Determining the dimensions of a payload shroud

[Graham2001]

Is there a simple formula for determining the maximum/minimum dimensions of a payload shroud for any given payload?

 

[kuddel]

As the convex hull of that object strongly depends on your constraints (see below) there is no "simple" formula.

Imagine following (example) constraints:
- Hull should be a six-sided box, or
- Hull should be a cylinder, or
- Hull should be a cone, or
- Hull should be a sphere, or
- Hull should be a mix of them.

 

[Urwumpe]

Generally, you should look for the difference between "dynamic envelope" and "static envelope" - the actual payload fairing (static) has to be much larger than the payload, because it vibrates and deforms quite strong during ascent, the room really available for a payload is the dynamic envelope.

This empty space around the payload is also needed for circulation of air on pad and during ascent.

So, for a given payload, you could simply assume a cylindrical dynamic payload envelope.

How you minimize the radius of the envelope is up to you, generally you have a small conflict between the size of the envelope and the position of the payload CoG off the center line. A small antenna boom sticking out does little to the CoG, but means a large change to dynamic envelope, so you might want to move the payload a bit off center during launch and deployment to fit it into a given envelope.