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.
--Steve
On 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
