Elaborating further.
When the motor is static fired, let's assume at sea level, the thrust goes to
zero when the combination of the exhaust velocity term and the pressure
differential term combine to have the thrust go to zero.
As noted, with the simple variation of thrust with altitude model described
previously, when the next to last thrust is 0.01 lbs, the pressure difference
between the atmospheric pressure at altitude and sea level atmospheric pressure
is applied to the nozzle exit area, and that thrust is added at that altitude.
Then the assumption is made that at zero thrust (zero sea level thrust from the
thrust curve), the motor has burned out, and the thrust is zero.
With a more sophisticated model, you would back out the chamber pressure time
history from the sea level thrust curve, and use the chamber pressure time
history to model the thrust at altitude. I've built these types of models in
the past, including flow separation in the nozzle. The rule I've always used
is that when the nozzle unchokes, assuming that the nozzle unchokes when the
chamber pressure falls below twice the atmospheric pressure, then the thrust is
over, the motor is burned out. There is still a little thrust left (basically
a subsonic, non-choked venting of a pressure vessel), but I leave that last
little bit of thrust out.
This residual thrust effect is not included in the simplified model described
previously that is used in the RASAero II software. That is why you get that
steep drop-off in the thrust curve at altitude. Why use this simplified
approach in the RASAero II software? The alternative would be that the RASAero
II Users would have to enter the chamber pressure time history. :)
(Or RASAero II could back out the chamber pressure time history from the motor
thrust curve, but that would require the User to have to enter additional
details on the motor nozzle geometry. As implemented in RASAero II, all the
User has to enter is the nozzle exit diameter for the nozzle exit area.
Actually for high power rocket motors, it takes a little digging just to get
the nozzle exit diameter.)
Charles E. (Chuck) RogersRogers Aeroscience
-----Original Message-----
From: crogers168 <dmarc-noreply@xxxxxxxxxxxxx>
To: mark.spiegl@xxxxxxxxx <mark.spiegl@xxxxxxxxx>; arocket@xxxxxxxxxxxxx
<arocket@xxxxxxxxxxxxx>
Sent: Mon, Jan 4, 2021 8:23 am
Subject: [AR] Re: Calculating CDs (was Re: In praise of Open Rocket)
Mark:
I'd previously posted an example, which is attached, which was a long burn
Aerotech N1048 motor (16 sec burn time) rocket which burned out at 20K ft. The
data from the thrustcurve.org web site (TC on the plot, the original rasp.eng
motor data used by RASAero II) is shown, and the thrust curve from the RASAero
II trajectory output (RA on the plot) which includes variation of thrust with
altitude is shown. (Thrust on the plot is in lbs.)
As was shown on the thrust curve plot (which is attached), for the last thrust
data point there was a straight line drop to zero thrust. At the last point on
the sea level thrust curve, lets say 0.01 lbs at sea level, the pressure
difference at altitude is applied to the nozzle exit area and you get the last
thrust value, then zero thrust.
What happens with more detailed modeling is that as the chamber pressure tails
off the motor nozzle will unchoke at different chamber pressures because of the
different atmospheric pressures. The motor nozzle will stay choked longer at
higher altitude (the nozzle is choked [Mach 1 at the throat] at chamber
pressures greater than twice atmospheric pressure), so with more detailed
modeling you don't get an abrupt shutdown, but a longer tail-off.
Again, taking the thrust curve data from the thrust stand, correcting it for
sea level, and then using the pressure difference between sea level and
atmospheric pressure as the rocket ascends is a good simple model.
Note that this simplified model works only if it is assumed that the chamber
pressure time history stays the same. The chamber pressure can vary, but it
has to always vary the same with time with the same chamber pressure/time data
points.
<< Is there ever a case where site altitude 0 yields a higher max altitude
than site altitude 1000? (assume everything else is equal) >>
See my previous post on the launch site temperature inputs. If the launch site
altitude of 0 ft is in a very hot area, and the launch site altitude of 1,000
ft is in a very cold area, maybe. RASAero II will model this effect.
Charles E. (Chuck) RogersRogers Aeroscience
-----Original Message-----
From: mark.spiegl@xxxxxxxxx
To: arocket@xxxxxxxxxxxxx
Sent: Sun, Jan 3, 2021 6:46 pm
Subject: [AR] Re: Calculating CDs (was Re: In praise of Open Rocket)
#yiv4430420265 -- filtered {}#yiv4430420265 filtered {}#yiv4430420265
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{}#yiv4430420265 div.yiv4430420265WordSection1 {}#yiv4430420265 >> For the
Coast aero database (Step 5) you set the nozzle exit diameter to zero.
(Power-Off.) A question about nozzle diameter… Hypothetically assume a nozzle
attitude correction of +1000 lbf. If the motor outputs 0.001 lbf measured on
the test stand at msl, is the total thrust really 1000.001 lbf? This effect
leads to a strange jump discontinuity at the end of boost. (Possibly related to
the site altitude bug) Is there ever a case where site altitude 0 yields a
higher max altitude than site altitude 1000? (assume everything else is equal)
--MCS