Number: 485 Name: MOONCABLE PROJECT
Address: J.E.D.CLINE1 Date: 880717
Approximate # of bytes: 16380
Number of Accesses: 22 Library: 3
An unusual, highly specialized space transportation concept was generated to provide a profitmaking space enterprise. The concept offers highly energy efficient transportation of payload from the Lunar surface. Includes early calculations on a constant-stress crossection cable.
By J. E. D. Cline, July 16, 1988
The Earth's physical makeup has so many incredible coincidences that are needed for life to exist upon it, and The Earth's moon seems an extention of those coincidences in the possible extention of Earthlife into space. The Lunar tides of earth's oceans upon her beaches has stirred tidal life onto land from the sea; now the fact that the Moon always has the same face turned toward the Earth, and its relatively large mass near the Earth, show promise of a major stepping-stone for the extension of Earthlife into space. And the Lunar terrain is a potential source for raw materials for building space colony structures, closed-ecology very-large-spacecraft for exploration/colonization beyond the Earth-Moon system, and for exotic construction materials for use here on Earth such as foamed-nickle-iron-steel.
Space transport systems are necessary to transfer material and energy from where it is now, over to where it will be needed. Theoretically there are alternatives to the traditional reaction engine propelled vehicles which use energy stored in propellants. The energy differentials in space are another source of transportation energy. Picture the Earth and Moon as being two adjacent depressions in a gravitational field. The Earth's depression is much deeper than that of the Moon's, so it is imaginable that material might be "siphoned" from the shallower depression into the deeper one. Could an electromechanical analogy of a siphon be constructed to move raw materials from the Lunar surface over to a somewhat deeper level in the adjacent Earth's gravitational well, using the energy differential itself to power the process?
The work involved in getting out of the Moon's gravitational well to L-1 is only about 800 watt-hours per kilogram; and going from L-1 to Earth requires each kilogram to give up about 16,000 watt-hours of energy, so there is plenty of energy to tap off for use in lifting mass up from the Moon to L-1. Of course, most of the 16.5 KwHr/Kg must be dissapated in the atmospheric entry process after the payload leaves the end of the end of the "siphon". With the end of the siphon-like electromechanical transport system extending deeper into Earth's gravitational well, surplus energy is produced which could be used to lift some of the payload up only to L-1, and leave from there with relative ease toward other parts of space near the Earth-Moon system. L-4, L-5, Mars and the asteroid belt, here we come!
[Calculation reference point: the work performed in lifting all the way out of a planet's gravitational well is the same as lifting out of a well which is one planet radius deep,with a constant accelleration the same as found on the planet's surface (reference Arthur C. Clarke's "TheExploration of Space" p.33), or
Work = G*M*m*(integral from 1 to infinity)1/(R**2) dR
As a hobby, by the end of 1971 I had worked out just such a conceptual system; then there were extra Saturn 5 Moon rockets available from the Apollo flights that were cancelled, and they could be used to emplace the "seed"electromechanical transport system. I called it the Mooncable Project. It would be a profitmaking enterprise through the sale of space-environment processed materials originating on the Moon, processed and fabricated at L-1,and delivered for sale to Earth markets. Space exploration would henceforth pay for itself!
(But the reality was that NASA was at that time starving for funds just for the Space Shuttle project to be started soon; and anyway NASA was prohibited by charter from financially supporting profit-making enterprises...so said a letter to me from NASA's Inventions and Contributions Board on June 23, 1972. With no income from my efforts, my wife soon divoriced me, and it became appearant that my advertising of the Mooncable Project had attracted the wrong kind of attention: I soon lost my house too and then my job...mere survival became my focus of attention from then on.)
The foundation analogy for this concept is that a siphon can draw water out of an aquarium without using a pump, and does it a lot easier than dipping it out by hand. Picture the Earth and Moon being two adjacent depressions in a gravitational field. The Earth's depression, or well, is much deeper than that of the Moon's, so it is imaginable that payload mass might be "siphoned" from the shallower well into the deeper one. Basically this means that energy given up by payload mass falling down Earth's gravitational well is used to perform the work of lifting up more payload mass from the Moon up toward the earth, thus forming a regenerative energy loop, self-sustaining, as is a siphon, so long as the output end is at a lower gravitational energy level than is the input end.
The work involved in getting out of the Moon's gravitational well is only about 800 watt-hours per kilogram of payload; and going from the balance point between Earth and its moon, L-1, to Earth requires each kilogram of payload to perform about 16,000 watt-hours of work during its decent to the Earth surface. So there is plenty of energy to tap off for use in lifting mass up from the Moon to L-1.
The key is to find a way to transfer the energy from the decending mass over to lift the rising mass. One way might be to transfer energy electrically through superconductors linking the two masses; the superconductors could be part of a frictionless magnetic-levitation railroad track laid on a strong tensile structure coupling the two masses. Coupling the energy between payload masses would be tractor motor-generators magnetically coupled to the maglev track, pouring energy into the track while braking the fall of mass down the earthside end of the track, and consuming that energy by lifting more payload mass up the other side of the track. The Lunar surface spatial reference for this process is created by a very long tensile structure anchored on the Lunar surface and extending up through the balance point L-1 and over into the Earth's gravitational well. At the end of this document, the original calculations are shown which show that fiberglass is strong enough for this application, if it is formed into a constant-stress crossection cable. Glass is one of the most abundant materials found on the Lunar surface, making it ideal for building this very large tensile structure.
To protect the mooncable from being accidentally severed bysmall hurtling objects, the area of the cable might best be distributed in the form of a net or pair of hollow tubes.The conductors would be distributed for the same reason and to allow continuous power during repair activities and to allow bi-directional traffic along the cable for the returning traction motor/generators and delivery of goods from Earth.
While at the null-g balance point L-1, the Lunar ores are processed into useable forms. Nicle-iron, aluminum, titanium, ceramics, and glass are foamed into large molds, casting them into glider shapes for the atmospheric re-entry portion of the journey to the Earth's surface. Pockets in those gliders hold smaller amounts of more exotic materials processed in the space environment. Here at L-1, 64,000 Km above the Lunar surface, material is also launched out toward other sites, such as L-4 & L-5 for building space colonies, for building very large spacecraft for leisurely manned exploration of the solar system, and for building Solar Power Sattellite powerplants. From L-1 a space tug would be needed to transport the material to L-5 or other sites.
The specific concept presented here is intended primarily for bringing Lunar and null-g vacuum environment commercial products to Earth at potentially very low expense on a long-term, high-mass payload, continuous operation basis. It should also be useable to supply the materials for constructing powersats (SPS), and the help supply materials for building colonies at L-4 & L-5 and large manned spacecraft for the further exploration of space. The general concept presented here is intended to arouse the readers' creative imagination toward seeking alternative paths for bringing mankind and other Earthlife into nearby extra-terrestrial space.
Addendum: at the time this concept was completed as a personal hobby activity, my only calculating tools were a slide rule and pen and paper. Believing that all I had to do was to show that an abundant material was capable for use in constructing the major portion of the mooncable, and then others with adequate computers would eagerly fill in the refinements, I set out set out to the disagreeable task of figuring out how to calculate the forces and configuration of the Mooncable. Making some outside limit observations by seeing the "big picture", I could more easily show that fiberglass was strong enough for a related but even more demanding structure. The weight of the mooncable essentially is the same on either side of thebalance L-1 point, even though the mass on either side wouldn't necessarily be the same due to the varying gravitational fields it crossed. So the structure just from one side, the Lunar side, was calculated; and it was easier to calculate from the Moon's surface out to infinity than to L-1, which I did not then want to calculate its location. My old college calculus books did not seem to have any applicable equations for integrating through varying gravitational fields., but I did find relevant equations in George Gamow's book "Gravity": the total work of lifting an object from R0 to some radius R, is the area under the curve representing the force of attraction:
Work = integral from R0 to R of (GMm)/R2) dr
= G*M*m*integral R0 to R (1/R2)dr
The integral of 1/r2 is -1/r: in general,
integral Rexp n dR = - (R exp (n+1))/(n+1), from Handbook of
Chemistry and Physics. Thus the work "W" done is
W = - (GMm)/R - (-(GMm)/R0)
W = GMm(1/R0 - 1/R)
A constant-crossection glass cable extending from the surface of the Moon and going an infinite distance away (ignoring the presence of Earth and other bodies), would experience a supporting tensile force at its far end of :
F = m*a
F = m*(1/68g)*integral from 1R to infinite R of 1/r2 dr
F = m*(1/6)*g*((1/1*R)-(1/infinite R)
F = m*(1?6)*g*(1/R)*(1/12 - 1/ infinity)
F = (1/6)*g*m/R
Now m/R is the mass of a length of one radius, and making the area equal to 1 square inch to make the results in engineering terms,
m = area * length * density
m = (1 in2)*(6.85 E7 inches)*(8.3 E-2 lbm/in3)
m = 5.68 E6 lbm
Returning to F = (1/6)*g*(m/R)/in2
F = (1/6)*g*5.68 E6 ;bm/in2
F = 9.4 E5 ;bf/in2
Since glass fiber cable has a strength of 5 E5 lbf/in2, it is only half strong enough for this configuration. It probably can be made strong enough, however, by controlling its cross-sectional area, with an optimum distribution of area with distance being that which creates a constant stress within all parts of the cable's volume.
My personal ability to manipulate the concepts of calculus confidently does not allow me to write and solve the equations required to easily derive the cable's dimensions for a given set of loads. However, I can show that a glass cable can be sufficiently strong by integration through summation of sections of cable, each section having the same maximum stress, that stress being in a cross-sectional area great enough to support the weight of that section with its loads plus the force applied at its lower end supporting the weight below it.
The characteristics of each section are derived as follows; assuming each section has a constant cross-sectional area throughout its length:
The weight of cable in each section is
Fs = A*d*R* integral i/r2 dr
where Fs = weight of this section of cable
A = cross-sectional area of this section of cable
d = density of glass = 8.3E-2 lbm/in3
R + radius length of Moon = 6.85 E7 inches
The stress at the top of each section is the greatest stress anywhere in the section, and with a safeth factor of two is2.5 E5 lbf/in2. This stress is equal to the force on the cross-section divided by the area of the cross-section:
S = (Fs + Fl)/A
where S = stress at top pf the section = 2.5 E5 lbf/in2
Fl = attached load (bottom weight + conductor etc)
A = cross-sectional area of cable section
Expanded, this equation becomes
S = ((A*d*R*integral 1/r2 dR)+Fl)/A
Solving for Area A:
A = Fl/(S-d*R*integral 1/r2 dR
The force at the secion top then is
F = A*S = (Fl*S)/(S-d*R*integral 1/r2 dR, or
Fn+1 = (Fn*S)/(S-d*R*(1/6)*g integral 1/r2 dR
The force, F, then becomes part of the attached load, Fl, of
the next cable secion above it.
F0 = force pulling upward on Moon's surface by the
F1 = force atop first section of cable, and at bottom
of second section
F2 = force atop second section of cable and at bottom
of third secion, and so forth.
S, d, and R are constants:
S= 2.5 E5 lbf/in2
d= 8.3 E-2 lbm/in3
R = 6.85 E7 in
To make an example Mooncable calculation, some values willbe somewhat arbitrarily assigned:
maximum upward pull on the Moon's surface by the cable and its loads is to be 25,000 lbf
superconducting maglev track will be equal in mass to two #12 copper wires, resulting in a mass of 2.2 E5 lbm per radius. When this becomes a hundredth of the glass cable'sweight it will be left out of the calculations for simplicity.
the maximum force due to the live load will be 1 E4 lbf This would be something less than 6 E4 lbm on the lunar surface; it is a dynamic load.
Dividing the cable up into 23 sections, summing the forces atop each section, reached a value of less than 21 in2 at infinity, a realistic number. This shows that fiberglass cable does inded have an adequate strength/mass ratio to do the job. Since the calculations were "outside approximations" the area would be less than this figure; also the attraction of the Earth on the cable, and the centrifugal orbital force on the cable would affect the full parameter calculations, while the mooncable lies in the saddle formed between two adjacent gravitational wells of the Earth and its Moon.
James Edward David Cline (GEnie J.CLINE2)
Van Nuys, CA July 16, 1988