I don't know what the "best" unit of stability would be for all cases, or if one even exists, but it seems like any system that reduces stability measurement to a simple ratio of CP-CG over either length or diameter, while ignoring the other measurement, is probably over-simplifying things and won't work well for unusually long, short, skinny or fat rockets. Most likely a "universal" unit for stability would have to consider BOTH length and diameter (or "girth", if you prefer :eyeroll
, not just one or the other.
I wasn't clear but I'm saying diameter is a subtraction, not an addition -- although probably not true for all cases. A wider rocket is more sensitive to imperfections of build so maybe in some cases there really is a need for increased margin, but more often not. Say you have 2 rockets that are both 30" long and have a 3" stability margin. I haven't said anything about diameter yet. If one is 1.5", making the margin 2 calibers, and the other is 3" diameter, so only 1 cal., is the latter less stable? It might or might not be but I'd definitely feel better calling the stability margins the same (3" or 1/10 of L) and saying the needed margin is different than saying they actually have different margins (2 vs. 1). But, whatever works. I'm not saying using an equation for needed stability margin that comes up with a negative number for saucers is actually "correct" either, it would be a correction for calculated vs. actual CP, but if everyone did that long enough I bet some would argue until they're blue in the face that saucers are fine with a negative stability margin. As it is, the idea of calibers of stability has been around so long that some seem to confuse the words with the actual things.
There some rockets that need special explanation of the aerodynamics to explain why they are stable, but typical short and stubby rockets just don't seem to be among them, to me. They still need a positive stability margin, just small in caliber units, because they're large caliber! In many cases, the margin as a proportion of length
, is as large or larger than long and skinny rockets. If the CP calculations were just wrong in ignoring a large base drag, these rockets could fly with a negative margin (in that calculation) and that they definitely can't do. One thing is short rockets usually have their CG and CP closer to the center of their length, while some long rockets have the CP just forward of the fins. As the angle of attack increases, the CP moves towards the center of the airframe tube, because straight tube is insignificant at zero and low AoA. With OR, check it with Tools>Component Analysis. For a Big Daddy at .276 cal. stability, worst case was -.086 cal. at 55 degrees. There are some long rockets you can't make it much past 10 degrees before the large margin goes negative.