One-sided sling Two-sided sling
One-sided sling Two-sided sling

If the sling is shorter than about 10 km, gravity can be ignored and the mass of one-sided sling is:

X = P0.5 Y exp(Y2) erf(Y)

X is the mass of the one-sided sling divided by the projectile mass
P is pi (3.141592...)
Y = V/U
V is the velocity of the sling tip
U is characteristic velocity = (2S)0.5
S is the specific strength of the sling material = (tensile strength)/(density)
erf is the error function (area under the gaussian probability bell curve)

The sling must be made of a material having high specific strength (strength-to-mass ratio). It cannot be used in the atmosphere because drag overheats it. It can be used only in a vacuum, for example in outer space or in a vacuum chamber built inside a stratospheric balloon. (Scientific balloons have attained an altitude of 52 kilometers.) The strongest materials available today are plastic fibers, especially PBO. Although plastics are damaged by radiation and temperature extremes of the outer space, they can be shielded by a pile of dust or rubble. A sling located in a Moon cave is much more economical than guns. For example, a coilgun erected on the Moon (sometimes called mass driver) is about 1000 times heavier and more expensive than a plastic sling. (The Moon's escape velocity is only 2.4 km/s, and the orbital velocity just above the Moon's surface is only 1.7 km/s.) Perhaps the best material for an orbital sling is a rope made of strong (6.5GPa) carbon fibers coated with a thin layer of aluminum and fused together in a hot press.

Mass of one-sided 

Mass of one-sided sling


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