Yup, and that data sheet did in fact describe a 38Ns E-class motor with an
average thrust of just over 6N and a burn time of just over 6 seconds - an
Anyway, doesn't really matter an awful lot! As Darren said, check out the
thrust curve of a Rocket Services 'F36' - I think that *is* an E6! (Just
with a massive initial spike).
While from a 'purist' point of view the average thrust number should be
accurate, for motors with high initial thrust an 'adjusted' or 'advisory'
designation has its merits.
I believe that means the "new" version uses a different propellant than
the "old" version.
I also flew pre-production E6's known then as E5's. I flew it in an
approx 2.5" x 24" rocket which with very careful pad set-up went almost
perfectly vertical, but the flight was slower than any I have seen since.
Gary was there. It was his prototype.
The rocket was later the first rocket flown at LDRS-1.
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: email@example.com>
That the thrust curve that maximizes altitude seeks to satisfy:
V(t)=Terminal Velocity (C,A,rho(t))
i.e. the most efficient vertical velocity is the same as terminal
velocity at a given altitude for a given rocket.
Close enough. The optimal thrust for most MR and HPR is bang-sigular
arc-coast. In practical terms it is max trust (ideally an impulse) to
get you up to speed, followed by approximately T=2W until burn out,
followed by coast to apogee.
Now then, assuming a case where your optimal trust time exceeds 15
seconds, how does the optimal thrust change when a 15 second burn time
limit is imposed?
Yeah, T=2W gives you terminal velocity, only in the positive direction.
As you start getting into the higher atmosphere, that ratio starts to
increase, and in a vaccuum it'd be infinite.
Given the same amount of fuel as the thrust curve that exceeded 15
seconds? I imagine it would be boost, sustain at terminal velocity
(i.e. T=2W), then at 14.9 seconds, an impulse of all remaining fuel.
Well, yes T=-2W would not get you much positive altitude. "Terminal
velocity" is a poor description in this case. I usually refer to the
optimal cruise (or singular arc) speed to distinguish it from the
initial optimal acceleration phase, and the final coasting phase.
That is true, but even large HPR flights seldom exceed 20K Ft. T=2W
is quite practical for typical MR, HPR flights. There are two
interesting consequences of thrusting to stay on the optimal singular
arc. On the one hand, as mass burns off, optimal thrust tends to
decrease, while on the other hand as density decreases with altitude,
trust tends to increase to accelerate the rocket and maintain "optimal
drag' (or even "terminal velocity"). For some things like MR altitude
with an AT E6 sustainer, constant thrust can be just about right.
Yes, and assume constant ISP for all thrusting, just to keep it
simple. The 15 seconds is cumulative for all thrust phases, but
impulse thrusting is OK. Actually I'd like to suggest an example of a
62.5 gram, 200 sec ISP, propellant MR motor with less than 80N average
thrust, but of course you also need a rocket mass and Cd such at that
the optimal thrust is well over 15 seconds, making the 15 second limit
active in the thrust time lime limited optimization problem.
OK. I had a more impractical solution in mind. I should probably
just solve this problem, but it is more fun to pose it as an open
problem, especially when you said that you had a simulation program
set up to optimize thrust.
I find your maximum thrust limitation odd, and interesting.
A related problem is to assume a high thrust motor that is not
throttleable, but that can be turned on and off at will. E.g. an 80N
motor that would accelerate the model to speed and then be turned on
and off in some duty cycle to maintain the desired speed.
BTW, which Dave Harper are you? Is you dad's name Roy? Where do you
If I didn't limit thrust, the rocket would experience over 1000g's
(10,000+ lbs of thrust) during the first loop iteration. The
optimizing routine would try to get the rocket to it's most efficient
vertical speed in 1 step. Secondly, if it did accelerate to it's most
efficient velocity in one step, it would leave drag out of the picture
during that first step, since drag is determined by the initial
velocity at the begining of the loop. That's why I put the limitation
That's certainly possible... similar to pulse detonation engines...
Sorry, but no, my dad's name is not Roy. And I'm in Georgia, but
I'm amazed that you apparently came to such a profound conclusion
using such a crude tool. You could probably do better using F-M, but I
recommend that you use a RK-4/5 ODE solver.
No PDE's. Think in terms of MR/HPR solid rocket motors, except that
we are going theoretical. It is an exercise to get you think about
how the form of optimal thrust might change with different
You can't really design a motor to deliver optimum thrust, but there
are some things you can do to get closer to optimum thrust. You can't
really have thrust through a fixed nozzle at high constant ISP at both
the high boost thrust and low sustain thrust. Of course in practice
you get the initial boost from a stage, or strap ons. You could get
constant ISP at constant chamber pressure and thrust, but even if you
could essentially turn the thrust on and off, you would have transient
loses. The 15 second burn time limit is artificial, but it comes from
a real regulatory constraint.
You might be able to throttle a hybrid over a suitable range, but that
is still a heavy clunky lower performance motor.
Realistically, you can optimize the initial propellant grain geometry
to get a thrust profile that is better than nothing.
I'm amazed you can make that statement since you haven't seen the tool,
nor have I haven't pasted any of the code. :-) Using ODE's (or going
the PDE approach) have limitations via assumptions and simplifications
you have to make. Using a finite interval method, it's very easy to
adjust for atmospheric density, drag coefficent (as a function of
Mach), propellant weight reduction, decreased gravity (for space
I should not have not have called your tool crude as I have not seen
it. It may be quite effective, but your brief description of it did
not convey its adequacy or effectiveness. I have to admit that I
don't know exactly what you mean by your finite interval method.
Nevertheless, I stand by my recommendation to sport rocketeers to use
fourth order Runge-Kutta-Fehlbeg numerical integration with fifth
order step size control to numerically integrate Ordinary Differential
Equations, thereby solving sport rocket trajectory problems (an
Initial Value Problem). It is easy to incorporated all the model
featured that you mentioned and more directly into the differential
equations without "adjustment".
Once again, even HPR models are not capable of space shots. You can
model the gravity field if you want, but constant gravity suffices for
sport rocket work, and even much of professional rocket work.
My "crude" comment was not intended as a put down. Rather, I am more
impressed by the skillful use of simple tools and the drawing of
insightful conclusions thereof, than by unskilled use of more
sophisticated tools. Again, I have not seen your tool, so it may not
On 5/7/05 3:00 PM, in article
Assuming you don't care about practical considerations, and are only doing
1-dimensional analysis - slow, so you don't waste any more energy on drag
In practice it doesn't quite work the same way, since you have to handle
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