Most efficient vertical flight speed?

On Thu, 12 May 2005 21:42:00 GMT, "Niall Oswald"


Sounds like Rocket Services "F36" territory here Niall ;)
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Darren J Longhorn http://www.geocities.com/darrenlonghorn /
NSRG #005 http://www.northstarrocketry.org.uk /
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Fred Shecter posted a link to the NAR cert sheet on the motor.
Jerry
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Jerry Irvine, Box 1242, Claremont, California 91711 USA
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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 accurate designation.
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.
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Niall Oswald
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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
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Jerry Irvine, Box 1242, Claremont, California 91711 USA
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Jerry Irvine wrote:

I view motor designations as having, in practice, a somewhat arbitrary element to them - rather like firearm cartridge "caliber" designations.
-dave w
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Niall Oswald wrote:

That's 18

question has

Niall, Please excuse Jerry. He was mearly taking liberties with the truth as instructed by his co-worker in his company of less than two individuals.
steve
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wrote:

Hint: this is a classic problem problem known as the Goddard problem.
What did you find surprising?
Alan
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Alan Jones wrote:

profile
of
(in
this
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.
Dave
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wrote:

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?
Alan
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Alan Jones wrote:

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.

time
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.
Dave
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wrote:

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.
Alan
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Alan Jones wrote:

I'd have to add some coding to make it a simulation program to "optimize thrust" given specific limitations... the simulation I use right now only limits the max thrust of the engine.
Dave
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wrote:

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.
Alan
BTW, which Dave Harper are you? Is you dad's name Roy? Where do you live now?
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Alan Jones wrote:

fuel.
program
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 in.

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 Birmingham originally.
Dave
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wrote:

There is nothing wrong with that. ;)

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 constraints.
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.
Alan

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Alan Jones wrote:

I
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 shots), etc...
Dave
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wrote:

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 be "simple".
Alan
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Good point.
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Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>
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Alan Jones wrote:

but
tool,
going
simplifications
No hard feelings. :-)

from a high altitude balloon before... (aka rockoon). Under the right conditions and with a little luck, it's possible to hit the 100km mark with something in the "L" motor range.
Dave
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On 5/7/05 3:00 PM, in article snipped-for-privacy@f14g2000cwb.googlegroups.com, "dave.harper"

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 than necessary.
In practice it doesn't quite work the same way, since you have to handle perturbations.
Brett
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