Did I hear a call for the 'Pie-eyed piper'?
Matthias is as observant, as he is conversant, with the language of the sling.....
Having reached harmony with nature's mathematical language early on in life, I have never had much desire to learn man's method of 'reverse engineering'. To my benefit, I have long ago acquiesced to the innate calculative ability of our inner programming....seeking not to understand it's process...but to instead profit from a harmonious blend of blind trust and shared intuition. (So much easier and enjoyable....to my limited way of thinking)
Matthias is correct in his observation that a quantitative analysis of spin ratio to forward velocity is problematic....that is, assuming one is working toward an exercise which, to me, would simply be overkill for the hobby of slinging. (of course, to each his own)
Often man will succumb to a process....learning to prefer it's comfortable confines over the more relevant solution/conclusion.
Just as in nature, creatures of all kinds will perform amazing and seeming contrary actions to what man believes possible......taking for granted what man can only dream to one day fully extrapolate, we humans do the same on a daily basis.
Sorry, momentarily forgot which forum I was in.....
Suffice it to say that good old hands on trial and error can quickly reveal (by simple observation) the minimum spin that need be imparted to an aerodynamically neutral projectile to maintain stability. (This can even be gauged generally by sound (or lack thereof) with some projectile shapes.)
Any more is, technically, wasted energy.
The reason that darts outperform obloid ammo is simply that they can be released with a bare minimum of traded energy while maintaining their flight stability aerodynamically.
If one chooses to stay with obloid ammo for their distance efforts.....it is advantageous to trade as little forward momentum for gyroscopic stability as is allowable.
Of course, this does not begin to cover the anomalous (though repeatable) results one can achieve with certain ammo shapes coupled with robust spin rates which actually serve to enhance velocity and markedly reduce atmospheric friction.
Such systems rely upon biaxial spin characteristics and 'virtual vortex' effects to achieve these amazing results.
(Larry Bray may be able to provide attestation to such principle)
For those who wish to properly investigate this and many other natural phenomena......I cannot say enough about Callum Coates' book: Living energies, written about the life and research of Victor Schauberger, the Austrian naturalist.
Or google Frank Germano.
P.S. Matthias, you should know by now to avoid using any trigger phrases such as ...."pipe up" "pipe in", in my direction.....(you have certain 'empathic' abilities, it seems)
(lol)
Now if you don't mind....(and have managed to put up with my 'meanderings' down to this point)...I do believe it is high time for me to...
"pipe down" as it were.
8)