 9, vertical cable 6, and wind speed sensors 7; d - keeping of the installation at a high altitude by rotate propeller; e - three lines of the transmission - keeper system. That includes: main (central) cable and two mobile transmission cables; f - energy transport system with variable altitude; 8 - mobile roller.

Torque moment is balanced by transmission and wing ailerons (see figs.2 - 5).

The wing lift force, stress of main cable are all regulated automatic by the wing flap or blade stabilizer.

The location of the installation of Figure 3 at a given point in the atmosphere may be provided by tension elements. These tension elements provide a turning capability for the installation of approximately Ђ 45⁰ degrees in the direction of flow (see Figure 3.).

Figure 3. High altitude wind energy installation with the cable turbine. Notation: 10 - blades.

Figure 4. High altitude wind energy installation with the parachute turbine.

Figure 5. High altitude wind energy installation with Darrieus turbine.

Minimum wind speed. The required minimum wind-speed for most of the suggested installation designs is about 2 ¤ 3 m/s. The probability of this low wing speed at high altitude is very small (less 0.001). This minimum may be decreased still further by using the turning propeller in an autogiro mode. If the wind speed is approximately zero, the rotor can be supported in the atmosphere by a balloon (dirigible) as is shown on Figure 2c or a propeller rotated by the ground power station as is shown on Figure 2d. The rotor system may also land on the ground and start again when the wind speed attains the minimum speed for flight.

A Gusty winds. Large pulsations of wind (aerodynamic energy) can be smoothed out by inertial fly-wheels.

The suggested Method and Installations for utilization of wind energy has following uniqueness ion comparison with current conventional methods and installations:

All previous attempts to place the generator near the rotor and connect it to ground by electric transmission wires were not successful because the generator and wires are heavy. The author offers the new electric high frequency generator and transformer, new electric wires which degrease the mass of the electric system by tenths times and make one acceptable for airborne wind installation. This author also suggests in this proposed system a new electrostatic generator which has the specific mass ten times less yet produces high voltage.

Cable Energy Transmitter

The primary innovations presented in this paper are locating the rotor at high altitude, and an energy transfer system using a cable to transfer mechanical energy from the rotor to a ground power station. The critical factor for this transfer system is the weight of the cable, and its air drag.

Thirty years ago, the mass and air drag of the required cable would not allow this proposal to be possible. However, artificial fibers are currently being manufactured, which have tensile strengths of 3 - 5 times more than steel and densities 4 - 5 times less than steel. There are also experimental fibers (whiskers) which have tensile strengths 30 - 100 times more than a steel and densities 2 to 5 times less than steel. For example, in the book [9] p.158 (1989), there is a fiber (whisker) C_D, which has a tensile strength of ? = 8000 kg/mm² and density (specific gravity) of ? = 3.5 g/cm³. If we use an estimated strength of 3500 kg/mm² (? = 7^.10¹⁰ N/m²), ? = 3500 kg/m³, then the ratio is ?/? = 5в10^-8 or ?/? = 2в10⁷. Although the described (1989) graphite fibers are strong (?/? = 10в10⁶), they are at least still ten times weaker than theory predicts. A steel fiber has a tensile strength of 5000 MPA (500 kg/sq.mm), the theoretical limit is 22,000 MPA (2200 kg/mm²)(1987); the polyethylene fiber has a tensile strength 20,000 MPA with a theoretical limit of 35,000 MPA (1987). The very high tensile strength is due to its nanotubes structure.

Apart from unique electronic properties, the mechanical behavior of nanotubes also has pique interest because nanotubes are seen as the ultimate carbon fiber, which can be used as reinforcements in advanced composite technology. Early theoretical work and recent experiments on individual nanotubes (mostly MWNT's, Multi Wall Nano Tubes) have confirmed that nanotubes are one of the stiffest materials ever made. Whereas carbon-carbon covalent bonds are one of the strongest in nature, a structure based on a perfect arrangement of these bonds oriented along the axis of nanotubes would produce an exceedingly strong material. Traditional carbon fibers show high strength and stiffness, but fall far short of the theoretical, in-plane strength of graphite layers by an order of magnitude. Nanotubes come close to being the best fiber that can be made from graphite.

For example, whiskers of Carbon nanotube (CNT) material have a tensile strength of 200 Giga-Pascals and a Young's modulus over 1 Tera Pascals (1999). The theory predicts 1 Tera Pascals and a Young's modules of 1-5 Tera Pascals. The hollow structure of nanotubes makes them very light (the specific density varies from 0.8 g/cc for SWNT's (Single Wall Nano Tubes) up to 1.8 g/cc for MWNT's, compared to 2.26 g/cc for graphite or 7.8 g/cc for steel).

The artificial fibers are cheap and widely used in tires, fiber and many other products. The price of SiC whiskers produced by Carborundum Co. with ? = 20,690 MPa and ? = 3.22 g/cc was $440 /kg in 1989. The market price of nanotubes is too high presently (~ $200 per gram) (2000). In the last 2 - 3 years, there have been several US companies that were established to produce and market nanotubes. It is anticipated that in the next few years, nanotubes will be available to consumers for less than $100/pound.

Below, the author provides a brief overview of recent research information regarding the proposed experimental (tested) fibers. In addition, the author also addresses additional examples, which appear in these projects and which can appear as difficult as the proposed technology itself. Industrial fibers with ? = 500 - 600 kg/mm², ? = -1800 kg/m³, (safety ? = 50 - 150 kg/mm²) (see below).

In theory, metallic nanotubes can carry an electric current density of 4в10⁹ A/cm², which is more than 1,000 times greater than those of metals such as copper.

The temperature stability of carbon nanotubes is estimated to be up to 2800 ®C in vacuum and about 750 ®C in air.

Figures for some other experimental whiskers and industrial fibers are given in Table 1.

Table 1. Properties whiskers and fibers

See References [9]-[12].

Brief Theory of Estimation of Airborne Wind Installations

Wind (Speed, Duration, Altitude Distribution, Speed Distribution)

We can calculate the minimum and maximum acceptable wind necessary for operation of the air borne wind installation (ABWI). Our purpose is estimation of time (% or a number of days/hours in year) when the ABWI cannot operate.

Annual average wind speed. The United States Annual Average Wing Speed is taken from a map in Wind Energy Resource Atlas of the United States. The map was published in 1987 by Battelle's Pacific Northwest Laboratory for the U.S. Department of Energy. The complete atlas can be obtained by writing the American Wind Energy Association or the National Technical Information Service. The same maps are accessible around the world. They are presented in publication of the USA Department of Energy. The maps show the average wind speed at altitude 10 and 50 meters. This speed is 4 - 8 m/sec.

Wind speed and Height. Wind speed increases with height. The speed may be computed by equation

(1)

where V₀ is the wind speed at the original height, V the speed at the new height, H₀ the original height, H the new height, and ? the surface roughness exponent (Table 2).

Table 2. Typical surface roughness exponents for power
law method of estimating changes in wind speed with height

Reference: P.Gipe, Wind Energy comes of Age, 1995,[7].

The result of computation of equation (1) for different ? is presented at Figure 6. The wind speed increases on 20 - 50% with height 1000 m.

Annual Wind speed distribution. Annual speed distributions vary widely from one site to another, reflecting climatic and geographic conditions. Meteorologists have found that Weibull probability function best approximates the distribution of wind speeds over time at sites around the world where actual distributions of wind speeds are unavailable. The Rayleigh distribution is a special case of the Weibull function, requiring only the average speed to define the shape of the distribution.

Figure 6. Relative wind speed via altitude and Earth surface. For sea and ice ? = 0.1.

Equation of Rayleigh distribution is

where ? is parameter.

Figure 7 presents the annual wind distribution of average speeds 4, 5, and 6 m/s. These data gives possibility to easy calculate the amount (percent) days (time) when ABWI can operate in year (Figure 8). It is very important value for the estimation efficiency of offered turbines.
Let us compute two examples:

Assume, the observer has minimum wind speed 3 m/s, maximum safety speed 25 m/s, altitude 100 m, the average annual speed in given region is 6 m/s. From Figure 6, 7, 8, Eq. (1) , we can get the wind speed is 8.4 at H = 100m, the probability that the wind speed will be less the 2 m/s is 8%, less 3 m/sec is 15%, the probability that the wind speed will be more 25 m/s is closed to 0.

Figure 7. Wind speed distribution.

Figure 8. Probability of wind for annual average wind speed 4 - 8 m/s.

Forces of the Airborne Wind Installation

The next forces are acting in airborne wind installation: lift forces of wing and dirigible (air balloon), weight of installation (turbine + electric generator and transformer), approximately half of main cable weight, approximately half of transmission weight, drag of turbine, drag of wing, drag of dirigible (if one is used), approximately half drag of main cable, approximately half drag of transmission cable.

These forces are presented in figure 9.

The balance equations in axis x (horizontal) and axis y (vertical) are:
?_x F_c cos ? = D_r + D_w + D_d + 0.5D_c + 0.5D_{tr ,} (3)
?_y L_w + L_d = F_c sin ? + Mg + 0.5m_cg+ 0.5m_trg _. (4)

Here F_c is force of main cable, N; D_r is air drag of wind rotor/turbine, N; D_w is air drag of wing, N; D_d is air drag of dirigible, N; D_c is air of main cable, N; D_tr is air drag of transmission, N; L_w is wing lift force, N; L_d is dirigible lift force, N; M is mass of installation (air turbine + electric generator and transformer), kg; g = 9.81 m/s is Earth gravity; m_c is mass of main cable, kg; m_tr is mass of transmission cable, kg; ? is angle between line from initial point at Earth to air installation and Earth surface.

For given design parameters, given angle ? (? - 25^o ¤ 35^o) and the given row of the wind speed (from given V_min throw the safety V_max) we can find (after using the equation below) the cable force F_c from Eq. (3) and requested the wing force L_w from Eq. (4) and compare with initial data (cross section of main cable area). If they are significantly different - recalculate for new data.

Figure 9. Forces active in air borne wind installation

Rotor Computation.

Power of a wind energy N [Watt, Joule/sec]
N = 0.5?? AV³ [W] . (5)

The coefficient of efficiency, ?, equals 0.15 ¤ 0.35 for low speed propeller rotors (ratio of blade tip speed to wind speed equals ? - 1); ? = 0.45 ¤ 0.5 for high speed propeller rotors (? = 5-7). The Darrieus rotor has ? = 0.35 - 0.4. The gyroplane rotor has 0.1 ¤ 0.15. The air balloon and the drag (parachute) rotor has ? = 0.15 - 0.2. The Makani rotor has 0.15 ¤ 0.25. The theoretical maximum equals ? = 0.67. A - front area of rotor, air balloon or parachute [m²]. ? - density of air: ?_o =1.225 kg/m³ for air at sea level altitude H = 0; ? = 0.736 at altitude H = 5 km; ? = 0.413 at H = 10 km. V is average annually wind speed, m/s.

Table 3. Relative density ?_r and temperature of the standard atmosphere via altitude

Issue [ 6 ].

The salient point here is that the wind power very strong depends from the wind speed (in third order!). If the wind speed increases by two times, the power increases by 8 times. If the wind speed increases 3 times, the wind power increases 27 times!

The wind speed increases in altitude and can reach in constant air stream at altitude H = 5 - 7 km up V = 30 - 40 m/s. At altitude the wind is more stable/constant which is one of the major advantages that the airborne wind rotor can has over ground wind rotor.

For comparison of different systems of wind rotors the engineers must make computations for average annual wind speed V₀ = 6 m/s and altitude H₀ = 10 m. For standard wind speed and altitude the wind power equals 66 W. The modern propeller wind turbines have diameter up 132 - 154 m. For their comparison the engineers take the average standard the H₀ = 50 m and V₀ = 10 m/s. The power of the propeller turbine having rotor diameter 154 m reaches up 5.6 MW for standard conditions.

The energy, E, is produced in one year is (1 year - 30.2в10⁶ work sec) [J]

E = 3600в24в350N - 30в10⁶N, [J]. (6)

The drag of the rotor equals

D_r = N/V, [N]. (7)

The drag of the dirigible is
D_d = 0.5C_D,d?V²A_d , [N], (8)
C_D,d - 0.01¤ 0.03 is coefficient of air drag; A_d is cross section of dirigible A_d = ?d²/4 , m².

The lift force of the wing,
L_w, is L_w = 0.5C_L? V²A_w, [N], (9)

where C_L is lift coefficient (maximum C_L - 2 - 2.5); A_w is area of the wing, m².

The drag of the wing is

D_w = 0.5C_D?V²A_w, [N], (10)

where C_D is the drag coefficient (C_D - 0.02 ¤ 0.2).

The air drag, D_c , of main cable and air drag, D_tr , of the transmission cable is
D_c = 0.5C_d,c?V²Hd_c , D_tr = 0.5C_d,rV²Hd_tr, [N], (11)
where C_d,c - drag coefficient of main cable, C_d,c - 0.05 - 0.15; H is rotor altitude, m; d_c is diameter of the main cable, m. C_d,r - drag coefficient of the transmission cable, C_d,r - 0.05 - 0.15; d_tr is diameter of the transmission cable, m. Only half of this drag must be added to the total drag of wind installation:
D - D_r + D_w + D_d + 0.5D_c + 0.5D_tr, [N] (12)

If the wind installation is supported by dirigible, the lift force and air drag of dirigible must be added to wing lift force (6) and total (9) of system. The useful lift force of dirigible is about 5 N/m³ (0,5 kg/m³) at H = 0 and zero at H = 6 km. Full lift force is:
L = L_w + L_d - Mg - 0.5g(m_c + m_tr) , [N]. (13)

Here M is mass of installation (propeller + reducer + electro-generator + transformer), kg; g = 9.81 m/s² is Earth acceleration. Lift force of dirigible L_d - 5U_d [N], where U_d is dirigible volume, m³.

The mass of main and transmission cable are:
m_c = ?_cS_cL, m_tr = 2?_trS_trL, [kg], (14)
where ?_c is specific weight/density of cables, kg/m³, ?_c - 1500 ¤ 1800 kg/m³; S_c is cross section area of cables, m²; L is length of cable, m.

Required diameter of propeller for the power P = 100 kW and V = 10 m/s is 22.5 m; for speed V = 15 m/s diameter is 12.3 m.

The optimal speed of the parachute rotor equals 1/3V and the theoretical maximum of efficiency coefficient is ? = 0.5, real is 0.2.

The average angle ? of connection line to horizon is

sin ? - L/D, (15)

The annual energy produced by the wind energy extraction installation equals

E = 8.33N [kWh] . (16)

Cable Energy Transfer, Wing Area, and other Parameters

Cross-section area of the mechanical transmission cable,
S_t , is S_t = N/v? , (17)

where N is transmission energy, W; v is speed of mechanical transmission, m/s; ? is safety stress of the mechanical transmission cable N/m², for good artificial fibers ? - 50 ¤ 100 N/mm² (? - (50 ¤ 100)в10⁶ N/m²). For long mechanical transmission v - 50 ¤ 150 m/s.

The cable force from wind turbine is
F_t = N/v, (18)
For example, if the transmission energy is N = 100 kW, speed of the mechanical transmission is v = 50 m/s, safety stress of artificial fiber is ? = 100 kg/mm² = 10⁹ N/m², the cross-section area of the mechanical transmission cable is s_m = 2 mm² = 2в10^-6 m². Diameter of the cable is d = 1.6 mm². F_t = N/v = 10⁵/50 = 2000 N.

The air drag of transmission cable D_t , opposed the moving force is

D_t = 0.5C_D?v²S_t , (19)
where C_D - 0.008 ¤ 0.012 is air drag coefficient; ? is air density, kg/m³, S_t is surface area of cable, m². The surface area of double transmission cable is

S_t = ?d²L_c/2, (20)
where d is diameter of the cable, m; L_c is length of the cable, m.

The coefficient of transmission efficiency is

? = 1 - D_t/F_t , (21)
For our cable and L_c = 1 km = 1000 m, the S_t = 10 m² . N = 100 kW, F_t = 2000 N and air drag D_t = 150 N (Newton)/km, coefficient efficiency is ? = 0.9625 km^-1.

Cross-section area of main cable, S_m , is
S_m
[m²] , (22)
where ? is the safety stress of the main cable N/m².

The production cost, c, in kWh is

, (23)

where M₀ - annual maintenance [$]; I₀ - cost of Installation [$]; K₁ - life time (years); E - annual energy produced by flow installation [J];

The annual profit

F₀ = (C-c)E . (24)
where F₀ - annual profit [$]; C - retail price of 1 kWh [$].

In first estimation of the required area of the support wing is about

A_w - ?Asin?/C_{L ,} (25)

where ? is the angle between the support cable and horizontal surface.

The wing area is served by ailerons for balancing of the rotor (propeller) torque moment

, (26)
r - distance from center of wing to center of aileron [m]; R - radius of rotor (turbine)[m]; ?C_L,a - difference of lift coefficient between left and right ailerons;

The minimum wind speed for installation support by the wing alone

, (27)

where W = L is force of the total weight of the airborne system including transmission, [N]. If a propeller rotor is used in a gyroplane mode, minimal speed will decrease by 2 - 2.5 times. If wind speed equals zero, the required power for driving the propeller in a propulsion (helicopter) mode is
N_s = W/K₂ [kW], (28)

where W - weight of installation (rotor + generator + transformer + cables)[kg]; K₂ - rotor lift coefficient (5 - 12 [kg/kW]).

The specific weight of energy storage (flywheel) can be estimated by

E_s=?/2? [J/kg]. (29)

For example, if ? = 200 kg/mm², ? = 1800 kg/m³, then E_s= 0.56 MJ/kg or E_s= 0.15 kWh/kg.
Electric Transfer of Energy

Properties of the matter needed for computation of characteristics of the electric line from airborne rotor to ground installation is below.

1. Electric current safety for different wires.
Table 4. Safe electric currents via different materials and cross-section of wires [16 ] p.115.

Author employs electric wire design which allows permanently maintaining the electric current safely at about 10 A/mm². It is that value which we use in our calculation.

Table 5. Spark gap between bare wires in atmosphere. [16] p.126.

Table 6. Dielectric strength of insulators [5]-[6].

*For room temperature

2. Mass m_e [kg/kW.km] of the 1 km electric wires is
s = P/(pU) , m_e = 2k₂?sL, (30)

were s is cross section of electric wire, m²; p - 5 ¤ 10 A/mm² is safety electric current A/m²; U is voltage, V; k₂ - 2 ¤ 3 is insulator coefficient, ? is the specific weight of wire, kg/m³; L is length of wire, m; P is electric power, W. For example, if P = 10⁵ W = 100 kW, U = 10⁴ V, p = 10 A/mm² = 10⁷A/m², ? = 2800 kg/m³ (aluminum wire), L = 1000 m, the s = 1 mm², than m_c - 11 kg/km, or m_c - 0.11 kg/(kW.km).

3. Electric resistance and coefficient of electric efficiency are:
R = ?_eL/s, ? = 1 - ?U/U = 1 - 2I?_eL/sU , (31)
where R is electric resistance, ?; ?_e is coefficient of electric resistance (Table # 1), ohm.m; ? is coefficient electric efficiency; I is electric currency, A; ?U is the loss of voltage in transmission wire, V; s is cross-section of wire, m². Example, if P = 10⁵ W = 100 kW, U = 10⁴ V, p = 10 A/mm² = 10⁷A/m², ?_e = 2.8в10^-8 ?.m (aluminum wire), L = 1000 m, the s = 1 mm², then ? = 0.944 km^-1.

4. Air drag of main cable and electric wires, connected in one cable is
D_c+w = 0.5C_D?_aV²A_c+w , [N], A_c+w = s_c+wH , (32)
where C_D is the drag coefficient C_D = 0.015 ¤ 0.15; ?_a - air density, ?_a - 1 kg/m³; s_c+w is cross-section area of common cable, H is altitude, m. Example, if s_c+w = 3в10^-6 m², H = 1000 m, V = 15 m/s, C_D = 0.02, then D_c+w = 500 N/km.

5. Electric generator.
Specific mass of the conventional (car) electric generator is about 4 - 5 kg/kW. This mass is inversely related to electric frequency. Standard electric frequency is 50 Hertz. Aviation generator which has frequency 400 Hertz has specific mass of about 0.5 kg/kW. Example, the aviation electric generator ГТ120 П46А (Russia) has power N = 120 kW, U = 120/208 V, frequency is ? = 400 Hertz, n = 100 ¤ 6000 revolution/min, mass 67 kg, cooling by air. That means we can take for our estimation the specific weight about 0.5 kg/kW.

6. Transformer.

For passing the electric energy from airborne turbine to the Earth we need the electric transformer which converts the electric energy to high voltage. That allows decreasing the weight the electric wire. The typical data of the conventional 3-fases transformer is following: the transformer having power 100 kW, frequency 50 Hertz has weight 505 kg, site 890в1105в600 mm, enter 400 V, exit 6/10 kV. The Transformer ТМГ-1000/6-10 has power 1000 kW, weight 2900 kg, frequency 50 Hertz, enter 400 V, exit 6/10 kV, cooling - oil. That is not suitable for us because the weight and size is big. If we will use the frequency 400 Hertz the transformer weight decreases in 400/50 = 8 times and equals about 0.5 kg/kW. That is acceptable. But it is possible that there will be cooling problem of generator and transformer.

The offered electric system needs in the frequency convector 400 Hertz to 50 Hertz or rectifier. But one is located on Earth surface and is needed for all airborne turbines having the electric transmission.

The total mass of electric transmission system (electric generator + transformer + wires) is about additional 1.2 ¤ 1.5 kg/kW in comparison with mechanical system having 0.3 ¤ 0.5 kg/kW. That also increases also the requested the wing area and weight, because the wing must support the full installation in minimal wind speed. But the electric translation system is better equipped for changing the altitude which allows selection of the altitude where is the wind speed is optimal. If we want an airborne wind system without transformer, we must design special high voltage generator.

The ABWI having an electric transmission is a high altitude lighting conductor in storm and, as such, is in need of special equipment for this case as protection or landing system.

7. Result of estimation the electric transfer/system.
The total mass of the airborne wind installation (P = 100 KW, L = 1 km) with electric transfer is:
Rotor (propeller): 1 kg/kW,
Wing: 1 ¤ 2 kg/m² , or 1.5 ¤ 3 kg/kW ,
Electric generator + transformer: 1 ¤ 1.2 kg/kW,
Main cable: 0.4 ¤ 0.6 kg/kW.km (turbine gets - 50% of this weight),
Electric wires: 0.1 ¤ 0.15 kg/kW.km (turbine gets - 50% of this weight); or
Mechanical transmission 0.1 ¤ 0.15 kg/kW.km (turbine gets - 50% of this weight).
Total mass is about 4 ¤ 5 kg/kW, or 400 ¤ 500 kg (for average P = 100 kW). Mass of wing is 200 ¤ 250 kg (wing have the area 150 ¤ 200 m² and support the installation for a minimal wind speed 3 ¤ 5 m/s).

If airborne wind installation has the mechanical transmission then the total mass of installation will be about two times less, but airborne wind installation will require developing a special system for change the altitude.

The dirigible (special air balloon) can support the airborne in windless conditions. The needed volume is about 900 m³ for the electric transmission and 500 m³ for the mechanical transmission. Size of dirigible is 14в60 m and 10в45 m respectively. Support by dirigible is very useful because for exploitation of the airborne wind installation because we not expend energy for supporting the turbine at altitude in weak winds (speed less 3 m/s) or in windless conditions. This situation may be in 5 ¤ 10% of total time in low (< 1 ¤ 2 km) altitudes.
8. Electrostatic generator.

Electrostatic generator produces electricity of a very high voltage and is not encumbered by have heavy iron and wire, nor does it have a cooling problem. The relative mass may be less than mass of the magnetic generator and transformer. The estimation of mass can be made by equations: m_g = M_g/P, P = IV, I = qv, q = cU, c = ?_oS/a, (33)
where m_g is relative mass of electrostatic generator, kg/kW; M_g is mass of generator, kg; P is power, kW; I is electric currency, A; V is voltage, produced by generator, V; q is electric charge, C; v is relative speed of generator plates, m/s; c is electric capacity of plates, F; U is voltage between plates, V; ?_o = 8.85в10^-12 is electric constant, F/m; S is area of plates, m²; a is distance between plates, m.

Let us, for example, take 250 plates of area 1 m² each with distance 2 mm and voltage between plates U = 10⁵ V and thickness of isolator 1 mm, the plate speed v = 700 m/s. We take the exit voltage of generator V = 2в10⁵ V. Produced voltage V may be any (up 1 MV), but transfer more high voltage to Earth surface is difficult. Estimation show: the electric current may be I = 350 A and mass of generator M_g = 1000 kg, size 1.2в1.2 m (diameter в length). The produced energy will be P = 70 MW. The relative mass is m_g - 0.015 kg/kW which is a very small value which shows the electrostatic generator/engine is very perspective for R&D. But design power electrostatic generator is not an easy problem to solve.

Total Estimation and Optimization Airborne Wind System

Below are summary equations which help estimate and select the suitable parameters of installation. The first equation is preliminary; the second/last equation is final.

m_t = M_t/N, m_t = ?_tL/?V, (38)
where M_t is mass of transmission cable, kg; ? is safety stress of transmission cable, N/m²; V is wind speed, m/s; ?_t is the specific mass of the transmission cable.

Cost of construction and economy of wind turbines.
Cost of renewable energy

Average cost of the ground wind installation in 2012 were: 1 kW - $2K, 2 kW - $3.5K, 5 kW - $14K, 10kW - 35 ¤ 50K. Wind turbine $1,3 ¤ 2,2M per MW. Ground transmission $1500/km. The average allocation of cost: tower 27%, rotor blades 21%, generator 4%, transformer 4%, power convertor 6%, gearbox 11%, others 27%.

Table 7: Comparison of capital cost breakdown for typical onshore and offshore wind power systems in developed countries, 2011

Source: Blanco, 2009; EWEA, 2009; Douglas-Westwood, 2010; and Make Consulting, 2011c.

Onshore Offshore

Capital investment costs (USD/kW) 1 700-2 450 3 300-5 000

Wind turbine cost share¹ (%) 65-84 30-50

Grid connection cost share² (%) 9-14 15-30

Construction cost share³ (%) 4-16 15-25

Other capital cost share⁴ (%) 4-10 8-30
----------------------------------------------------------------------------------------------------------------

¹ Wind turbine costs includes the turbine production, transportation and installation of the turbine.

² Grid connection costs include cabling, substations and buildings.

³ The construction costs include transportation and installation of wind turbine and tower, construction wind turbine foundation (tower), and building roads and other related infrastructure required for installation of wind turbines.

⁴ Other capital cost here include development and engineering costs, licensing procedures, consultancy and permits, SCADA (Supervisory, Control and Data Acquisition) and monitoring systems.

Comparison of different airborne designs

There are a number of alternative designs of airborne wind turbines. Unfortunately in many cases the inventors are people who do not have the needed technical education, cannot develop the corresponded theory, and make the correct estimations and computations. Unfortunately, the entire wind energy industry is plagued by the paucity of contiguity of scientific knowhow and business acumen. Governmental agency and business leaders most often do not select the projects that are scientifically feasible. Conversely, some inventors are well connected with funding sources; be they governmental authorities or heads of large companies. They may receive large grants for perspective projects with little scientific merit. Before funding a high altitude wind energy device, mathematical modeling is necessary to detail the physics in order to persuade the experts that it is not only physically feasible but economically feasible and largely profitable.

Wind at high altitudes is faster and more consistent than winds near the Earth's surface and contains more than three times the power providing a phenomenal untapped resource. A comprehensive understanding of winds ranging from the upper boundary layer through the upper troposphere and its availability is critical to the development of our technology. Let us estimate the parameters of some airborne wind systems same power (100 kW). The first systems will have this power.

1. Mogenn and system is lighter than air (MARS).

Some of these systems shown in Fig. 10 are air balloon having shoulder blades which rotate the balloon under wind.
If the strong wind is V = 15 m/s and coefficient of efficiency ? = 0.15 the requested the frond area of balloon is
A = P/(0.5??V³) - 400 m² , (38)

If length of balloon is 3 times of diameter, the diameter of balloon will be about 12 m, length 36 m and volume 4500 m³. The helium cost was - $16/m³ at 2012. Total cost only helium is $72K. Useful (without weight of balloon) lift force is 23000 N = 2300 kg. The mass of good generator + transmission - 300 kg.

Fig.10. The airborne wind system which are lighter than air.
Air drag of balloon is
D = 0.5C_D?V²A = 0.5в0.3в1в15²в400 = 13500 N . (39)
Angle of the main cable to horizon in wind 15 m/s is about 35 ¤ 40^o. It is acceptable. But in storm the wind can reach the speed up 35 m/s and angle will be about 10 ¤ 12^o. That is not good especially at city having high buildings.

Magenn Power is developing a 10 kW airborne wind turbine system that floats 1,000 feet in the air, tethered to the ground. The inflatable Helium balloon portion of the device has vanes on it that capture the wind energy, similar to a paddle wheel, turning it on a horizontal axis that is fastened on two ends. A generator is affixed to both ends, and the electricity is transmitted down the tether to the ground.

The set-up costs for MARS are projected to run around $4 to $5 per Watt. In comparison, the set-up costs for a traditional utility-scale wind farm run around $2.5 to $3 per Watt. But those are huge installations, and require a good ground-level wind profile. The Magenn system can go where the wind farms are not feasible. The installation costs for a comparable Diesel generator system are about $1.00 per Watt, but then there is the continual cost of the fuel to run the generators. Magenn has secured around a $1 million (Canadian) grant from the Canadian government to further their refinement of the design. The grant is a matching-funds grant, contingent on Magenn being able to raise $2 million from private sources. Magenn landed a separate $300,000 grant to build a 1 kW sized unit. It is unknown what was actually built.

2. The airborne wind propeller supported by dirigible.

This design is presented in fig. 11. It is acceptable for altitude up 3 - 5 km. One may be also used for lifting and delivering of loads. Disadvantage is high cost of installation.
The properties and data of this ABWI can be easily estimated by our theory.

Fig. 11. Air borne wind propeller supported by dirigible.

3. The autogyro (gyroplane) rotor

Fig. 12 illustrates one of the autogyro designs by inventor Roberts.

Fig. 12. Autogyro wind rotor

In Roberts design, if the wind is V = 15 m/s and coefficient of efficiency ? = 0.15, the requested the area of propellers is A = 400 m². Or diameter of the 4 propellers is D = 11.3 m each. Gyroplanes rotor is easy for design. The flying windmills would initially get in position under their own power, using their motors to drive the propeller blades and helicopter upwards until they reached altitude. Then the motors would turn off and become generators as wind pushes the propeller blades, and the whirligig would float instead of fall because when tethered, the lift generated by the wind would overcome the craft's weight as it also generates power.

His claims are unrealistic because the power 240 kW for a diameter less than 10.7 m because the autogyro rotor axis has small angle to vertical line (10 ¤ 20^o not 90^o as conventional wind propeller). It is necessary because the autogyro rotor must also produce the vertical force for supporting the weight of installation. The problem of transporting of wind energy to the Earth surface is the same problem for all airborne wind rotors. The other problem is saving the installation in stormy weather because the propellers may be damaged by very strong wind. In contrast, the designs detailed in this paper include proposals which avoid these disadvantages.

4. Tube Airborne Wind Energy.
An air balloon tube and propeller installed inside tube is a wind installation is shown in fig. 13.

Fig.13. Altaeros Wind turbines

The company describes the installation as the Altaerod Airborne Wind Turbine, which makes use of an inflatable shell filled with helium, allowing it to gain high altitude. This gives it better access to more consistent and stronger winds, much higher than those turbines mounted on towers. The power uses tethers to reach the ground. Harnessing winds at higher altitudes will allow the turbine to reduce the costs of energy by almost 65%. Since it has a unique design that is easily installed, the start-up time amounts to only days, which means that each shell can be prepared and assembled more readily, for increased energy production."

The corrected design of tube can increase the speed inside maximum in 2^0.5 times or the power in 2.8 times. But from figure 13 it is obvious that the inventor does not know aerodynamics and the presented installation is not efficient.

5. Makani Airborne Wind Turbine.

The original airborne turbine was offered by Makani figs.14 - 15. That is a single blade which flies in a circle. Blade has the propellers which produce the electric energy. If no wind the propellers may consume the energy from ground installation. They also lift the installation to altitude.

Joby Energy Co. is developing airborne wind turbines which will operate in the upper boundary layer and the upper troposphere. Their description from their company advertising: "Joby Energy's multi-wing structure supports an array of turbines. The turbines connect to motor-generators which produce thrust during takeoff and generate power during crosswind flight. Orientation in flight is maintained by an advanced computer system that drives aerodynamic surfaces on the wings and differentially controls rotor speeds. A reinforced composite tether transmits electricity and moors the system to the ground. The high redundancy of the array configuration can handle multiple points of failure and remain airborne. For launch, the turbines are supplied with power to enable vertical take-off. Upon reaching operating altitude, the system uses the power of the wind to fly cross-wind in a circular path. The high cross-wind speeds result in the turbines spinning the generators at high speeds, eliminating the need for gearboxes and increasing efficiency. The energy is transferred to the ground through the electrical tether. During occasional periods of low wind the turbines are powered to land the system safely."

Fig. 14. Makani airborne wind turbine at Earth surface.

Fig.15. Makani Airborne Wind Turbine in air.

Capacity Comparison. A comparison between the energy output potential of a 2 MW conventional turbine operating at 400 feet and a 2 MW Joby Energy airborne wind turbine operating at 2,000 feet shows a significant improvement in capacity factor. Our airborne wind turbine yields a capacity factor of nearly double the conventional turbine.

An airborne wind turbine must utilize less material than those found in ground based wind turbines. It is estimated that the Makani turbine will be 1/10 the weight of a standard wind turbine and cost half the price to install. It will be rated at the same amount of power. The price per kilowatt-hour would be even lower than coal-fired power at the present time, or about three cents per kilowatt hour.

The rotors on the flying wing of the Makani turbine function as generators and propellers. They use stored or backup power to reach their cruising altitude. When they reach 1,000 feet (- 300 m) in altitude, they begin creating resistance to the higher winds and then generate electricity just like electric cars do with their brakes.

Is this turbine affected when there is no wind? The wing structures can use steady breezes to remain aloft, but if the wind goes below nine miles per hour, they would actually use electricity instead of generating it. Plans are to land the wing if there are long periods of forecasted low winds. But it will still be able to generate electricity with double the consistency of wind farms that are in operation today. This is due to the winds at the increased altitude, which may be twice as strong as those on the ground.

The future of the Makani airborne wind turbine looks quite bright. It won Popular Mechanics' Energy Breakthrough Award and got three million dollars in grant money from the Department of Energy. It also received 20 million dollars from Google, for venture capital funding.

In order to be fully successful, the airborne wind turbine must be able to generate a consistent and high rate of power. They are developing a larger turbine system that will float at about 1600 feet (- 500 m) in altitude, and this can potentially produce enough power for 600 houses. The prototype of this design should be launched in 2013 and in operation commercially in 2015. The Makani turbine may also be used above deeper offshore water, where even more energy can be produced. Fig.14 shows the company does not have good specialists. The offered installation is unstable and very complex in operation. Company received large sums of money but did not create any successful design.

Projects with mechanical transmission

Project 1. High-speed air propeller rotor (fig.2)

For example, let us consider a rotor diameter of 100 m (A = 7850 m²), at an altitude H = 10 km (? = 0.4135 kg/m³), wind speed of V = 30 m/s, an efficiency coefficient of ? = 0.5, and a cable tensile stress of ? = 200 kg/mm². Then the power produced is N = 22 MW [Eq. (5)], which is sufficient for city with a population of 250,000. The rotor drag is D_r = 73 tons [Eq.(7)], the cross-section of the main cable area is S =1.4D_r/? =l.35в73/0.2 - 500 mm², the cable diameter equals d = 25 mm; and the cable weight is W = 22.5 tons (for L = 25 km). The cross-section of the transmission cable is 36.5 mm², d = 6.8 mm, weight of two transmission cables is 3.33 tons for cable speed v =300 m/s [Eq.(14)]. The required wing size is 20в100 m (C_L = 0.8), wing area served by ailerons is 820 sq.m. If C_L=2, the minimum speed is 3 m/s. The installation will produce an annual energy E =190 GWh [Eq.(16)]. If the installation cost is $200K, has a useful life of 10 years, and requires maintenance of $50K per year, the production cost is c = 0.37 cent per kWh [Eq(23)]. If retail price is $0.15 per kWh, profit $0.1 per kWh, the total annual profit is $19 million per year [Eq.(24)].

Project 2. Air low speed wind engine with free flying cable flexible rotor (fig.3)

Let us consider the size of cable rotor of width 50 m, a rotor diameter of 1000 m, then the rotor area is A = 50в1000 = 50,000 sq.m. The angle rope to a horizon is 70^o. The angle of ratio lift/drag is about 2.5^o. The average conventional wind speed at an altitude H = 10 m is V = 6 m/s. It means that the speed at the altitude 1000 m is 11.4 - 15 m/s. Let us take average wind speed V=13 m/s at an altitude H = 1 km. The power of flow is N=0.5^.?V³Acos20⁰=0.5в1.225в13³в1000в50в0.94=63 MW.