I tell beginning rocketeers that the commercial APCP motors we fly from Cesaroni and Aerotech can vary in Thrust and Impulse for any two of the same motors, maybe by about 10%. I had heard that from someone else, or maybe read it somewhere, though I also seem to remember that the certifying authorities require the values measured to be within 20% of the claimed/published values. The message that I try to bring to beginners is why we work with safety margins, like a minimum 5:1 thrust to weight ratio.
Rocketry isn't an exact science, and there is probably more variance between flights because of wind or other factors than motor variance.
I'm curious as to what contributes to any variance, and whether it does vary much between motors. If you take five identical motors from the same manufacturer, with different dates or batches, some brand new, some 3-4 years old, even motors from the same batch, and bench test them, will there be significant variance? 10% seems like a lot, 20% even more unbelievable, though I don't have the luxury or equipment to make the tests myself.
I'm also curious as to what may cause any variance, and whether some propellant formulations are more prone to variance than others. Do slow burners vary more than fast burners, for example.
Just something to talk about after the launch....
I just spotted this thread. If you check in on www.thrustcurve.org
you will find links to lots of the official certification letters. The data in those letters includes standard deviations from the mean for all of the measured parameters, if enough motors were tested to make such a calculation meaningful.
I'm sure the statisticians on this forum can give a better explanation for why we use standard deviation rather than variance for our qualifications. In my professional career, I tended to use variance and standard error when dealing with proportions (x/n) and standard deviation when dealing with numerical quantities. Might be wrong, that's just the way I did it.
There was one experiment that we (the TMT committee) did back in May of 2017 that is relevant, and which has never been reported. I had had some discussion with manufacturers about whether the orientation of a motor during the test burn affected the actual delay element timing. So, Tripoli bought me 12 AT I161W reload kits, and I fired 4 of them pointing up, 4 pointing sideways, and 4 pointing down, the orientation under which most rocket flights take place. Setting up the load cell so that the motor hung from the cell rather than pressed on it was a challenge, but we worked it out. Bottom line, orientation has no effect on delay element timing.
However, 12 motors gives a number that can be profitably analyzed statistically.
parameter average standard deviation
burn time 2.379 sec .086 sec
Total impulse 455.69 N.s 11.0 N.s
Average Thrust 191.65 N 7.18 N
Max Thrust 271.14 N 12.56 N