Rocket Stability
So taking the idealized fin shape at left, the normal force can be calculated as:
where:
n = number of fins (3, 4 or 6 only)
s = fin semi-span
d = body diameter at base of nosecone
a = root length
b = tip length
= mid chord line length
The equation above works only for 3, 4 or 6 fins. Any other number requires a different calculation. For multi-stage rockets, “n” refers to the number of fins per stage; note that each stage must be analyzed separately.
There is one more thing we must factor in. Because the airflow over the fins is influenced to a degree by the airflow over the body section to which the fins are attached, we must account for this. Jim Barrowman used the notion of an “interference factor”, Kfb, which for 3 or 4 fins is:
Kfb = 1 + R/(s+R)
where s = fin semi-span and R = radius of the body between the fins. Note that the subscript “fb” means “fins in the presence of the body”. The case with 6 fins is unusual - the interference between the fins themselves cancel out half of the effect of being attached to the body. In this case:
Kfb = 1 + 0.5 x R/(s+R)