To make things easy for the builder, Jim Barrowman developed a set of graphs which give forces and CP locations for the conical shoulder and boat-tail, and fins alone. The nosecone and overall calculations are derived via simple formulae.

Conclusion

So this is a simplified explanation of how to find the center of pressure, the point at which all the air pressure forces on the rocket seem to be concentrated. Provided there is one caliber distance between the CG and CP (remember, CP aft of CG), there will be sufficient moment arm to correct the rocket’s flight path if its angle of attack (α) starts to increase - the moment arm will reduce α back to zero.

Note that a rocket can be “over stable”, that is, have a CP several calibers aft of the CG. While this may seem to be good, what happens in this case is that the correcting moment is so large that it tends to weathercock into wind and its altitude performance will be reduced.

Acknowledgements:

All the credit goes to Jim Barrowman - I am simply reproducing his thoughts here. If you are interested in more details, the Centuri TIR-33 report has all the details. If you really want all the mathematical formulae, including the differential equations, look up the “Barrowman Report” from NARAM-8 in August 1966.

I did also pull data from a report by Robert Galejs at MIT on the extreme cases where one caliber is either drastically insufficent, or too much.

Lastly, a book by J.J.Jerger called “Systems Preliminary Design” in the “Principles of Guided Missile Design” series published by Van Nostrand Co. in 1960 is very helpful.

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