FAA is a mass-driven regulation for "unmanned rockets".
Care to change it?
You better hurry. The "Sport rocket caucus" has added water rockets to
NFPA-1122 and have already restricted them there too!
Gotta be safe from those scary water rockets!
Care to guess who is on the "sport rocket caucus" for NFPA??
"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
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. :-)
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
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
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.
-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.)
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.