- #1

charlesrwest

- 2

- 0

I tried to work it out for a constant with cable with no payload (result below, I think it's right?). However, a constant stress design with variable cable width would definitely do better. That said, the math for that is beyond me. If I may ask, would anyone care to take a crack at it? It's probably similar to the equations for space elevator cable thickness (https://en.wikipedia.org/wiki/Space_elevator#Cable_section), but I'm not sure how to adapt it.

Thanks!

Code:

```
Dyneema specific strength = 3711000 N*m/kg
Carbon Epoxy composite: 785 N*m/kg
Payload mass = Pa
Cable specific strength = Css
Centripetal Acceleration = Ca = V^2/r
Cable Linear Mass = CLM = F/Css
Cable Linear Speed = Cls = Cev*r/Cl
Cable Length = Cl
Cable Edge Velocity = Cev
Force at cable center with just constant thickness cable:
F = (integral over r from 0 to Cl (CLM*V^2/r))
F = (integral over r from 0 to Cl (CLM*Cls^2/r))
F = (integral over r from 0 to Cl ((F/Css)*(Cev*r/Cl)^2/r))
F = (integral over r from 0 to Cl ((F/Css)*(Cev*r/Cl)^2/r))
F = (F/Css)*(integral over r from 0 to Cl ((Cev*r/Cl)^2/r))
F = (F/Css)*(integral over r from 0 to Cl ((Cev^2*r^2/Cl^2)/r))
F = (F/Css)*Cev^2*(integral over r from 0 to Cl ((r^2)/r))/Cl^2
F = (F/Css)*Cev^2*(integral over r from 0 to Cl (r))/Cl^2
F = (F/Css)*Cev^2*(Cl^2/2)/Cl^2
F = (F/Css)*Cev^2*(1/2)
1 = (1/Css)*Cev^2*(1/2)
1 = (1/Css)*Cev^2*(1/2)
2*Css = Cev^2
Cev^2 = 2*Css
Cev = sqrt(2*Css)
With Dyneema:
Cev = sqrt(2*3711000)
Cev = 2724 m/s
With Carbon Composite:
Cev = sqrt(2*785)
Cev = 396.2 m/s
```