Article Kinetic Towers
Kinetic
Alexander Bolonkin
1310а
Avenue R, #6-F,
Tel/Fax 718-339-4563
E-mail: aBolonkin@juno.com,а http://Bolonkin.narod.ru
аAbstract
а The article discusses a new revolutionary
method to access to outer space. A cable stands up vertically and pulls up its
payload to space with maximum force determined by its strength. From the ground
the cable is allowed to rise up to the required altitude.а After this, one can climb to an altitude by
this cable or delivery to altitude a required load. The paper shows this
possible does not infringe on the law of gravity.
а The article contains the theory of the method
and the computations for four projects for towers that are 4, 75, 225, 160,000
km height. The first three projects use the conventional artificial fiber
widely produced by current industry, while the fourth project use nanotubes
made in scientific laboratories.а The paper
also shows in a fifth project how this idea can be used to launch a load at
high altitude.
------------------------------------------------------------
*Presented as paper IAC-02-IAA.1.3.03 at Would
Space Congress 2002, 10-19 October,
Keywords:
1. Introduction
а Lyrical
note. Many people
have seen a video cassette with trick of
а I ask a lot of scientists: how is a
scientific explain of this truck. This is hypnosis. However, you can hypnoses a
people, but you can not hypnoses a camcorder.
аCurrent
access to outer space is described in [1]-[12].
а This
chapter suggests a very simple and inexpensive method and installation for
lifting and launching into space. This method is different from centrifugal
method [6]. In [6] a cable circle or semi-circle and a centrifugal force is
used, which keeps the space station at high altitude. In the offered method
there is a straight line vertical cable connecting the space station and
EarthТs surface. The space station is kept by reflected cable and cable kinetic
(shot) energy. The offered method expends more than two times less energy for
air drag because there is two times less length of cable than semi-circle and a
shorter way (vertical beeline) then a full circle.
а This
is a new method and transport system for delivering payloads and people into
space. This method uses a cable and any conventional engine (mechanical,
electrical, gas turbines) located on the ground. After completing an exhaustive
literature and patent search, the author cannot find the same space method or
similar facilities.
2. Description of Suggested
Launcher
аа ааааааааааааааааааааааааааааааааааааааааааа 2.1.
Brief Description of innovation.
The installation includes (see notations in
fig.1a,b and others): strong closed-loop cable,а
two rollers, any conventional engine, space station, load elevator, and
support stabilization ropes.
а The installation works in the following way.
The engine rotates the bottom roller and permanently sends up the closed-loop
cable with high speed. The cable reaches at a top roller at high altitude,
turns back and moves to bottom roller. When cable turns back that creates a
reflected (centrifugal) force. This force can easily be calculated by a
centrifugal theory. This force can be also calculated as reflected mass by a
reflection theory. This force keeps the space station suspended to the top
roller; and the cable (or special elevator) allows the delivery of a load to
the space station. The station has a parachute and saves people if the cable or
engine fails.
ааааааа 
Fig.1. a. Offered kinetic tower: 1 Ц mobile closed loop cable, 2 Ц top roller of
the tower, 3 Ц bottom roller of the tower, 4 Ц engine, 5 Ц space station, 6 Ц
elevator, 7 Ц load cabin, 8 Ц tensile element (stabilize rope).ааааа
b. Design of top roller.
а The
theory shows, that current widely produced artificial fibers (see [4-6] for
cable properties) allow the cable to reach altitudes up to 100 km (see Projects
1 and 2). If more altitude is required a multi-stage tower must be used (fig.
2, see also Project 3). If a very high altitude is needed (geosynchronous orbit
or more), a very strong cable made from nanotubes (see [4-6]) must be used (see
Projects 4).
аааааааааааааааааааааааааааааааааа аа 
аааааааааааааааааааааааааааааааааааааааааааааа Fig.2. Multi-stage
kinetic tower.
а The offered tower may be used for a horizon launch of the space
apparatus (fig.3). The vertical kinetic towers support horizontal closed-loop
cables rotated by the vertical cables. The space apparatus is lifted by
vertical cable, connected to horizontal cable and accelerated to required
velocity.
ааааааааааааа ааааааааа аа
Fig.3. a. Kinetic space installation with horizon accelerate parts. b. 10 - accelerated missile.
а The closed-loop cable can have a variable length. This allows a start
from zero altitude, the ability to increase the station altitude for a required
value, and to spool the cable for a repair. The device for this action is shown
in fig.4. The offered spool can reel the left and right branches of the cable
with different speed and can change the length of cable.
ааааааааааааааааааааааааааааааааааааааааааааааааааааааа
аааааааааааааааааааааааааааааааааааааааааааааа Fig.4.
Variable cable spool (11)
аа Advantages. The suggested towers and launch
system have big advances by comparison to the current sold towers and rocket
systems:
1.
They
allow to reach a very high altitude (up to geosynchronous orbit and more)
impossible for solid towers.
2. They are cheaper by some thousands
times than the current low towers. No expensive rockets.
3.
The
kinetic towers may be used for tourism, power TV and radio translator over very
big area, radio locator, as the space launcher.
4.
The
offered towers and space launcher decreases the delivery cost by some thousand
times (up to $1-$4 per LB).
5.
The
offered space tower launcher can be made in a few months. The modern rocket
launch system requires some years for development, design, and building.
6.
The
offered cable towers and space launcher does not require high technology and
can be made by any non-industrial country from current artificial fibers..
7.
The
rocket fuel is expensive. The offer cable towers and space launcher can use the
cheapest sources of energy such as wind, water, nuclear or the cheapest fuels
such as gaseous gas, coal, peat, etc., because the engine is located on the
EarthТs surface. The flywheels may be used as an accumulator of energy.
8.
It
is not necessary to have highly qualified personnel such as rocket specialists
with high salaries.
9.
The
fare for the space tourists is small.
10.
No
pollution of the atmosphere from toxic rocket fuel.
11.
We
can launch thousands of tons of useful loads annually.
аа The advantages of offered method are the
same as the centrifugal launcher [6](see also Chapter 3).а The suggested method has approximately two
times less cost than the semicircle launcher [6] because it uses only one
double vertical cable. It also has approximately two times lower delivery cost
(up to $2-4 per kg), because it has two times less air drag and fuel
consumption.
1.
аааCable
discussing.а
а The reader can find the cable discussing in Chapter
1, in [4] and cable characteristics in [5]-[8]. In our projects #1-3 we use
only cheap artificial fibers widely produced by current industry.
3. Theory of Kinetic Tower
and Launcher
1. Lift force of kinetic tower.
a) Find the lift force of
kinetic support device from centrifugal theory.а
Take a small part of the rotary circle and write the equilibrium
ааааааааааааааааааааааааааааааааааааааааа (1)
аа where V
is rotary cable speed [m/sec],аа R Ц circleа radius [m], a - angle of circle part [rad]. S Ц cross-section cable areas [m2],
s -
cable stress [n/m2], g - cable density [kg/m3].
When aо0 the relationship between maximum rotary speed V and tensile stress of the closed loop (curve) cable is
,аааааааааааааааааааааааааааааааааааааа (2)
where F is
lift force [n], k=s/gа is relative cable stress [m2/sec2].
This equation is received in [13] for centrifugal cable launcher. .The
computation of the first equation for intervals 0 Ц 1K, 1K Ц 10K (K=k/107) are presented in figs. 5 Ц 6.
аааааааааааааааааааааааааааааааааа Fig.5.
Admissible cable speed via stress coefficient K= 0 Ц 1.
аааааа аааааааааааааааа Fig.6.
Admissible cable speed via relative stress coefficient K= 1 Ц 10.
b) Let us to find the lift force of the offered installation from
theoretical mechanics. Write
momentum of reflected mass in one second
F=mV-(-mV)=2mV,ааа m=gSV,а orаа F=2gSV2,аааааааааааааааааааааааааааааааааааа (3)
Here m is the
cable mass reflected in one second [kg/sec].
а If substitute the first equation (2) in (3),
the expression for lift force F=2sS аwill be
same. The computation of the equation (2) for intervals 0 Ц 1K,а 1K Ц 10K а(K=k/107) are presented in
figs.5 Ц 6.а
2.а Lift force in constant gravity field. In constant gravity field
without air drag, the list force of the offered device equals the centrifugal
force F minus the cable weight W
,ааааааааа (4)
аа where Hа is altitude of kinetic tower [m].
3.
Maximum
tower height or a minimum cable speed in a constant gravity field are (from (4)):
.аааааааааааааааааааааааааааааааааааааааа (5)
аа
Computations for K =0 ¸1 are presented in figs.7, 8. In this case the installation does not
produce an useful lift force and one support only itself.
ааааааааааааааааааааааа Fig.7 Maximum tower height via relative cable
stress.
аааааааааааааааааааааааааааааааааа Fig.8.
Minimum cable speed via tower height.
4.а Kinetic lift force in a variable gravity field and
for the rotary Earth.
ааааааааааа (6)
where k is the
relative cable stress. We will use more comfortable value for graphs K=10-7k.
аMinimum cable stress or a minimum
cable speed of a variable rotary planet equals
аааааааааа (7)
ааааа Computation of these equations for Earth
are presented in figs. 9-10. If K >5 the height of the kinetic tower
may be more then the Earth geosynchronous orbit. For Mars this is K
>1, for Moon it is K >0.3. Pay your attention in fig.9: the
offered tower of a height 145000 km can keep its without a cable rotation, and
if the tower height is more 145000 km, the tower has a useful lift force. That
allows to lift payload by immobile cable.
ааааааааааааааааааааааа Fig.9. Relative cable stress via
altitude for rotary Earth with variable gravity.
ааааааааааа Fig.10. Minimum cable speed via altitude for rotary
Earth with variable gravity.
5. Estimation
of a cable friction in the air.
ааааа This estimation is very
difficult because there is no experimental data for air friction of an
infinitely very thin cable (especially at hypersonic speeds). A computational
method for plates at hypersonic speed described in the book УHypersonic and High Temperature Gas
DynamicsФ by J.D. Anderson, p.287, [9] was used. The computation is made
for two cases: laminar and turbulent boundary layers.
аааа а The results of this comparison are very
different. Turbulent friction is more then laminar friction in hundreds times.
About 80% of the friction drag occurs in the troposphere (from 0 to 12 km). If
cable end is located on the mountain at 4 km altitude the maximum air friction
will be decreased by 30%.
аааа аа It is postulated that half of the cable
surface will have the laminar boundary layer because a small wind or trajectory
angle will blow away the turbulent layer and restore the laminar flow. The
blowing away of the turbulent boundary layer is studied in aviation and is used
to restore laminar flow and decrease air friction. The laminar flow decreases
the friction in hypersonic flow about by 280 times! If half of the cable
surface has a laminar layer, it means that we must decrease the air drag
calculated for full turbulent layer by a minimum of two times.
аааа аа Below, the equation from
аааааааааааааааааааааа 
ааааааааааааааааа DL = 0.5Cf.lr*V2S ;аа DT
= 0.5Cf.tr*V2S .аааааааааааааааааааааааааааааааааааааааааааааааааааа (8)
аааа а Where: T*,
Re*, r*, m* are reference (evaluated) temperature, Reynolds Number, air density,
and air viscosity respectively. M is
Max Number, аa is
sound speed, V is speed, x is length of plate (distance from the
beginning of the cable), T is flow
temperature, Tw is body
temperature, Cf.l is a
local skin friction coefficient for laminar flow, Cf,t is aа local
skin friction coefficient for turbulent flow. S is area of skin [m2] of both plate sides, it means for
the cable we must take 0.5S; D is air drag (friction) [N]. It may be
shown, that the general air drag for the cable equals Dg=0.5DT+0.5DL,
where DT is turbulent drag
and DL is laminar drag.
аааааа From equation (8) we can
derive the following equations for turbulent and laminar flows of verticalа cable
(9)
аwhere d is diameter of cable [m], r0=1.225 is air density at H=0. The
laminar drag is less then turbulent drag in 200-300 times and we neglect it.
а Engine
power and an additional cable stress can be computed by conventional equations:
ааааааааааааааааааааааааааааааааааааааааааа (10)
where P is engine power [j, w]. Factor 2
is because we have two branches cable: one moves up and other moves down. The
drag does not decrease the lift force because in different branches the drag
has opposed directions.
а
Computation are presented in figs.11-12 for small cable speed and
relative cable stress K=0¸2, in fig. 11-14 for high cable speed and the stress K=0¸10.
ааааааа Fig.11.а Air cable drag via cable speed 0 Ц 2 km/sec
for different cable diameter.
ааааааааааааааааааааааа Fig.12. Engine power via cable speed 0 Ц 2 km/sec for
different cable diameter.
ааааааааааа Fig.13. Air cable drag via cable speed 2 Ц 8 km/sec for different cable
diameter.
ааааааааааа аFig.14.
Engine power via cable speed 2 Ц 8 km/sec for different cable diameter.
а 6. People
security. If the cable is damaged, the men can rescue by a parachute
with variable area. Below the reader finds equations and computation a
possibility of saving. The parachute area is changed so that overload do not
outreach a given value (N <5g).
ааааа (11)
where H
Ц altitude [m], V Ц speed [m/s], t Ц time [sec], m Ц mass
[kg], D Ц drag [n], g =9.81 m/sec2 Ц gravity, CD
Ц drag coefficient, r -
air density [kg/m3], a Ц sound speed [m/sec], p Ц
parachute specific load [kg/m2], N Ц overload [g].
а Computations are presented in figs. 15-17.
The conventional people (tourists) can be saved from altitude up 250-300 km.
The cosmonauts can outstay overload up 8g and may be save from more altitude.
Fig.15. Speed via altitude
for variable parachute area. (See hard copy)
Fig.16. Overload via altitude
for variable parachute area.
Fig.17. Parachute load via altitude.
4. Projects
4.1. Project #1. Kinetic Tower of Height 4
km
аа Take a conventional artificial fiber widely
produced by industry with following the cable performances: admissible stress
is s =180 kg/mm2 (maximum s =600 kg/mm2, safety
coefficient n =600/180=3.33), density is g =1800 kg/m3, cable
diameter d =10 mm.
а The special stress is k=sдg= 106 N/m2а (K=k/107=0.1), admissible
cable speed is V=k0.5 =1000 m/sec., the cable cross-section
area is S=pd2/4=78.5 mm2, useful lift
force is F=2Sg(k-gH)=27.13 tons. Requested engine power
is P=16а MW (Eq.(10)), cable mass
is M=2SgH =2.78.5.10-6.1800.4000=1130
kg.
аа Assume that tower is used for tourism with
payload 20 tons. It is means 20000/75=267а
tourists may be at same time in the station. We take 200 tourists every
30 minutes i.e. 200x48=9600 people/day.а
9000 tourists/day corresponds to 9000x350=3.15 million/year.
а Assume the cost of installation is 15
millions [8], life time is 10 years, maintenance cost isа $1 million per year. The cost from an
installation for a service of a single tourist is 2.5/3.15=0.8 $/man.
а Requested fuelа G=Pt/eh = 16.106.350.24.60.60/(42.106.0.3)=38.4.106
kg. If a fuel cost is 0.25 $/kg, the annual fuel cost is $9.6 millions, or
9.6/3.15=3.05 $/person. Here t is
annual time [sec], e is fuel heat capability [J/kg], hа is engine efficiency coefficient.
аа Total production cost is 0.8+3.05=3.85
$/tourist. If trip cost is $9, the annual profit is (9-3.85).3.15=16.22
millions of US dollars. If a reader does not agree with this estimation,
calculation can be made with other data.
Project #2. Kinetic
аTake the admissible cable stress K =0.1, the cross-section area S =90 mm2 (d=10.7 mm), the
cable density g =1800 kg/m3.а Then the lift force is F=2Sg(k-gH)=7 tons. Requested engine power is P=11
MW (Eq.(10), fig.12), cable mass is M=2SgH =2. 90.10-6.1800.75000=24.3
tons, the cable speed is 1000 m/sec.
Project #3.
Multi-Stages Kinetic
аа The current industry widely produced only a
cheap artificial fiber with maximum stress s =500-620 kg/mm2 and
density g =1800 kg/m3. We take
admissible stress s
=180 kg/mm2 (safety coefficient is n=600/180=3.33), g =1800 kg/m3. Thenа k=sдg=1000000а N/m2 or K=k/107=0.1. From this cable me can design the
one-stageа kinetic tower a maximum 100 km
(payload = 0).а Assume we want design the
tower of 225 km height from the current material. We design 3- stages tower
with every stage H=75 km with useful
load capability M3,p=3
tons at a tower top.
а In this case the 3-rd (top) stage (150-225
km) must have cross-section areaа S3=M3,p/[2g(k-gH)]=33.3 mm2а (d=6.5
mm), cable mass of 3-rd stage is M3,c=2S3gH = 9 tons.
Total mass of third stage is M3=
9+3=12 tons.аа
а The 2-nd stage (75-150 km) must have
cross-section areaа S2=M3/[2g(k-gH)]=133
mm2а (d=13 mm), cable mass of 3-rd stage is M2,c=2S2gH = 36 tons.
Total mass of third + second stages is M2 =12+36=48
tons.ааааа
а The 1-st stage (0-75 km) must have cross-section
areaа S1=M2/[2g(k-gH)]=533 mm2а (d=
26 mm), cable mass of 3-rd stage is M1,c=2S2gH = 144
tons. Total mass of third + second+ firstа
stages is M0 =48 +
144=192 tons.ааааа
Project #4. Kinetic
Tower with Height 160,000 km
ааа Assume that nanotube cable is used, with K=6 (for this height K must be
more than 5, see fig.8). This means the admissible stress is s =6,000 kg/mm2 and the
cable density is g=1000
kg/m3. At present time (2000) scientific laboratories produce
nanotubes with s =20,000 kg/mm2 and
density g =0.8 Ц 1.8 kg/m3. Theory predicts s =100,000 kg/mm2.а Unfortunately, there are no widely produced
nanotubes by industry and the laboratory simples are very expensive.
аа Take a cross-section cable area of 1 mm2.а The requested speed is V=(k)0.5=(6.107)0.5=
7.75 km/sec, the mass of cable is M=2SgH = 320 tons, and the engine power (only in an
installation launch) is P=50 KW
(Eq.(10)). When altitude is reached the engine can be turned off. The
centrifugal force of Earth rotation will support the cable. Moreover, the
installation has a lift force about 1000 kg and a useful load can be connected
to cable, the engine can be turned on with small speed and a load can be
delivered to space.
Project #5. Kinetic
Tower as Space Launcher
а The suggested installation of fig.3 can be
used as space launcher. The space apparatus is lifted at high altitude by left
kinetic tower, connected to horizon line and accelerated. The requested
accelerate distance depend from admissible acceleration. For projectile it may
be 10-50 km (N=64¸320g), for cosmonauts it may be 400
km (N=8g), for tourists it may be
1100 km (N=3g).
Discussing
а The proposed method offers a new, simpler,
cheaper, more realistic method for space launch than many others. It is
impossible to demand immediately solutions of all problems. This only a start
for many researches and development of accompanied problems. The purpose is to
offer a new idea and show that it has good prospects, but it needs in further
researches.
а It is thought that this method has a big
future. It does not need expensive rockets as current methods do, or rockets
for launching into space of a counterbalance and thousands of tons of nanotubes
cable as the space elevator does. It only needs conventional cable and a
conventional engine located on a planet.а
It is very important do not kill new ideas when they are born.аа
References
1.аа Space technology & Application.
International Forum, part.1-3,
ааааа 1997.
2.а D.V., Jrа Smitherman., Space Elevators, NASA/CP-2000-210429.
3. A.A.
Bolonkin, ФHypersonic Gas-Rocket Launch System.Ф, AIAA-2002-3927, 38th
AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 7-10 July, 2002.
4. A.A. Bolonkin, Asteroids as
Propulsion Systems of Space Ships, JBIS, vol.58, #3-4, pp.98-107.
5. A.A. Bolonkin, Space Cable
Launchers, Paper #8057 at Symposium УThe next 100 yearsФ, 14-17 July 2003,
6.а
A.A. Bolonkin, Centrifugal keeper for Space Stations and Satellites,
JBIS, vol 56, pp.314-322, Sept-Oct., 2003.
7.аа
J.D. Anderson, Hypersonic and High Temperature Gas Dynamics. McCrow-Hill
Book Co.,1989.
8.
D.E.
Koell, Handbook of Cost Engineering, TCS,
9.
A.A.
Bolonkin,
Figures Captures
Fig.1. a. Offered kinetic tower: 1 Ц mobile closed loop cable, 2 Ц top roller of
the tower, 3 Ц bottom roller of the tower, 4 Ц engine, 5 Ц space station, 6 Ц
elevator, 7 Ц load cabin, 8 Ц tensile element (stabilize rope).ааааа
b. Design of top roller.
Fig.2. Multi-stage kinetic
tower.
Fig.3. a. Kinetic space
installation with horizon accelerate parts. b. 10 - accelerated missile.
Fig.4. Variable cable spool (11)
Fig.5. Admissible cable speed via
stress coefficient K= 0 Ц 1.
Fig.6. Admissible cable speed via
relative stress coefficient K= 1 Ц 10.
Fig.7 Maximum tower height via
relative cable stress.
Fig.8. Minimum cable speed via
tower height.
Fig.9. Relative cable stress via
altitude for rotary Earth with variable gravity.
Fig.10. Minimum cable speed via
altitude for rotary Earth with variable gravity.
Fig.11.а Air cable drag via cable speed 0 Ц 2 km/sec
for different cable diameter.
Fig.12. Engine power via cable
speed 0 Ц 2 km/sec for different cable diameter.
Fig.13. Air cable drag via cable
speed 2 Ц 8 km/sec for different cable diameter.
Fig.14. Engine power via
cable speed 2 Ц 8 km/sec for different cable diameter.
Fig.15. Speed via altitude
for variable parachute area.
Fig.16. Overload via
altitude for variable parachute area.
Fig.17. Parachute load via
altitude.