FWIW: Refinement to Fehskens-Malewicki - New Equivalent MAss

"Scramjets - An ingenious answer to a non-existent problem."

"An alternative (maybe less rude) would be for the flamer to start a new thread instead of inserting a flaming branch into an FFT thread."

- Dwayne Surdu-Miller

Our enemies are never villains in their own eyes, but that does not make them less dangerous. Appeasement, however, nearly always makes them more so.

- Don Dixon

And your purpose is????

And your good deeds are? Please cite specific examples...

The next question is

What is the propellant here?

Is it the presurized air, which provides the energy?

Is it the working fluid, which provides the reaction force when it is propelled by the energy?

Is it both?

I like the first definition. :-)

Jerry, buy a clue.

Alan

Shh... He's asking for hemlock, but he can't be to obvious about it. ;)

Water rockets work on the principal of mass-flow.

Because the water does not change state and starts out and stays dense it has incredibly low ISP.

Is there an echo in this room?

It's you Jerry, it's you...

Yup. I figure about 4.5 lb*sec/lb. Micrograin beats it by ten fold :-)

I have flown quite a few micrograins and watched far more. That's just sad :)

You should make a post with several ISP's listed so I can FAQ it.

huh?

calculations,

(LaunchMass/BurnoutMass)

Larry,

Yes, your assumptions are good for small rockets of low altitude. But, why limit yourself? Numerical solutions are highly accurate wrt FM equations even with fairly large time steps (0.01 to 0.001 s). The solutions are in fact "exact" and the "digital error" is zero within the confines of machine precision. My R&D report of 1998 demonstrates my point:

Numerical methods (RockSim, wrasp, my own little code, etc.) allow for variable mass, thrust, density, Cd, etc. So, you can model any rocket and not worry about violating some assumption. The numerical results of the simple trajectory ODE's are fast and accurate for hobbyists with basic home computers.

Ken

True, but the same can be achieved with iterative root finding methods on numerical solutions. The computation times are fairly trivial on basic home computers. SMARTSim is a general-purpose solver for any variable in RockSim:

Ken

I agree, Ken. It is, however, a lot more convenient to optimize fluid fraction and launch mass of a water rocket if one takes advantage of the low altitude assumption.

This perspective is exactly what my initial apologies were about. In fact, I like the result for its unlikely form substantially more than I like it for its usefulness. As computer hardware becomes more powerful, approximate solutions become more and more like curiosities... except the few that are simple enough to shed light on the exact solutions.

Of course, as long as there are random variables at work (e.g.; motor performance, wind behavior, launch rod tip - not to mention altitude measurement error), exact solutions are probably more comforting than they should be.

Best Regards,

-Larry (Has a real digital program or two lying around) C.

The simple numerical sims I've run have been as good as the information I had available about drag and propulsion performance of the actual rocket.

(Cd of 0.6 turned out to be relatively realistic for KISS, if I remember.)

-dave w

Sorry, I was thinking of Socrates instead of Plato.

Of course, except for the speed and accuracy, which rarely matters.

BTW, There is little need to compute optimum mass accurately. What I do is compute only the first derivative of final altitude WRT mass and use a numerical method to find the zero crossing of the first derivative. Newton's method would require the second derivative as well, but that turns out to be more expensive to compute. It typically takes only 50% more computer time to compute and propagate a derivative, so it is cheaper and more accurate than approximating a derivative with a forward difference.

I do get the fact that there are few people these days who work with analytical equations and just crudely crunch numbers instead. Still, there are several symbolic math computer programs available, such as Maple, that people can use. Personally, I'm more of a numerical algorithm nut, but I find both math skills essential.

Yes, I do all my F-M magic on a Commodore 64 (8 bit 1Mhz CPU). It will also numerically solve ODEs and do simple CFD, but it will never run Rocksim. I don't think you will be running Rocksim on your programmable calculator or PDA.

Alan