Michael,The basics: if you have position (altitude) with respect to time, then the change in position over time is the velocity. The change in velocity with respect to time is acceleration. If you have the mass (at the same moment in time that you've calculated the acceleration for, then rearrange Mr. Newton's formula (F=ma) to get the net force. Any decent altimeter will give you altitude (to some precision/accuracy) vs. elapsed time (to some precision/accuracy). After that is when the gremlins get you....
Altitude: change in altitude may not represent a true change in position (that is, distance) because the rocket may be headed off at an angle. You will have to either assume a certain angle of flight and calculate the true distance, or assume that it flew vertically (in which case the change in altitude is the change in distance).
Mass: it isn't constant, so you'll have to calculate it based on the grain geometry and your static tests, etc. I don't know if any of Richard's spreadsheets list mass burned vs. time, but if they do, that would give you a good start, assuming your manufacturing is under tight enough control.
OK, so you've calculated F--but hang on, because that's *net* F. That is, thrust minus the force of gravity and minus the force of drag. The force due to gravity is just g*mass and we've already dealt with mass. However, the force due to drag is more problematic. As you know, it consists of the Cd of the rocket (which will vary with velocity), the angle of attack, atmospheric conditions (launch pad altitude, altitude of the rocket at any instant in time, temperature, barometric pressure at launch, etc.) and, of course, the square of the velocity.
Your question then becomes, will you know all that stuff with sufficient accuracy to give you a meaningful result? And will your altitude be accurate/precise enough to allow you to do all the math on it to get the acceleration with any kind of accuracy/precision?
From what I recall, the Featherweight altimeters are about the most accurate/precise out there (although I would also check with the altus metrum guys because I've read that their stuff is pretty darned good, too). Both will record fast enough to get you data with short enough time intervals. I know Adrian Adamson (Featherweight) has done a lot of study on this--you might check the Featherweight forum and also over on TRF.
I should also mention that the Featherweight altimeters (or at least the Raven), and possibly the altus metrum products, will also provide acceleration data so that you don't have to do the double differentiation to calculate acceleration from altitude. I haven't looked into how accurate/precise it is, however. But you still have to know the atmospheric info and the aerodynamics of your rocket--and those two are usually the killers.
A lot of people have looked into doing this and, as I recall, very few have managed to come up with anything that was very persuasive (and they were using commercial motors), although I am certainly no expert on this stuff. It's pretty easy (especially if you can program) to simulate a few data points and do the calcs to see what you come up with. Munge the altitude data a bit to simulate inaccuracies and see how much it throws off your answer. Vary the Cd by .1, .2, .3 or so and see what happens. Etc etc. You'll soon get a feel for just how hard this is.
--SteveOn 02/15/2015 10:17 AM, Michael Monteith (Redacted sender michael_r_monteith@xxxxxxxxx for DMARC) wrote:
I hope this isn't off topic as it has to do with verifying motor performance really. I was thinking on what I would need to verify rocket motor performance during a flight test. So I was thinking of what would be the requirements to gather the data in flight. There is so many altimeters and ranges of price. Some show they output thrust time. But not sure exactly if it's what I'm thinking it is or I'd be better off getting one cheaper and calculating it. http://data.rocketsetc.com/altimeter_data.html So to my question. What data is required and how fast? I see all the thrust curves for static testing but trying to figure out how you backtrack and figure from a flight test what the thrust curve is for comparison? This is what I want to arrive at, a thrust curve for flight test vs thrust curve on static testing. My initial guess is at least having time and altitude and having rocket mass etc. From there you can calculate acceleration etc and arrive at thrust. I don't want to think of the formula right now for this. It might be in my pile of books but those are boxed up in Missouri and won't see them for about a month now. But don't recall anything like that. I figured I might as well buy the right recording altimeter to begin with. I don't mind spending the money but only if I do it preferably once and right. Specifically the right data, accurate, and the right speed. I think the more time I spent on it the more confused I was with all the options on them all. At least until I know the bare minimum. I don't know if anyone has gone down this road or not. I saw Richard made mention on one of his pages that it was something for a future page. If we need to take it offline feel free to email me. Michael Monteith
