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Fortunately, it is not necessary to carry around a table of statistics for rope in order to get estimates for the strength and weight of various type of chord, line, and cable. All that is required is the use of two second-order polynomial equations for each type of rope - one equation for linear density, and another for tensile strength. Though not exact, these two parabolic equations will provide estimates that are sufficient for simulations.
Because both the density of the rope and the rope’s modulus (actually its estimated tensile strength, which the material modulus is used to derive) are dependent on its cross-section area, one would expect them to follow equations of the form
l = a1 r2 andFyield = b1 r2, respectively, where r is the rope radius and a1 & b1 are some corresponding constants for linear density and tensile strength, respectively. And this is very nearly what one sees, except for a few extra factors. If we just multiply the corresponding constants by the right ratio, we can use the diameter instead of the radius.
l = a1 d2 + a2 d + a3
F = b1 d2 +b2 d + b3
These two formulas won’t exactly correspond to all data for any given rope. There are splices, strain effects, etc to account for. However, they will be quite close, as these graphs of actual data for T-900 and Spectra ropes indicate.
The formulas given are best curve fits to the data, estimated using MS Excel. As you can see, these polynomial curves correspond to the actual data to within +/- 10% at all points. Similar estimates can be made for polyester, nylon, and other types of rope.
This makes things very simple for computer simulation of varying tether diameters, because no sorting through data tables is required. If you know the rope diameter, you have the strength and weight as well. Also, if you know the strength or weight required, you can compute the rope diameter required using the quadratic equation:
x = ( -c2 +/- SQRT( c22 – 4 c1 c3 ) ) / ( 2 c3 )