# basis for designing fins of a space launch vehicle

What was the basis for deciding the size, shape, location and number of fins for the Saturn V (or any other rocket for that matter)? Does it have any calculations or were they designed based on empirical data / previous experience?

• If there was a bonified method I don't think the Saturn V would follow it- at least not strictly as it had thrust vectoring engines and I think the fins were only some means of insurance. Jun 15 at 7:07
• I'm not sure about its design/result has effect on the Saturn V, but since you are also asking about rockets in general, this thesis by James Barrowman from 1967 might be helpful. Fin design for specific systems such as this one has several great resources. Jun 15 at 12:37
• Making a guess, as not an aerodynamicist. But, I would conjecture that the fins provide a resisting torque to rolling about the vehicle central axis. This gives the rcs engines a torque creating resisting force to adjust against. I think this makes controlling roll easier than without any resistance as less precise, lower response roll control might be needed. Without a resistive torque the rcs would have a more difficult time in adjusting roll. I'd think the sizing of the fins was based on the amount ot torque resistance needed. Jun 15 at 12:41
• @tckosvic: Your response seems to address the question "WHY fins are required", rather than "HOW" they are designed. Nevertheless, I appreciate your reply. It was helpful in the broader context. Jun 16 at 5:44

## Center of Pressure

The most basic consideration for rocket fins is the center of pressure. This is basically the point along the rocket where the surface area of the rocket above and below are equal. For stable flight, you want the center of pressure to be well below the center of gravity.

An arrow is a good illustration: the metal/stone tip is heavy, bringing the center of gravity forward, and the fletchings add surface area to the other end of the arrow, pulling the center of pressure towards the rear. Since the center of gravity is well forward of the center of pressure, the arrow is stable and will fly true.

Thus the basic purpose of fins is to add surface area near the bottom of the rocket. This drives the size and location considerations.

## Drag and Flow

Engineers will seek to minimize drag for efficiency sake (shape). They must also account for any maneuvers that might increase airflow along one side of the rocket, while lowering it on the other side (number) - the effective center of pressure changes if there is reduced air flow against the fin!

This is all complicated by the fact that fins can be used as control surfaces. I don't know how this influences the considerations exactly, but I'm confident that it does.

All of these design considerations are trade offs: the increasing performance in one metric impacts other metrics, often negatively. The specific end result is a balancing act between all the different needs of the rocket in question.

• pretty good summary! One other aspect I'd bring into the discussion is the airspeed(s) at which the fins need to be effective. Jun 15 at 20:54
• @codeMonkey: I am trying to figure out the difference between CG & CP. I believe that CG is a point in the object through which the gravitational force (on the entire object) can be assumed to act (such as to create a moment about some other point). Pressure applied on a certain area is a also a force, acting through the the CG of that area, which in turn is already considered (amongst other) while deciding the CG of the object. So, It would be helpful if you can please provide further details (like explanatory links etc.), to understand your reply. Thanks. Jun 16 at 5:56
• @Niranjan Page 3 of this report which refers to several pieces of literature mentions: (1) The Cg is a geometric property defined as by a single point that is the average location of the weight of an object, If a rocket was placed on a thin rod the Cg would be the location of the rocket where it balances on the rod. and (2) The Cp is a single point where aerodynamic forces, caused by pressure variations around the surface of the rocket, act through. Jun 16 at 7:01
• It also mentions on page 4, a rule of thumb starting point as: The Cp should atleast be 1 caliber behind the Cg. Jun 16 at 7:03
• @Niranjan - you can think of the Cp as the "Cg of the shadow" of the rocket. Take an arrow: the actual Cg is near the head, since the arrowhead is dense. But if you traced the arrow onto a piece of cardboard and cut out the result, the Cg of the cutout would be much closer to the back. The low-density fletchings at the back of the arrow demand a lot more cardboard than the high-density arrowhead. Cp describes force that the fluid (air) places on the rocket, which is driven by surface area of the rocket, so differences in density are important to understand the difference between Cg and Cp. Jun 21 at 16:23