Required mass of a cord used to turn an object
Author: JetAloneExecutions: 200
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| Proper velocity | km/sLimit terminal velocity of untapered cord |
| Mass ratio | Ratio of the mass of the string to the mass of the object |
When rotating a string without a taper, the limiting terminal velocity is determined by sqrt(2 * strength / density / safety factor).
When rotating an object with a string attached, a cross-sectional area function represented by a Gaussian function is effective for minimizing the mass of the string; in this case, the minimum mass ratio between the object and the string is given by sqrt(pi)*(terminal velocity/natural velocity)*exp((terminal velocity/natural velocity)^2)*erf(terminal velocity/natural velocity).
If only a single string extends from the center of rotation, the mass ratio is half this value; if there are n strings, it becomes n/2.
The default values are Zylon’s material properties
References:
Hans Moravec, “A Non-Synchronous Orbital Skyhook,” Journal of the Astronautical Sciences, Vol. 25, No. 4, pp. 307–322, 1977
AIAA-99-4802 Hypersonic Airplane Space Tether Orbital Launch (HASTOL) System: Interim Study Results, p. 4
Free Space Skyhooks, Hans Moravec, November 1978
https://frc.ri.cmu.edu/~hpm/project.archive/1976.skyhook/papers/free.txt
When rotating an object with a string attached, a cross-sectional area function represented by a Gaussian function is effective for minimizing the mass of the string; in this case, the minimum mass ratio between the object and the string is given by sqrt(pi)*(terminal velocity/natural velocity)*exp((terminal velocity/natural velocity)^2)*erf(terminal velocity/natural velocity).
If only a single string extends from the center of rotation, the mass ratio is half this value; if there are n strings, it becomes n/2.
The default values are Zylon’s material properties
References:
Hans Moravec, “A Non-Synchronous Orbital Skyhook,” Journal of the Astronautical Sciences, Vol. 25, No. 4, pp. 307–322, 1977
AIAA-99-4802 Hypersonic Airplane Space Tether Orbital Launch (HASTOL) System: Interim Study Results, p. 4
Free Space Skyhooks, Hans Moravec, November 1978
https://frc.ri.cmu.edu/~hpm/project.archive/1976.skyhook/papers/free.txt
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when rotating a string without a taper, and the minimum mass ratio between the object and the string
when rotating an object with a tapered string attached.