### TAPERED SLINGS

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)

where:
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 (gaussian probability bell curve)

The sling must be made of a material having high specific strength (strength-to-mass ratio). The strongest materials available today are plastic fibers, especially Spectra. Sling cannot be used in the atmosphere, because drag overheats it. It can be used only in a vacuum. A vacuum chamber built inside a stratospheric balloon is cheap because the atmospheric pressure is low at high altitude. 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.

#### Mass of one-sided sling

Practical slings are made of non-tapered Spectra fibers bound with resin. To improve specific strength, the mass of the resin must be minimized. Resin is applied only to the tips of the fibers, so most of the space between the fibers is empty. Diameter of a tapered sling changes abruptly in areas where the fibers overlap. The need to use binding resin and the abrupt changes of the sling diameter reduce the maximum mass of cargo.

#### Practical design of a tapered sling

When a pyrotechnic device releases cargo, the sling snaps back. The shock may damage the sling. Gunsling is thus preferable to sling because cargo is released more gradually and can be accelerated to a higher velocity.

#### BIBLIOGRAPHY

"Rotary Pellet Launcher," in: Space Habitats: A Design Study, Richard D. Johnson and Charles Holbrow (eds.) NASA special Publication SP-413, 1977.

Jerome Pearson, "Asteroid Retrieval by Rotary Rocket," AIAA 80-0116.

Joseph A. Carroll, "Tether Applications in Space Transportation," Acta Astronautica, Vol. 13, No. 4, 1986, pp. 165-174.

Robert L. Forward, "The Cable Catapult," AIAA-90-2108, AIAA/ASME/SAE/ASEE 26th Joint Propulsion Conference, Orlando, Florida, 16-18 July 1990.

J. Puig-Suari, J. M. Longuski and S. G. Tragesser, "A Tether Sling for Lunar and Interplanetary Exploration," Acta Astronautica, Vol. 36, No. 6, 1995, pp. 291-295.

Jerome Pearson, "Space Transportation Using Tethers," Ad Astra Vol. 8, No. 5, September/October 1996, pp. 42-46.