Characteristic velocity generally won't change much with chamber pressure. It's
the nozzle's contribution that's affected by various pressures (both in & out)
Troy
Sent from my iPad
On 12 Apr 2016, at 10:40 AM, Gerald Taylor <geraldtaylor3@xxxxxxxxxxxxx>
wrote:
I think that would mostly be a poor assumption. Delivered ISP is not a
constant as it depends on internal motor pressure (not a constant) and
atmospheric pressure (varies substantially with altitude).
As a first cut using inexpensive tools, which might be good enough, one might
try:
Using a tool such as Burn Sim to produce a thrust curve and duration matching
expected motor performance, with propellant density set correctly, and
juggling a and n to achieve a curve matching observation. Use a tool such as
one of the PEP tools to determine how characteristic velocity will vary with
respect to pressure for the propellant mix (assuming you know the mix). Go
back to Burn Sim and alter a and n slightly as needed to increase or decrease
the burn rate a bit. Determine the new pressures, feed in the PEP info for
each pressure range and re-run the burnsim curves.
Save out this family of thrust curves.
Generate a new family of thrust curves based off small variances of Kn,
generated in a similar fashion except Kn is varied rather than a and n.
Save those too.
One could get fancy and do a matrix. One can even add a third dimension for
variations in density.
Now one can take that family of thrust curves and feed them into a tool such
as RasAero to determine rocket performance sensitivity to these sorts of
motor inconsistencies.
Of course, one could alternatively work to produce a more consistent motor.
Note that BurnSim is simplistic and not without errors. Generally one does
not use geometries where the tool goes off into la-la land, and generally one
should avoid erosive burning if one is working on a performance motor of some
sort (IMHO) as one can generally get better performance without being erosive
through a change of design. One can compensate for some of its other issues
such as assuming constant pressure along the length of the motor which is
false.
For more accurate work one would have to have better characterization than
just a and n. But with many propellant formulas a and n are sufficient for
pretty good work. I was usually achieving altitude matching sims with errors
in the <2% range, motors in the M through O range. That's with my motors
though, not commercial ones. Mine tended to match predicted burn duration to
0.1 second, and burn curve matched design. That is, they matched my specs for
each launch. Each was purpose-designed, tending to deliver about 10% greater
delivered ISP (readily observed through altitude) compared to equivalent
sized commercial.
Back on subject - during burn Kn also changes through enlargement of the
nozzle throat. Burn rate is also affected by acceleration. Flight through the
atmosphere involves wind relative to ground vector changes. There are lots of
variables.
Gerald
-----Original Message-----
From: Ian Woollard
Sent: Apr 11, 2016 2:36 PM
To: arocket@xxxxxxxxxxxxx
Subject: [AR] Re: Probalistic model of solid rocket motor thrust curve?
I think a reasonably good model would be simply assuming that motor chemistry
is well mixed, and thus the Isp is fixed at launch, so it takes a gaussian
value centered on the manufacturers typical value with their standard
deviation, and wouldn't change over the flight (with the exception of nozzle
backpressure).
On 9 April 2016 at 18:18, Aaron Baker <bitmapverse@xxxxxxxxx> wrote:
I'm interested in using state-space tracking techniques to try to improve
position tracking for a rocket, but I need a process model for the motor.
I have the manufacturer thrust curve and a measure of variability, but
modeling the variability as noise doesn't really make sense because thrust
from moment to moment shouldn't be statistically independent of the previous
moment, it should be roughly the same and change only slowly.
What kind of model might be appropriate?
Aaron
--
-Ian Woollard
Sent from my Turing machine
