Just wait until the JBGTs make you get a PBUP...
Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD"
>>> To reply, remove the TRABoD! <<<
Kaplow Klips & Baffle: http://nira-rocketry.org/LeadingEdge/Phantom4000.pdf
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You [should] not examine legislation in the light of the
benefits it will convey if properly administered, but in the
light of the wrongs it would do and the harm it would cause if
improperly administered -- Lyndon Johnson, former President of
the U.S.

Nope. Water rockets are exempt only if powered by less than 250g (~8.4oz) of
water. 101.22 does not apply.
Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD"
>>> To reply, remove the TRABoD! <<<
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"Congress shall make no law respecting an establishment of religion, except
to encourage attendance in Christian churches; or prohibiting the free
exercise thereof, except to require prayer in schools; or abridging the
freedom of speech, except for those questioning the Bush administration; or
of the press, except that not owned by Rupert Murdoch; or the right of the
people peaceably to assemble, except those protesting pre-emptive wars; and
to petition the government for a redress of grievance, except those we don't
like." -former U.S. Sen. Gary Hart

Once again, FAA regs don't depend on power or altitude or anything that
actually makes sense. They depend on propellant weight. For our models,
anything under 113g is exempt, 114-125 requires notification, and 126 or
more requires a waiver. For water rockets, anything up to 250g is exempt,
any more requires a waiver.
It's the government, it doesn't have to make sense!
Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD"
>>> To reply, remove the TRABoD! <<<
Kaplow Klips & Baffle: http://nira-rocketry.org/LeadingEdge/Phantom4000.pdf
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"To enslave men, successfully and safely, it is necessary to have
their minds occupied with thoughts and aspirations short of the
liberty of which they are deprived. A certain degree of attainable
good must be kept before them." Frederick Douglas, "My Bondage and
My Freedom," 1855

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. :-)
writes:

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??
Jerry

--
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>

But it is easy to change air density stepwise over time intervals,
based on a standard atmosphere.

Yes, but it is easy to model variable thrust and mass by modeling the
thrust-time curve a sequence of constant thrust intervals. I
typically use four intervals per motor for greater accuracy.

The best m will lie between m0 and m1 in an interval. You probably
want to use one of several easy to compute mean values, or try could
try to pick a optimal value say based on the classic rocket equation.
Because thrust is typically high, a good mean to use is the geometric
mean: m = 2/(1/m0 + 1/m1). The easiest and most used is the algebraic
mean: m = (m0 + m1)/2. I use the algebraic mean, but not because it
is the most accurate. The real power of the F-M equations are that
they are analytic equations. You can differentiate them WRT parameters
and propagate them through the computations. This enables you to do
things like solve for optimal mass very quickly and accurately using a
true Newton's method algorithm. In this sense, using the geometric
mean is more trouble than it is worth, and the difference is made
smaller by modeling the thrust-time curve a sequence of constant mass,
constant thrust intervals.

Water rockets are OK. I typically see water rockets with much longer
thrust times than your example. My complaint is that they are not
constant thrust. Typically the air pressure, and hence thrust, drops
by a factor of two over the thrust interval. There are also come
clever things that can be done with water rockets to deliver more
optimum thrust. I don't have any good math models for water rockets.
One thing about water rockets is that many of them may be under
optimal mass.

Nicely done, I think. Tom Keuchler(sp?) also developed some analytic
solutions for variable air density and thrust, although he had to
resort the use of Bessel functions.
Alan

I like to use inflection points and let the computer do the work of
interpolating between points (Jerry's endpoint method - JEND).
Then lose propellant mass scaled to motor thrust.
Simple and effective, I have posted the code before.
Here are some popular sample thrust curve data sets:
ES D12= .01-.1124,.03-.365,.2-4.92,.22-5.10,.24-5,.28-3.68,.38-2.87,
.45-2.47,.56-2.14,1.51-2.14,1.53-1.63,1.55-0 21.1G 44G
USR E6= .01-4.5, .10-4.69, .40-3.75, .5-1.38, 1-1.06, 2-0.94, 7.6-0.94,
8.2-0 21.5G 39.7G 8.2S
now apogee
USR F10= .01-6.75, .4-5.5, .8-2.5, 1.2-2, 3.1-1.88, 6.6-2.25, 7.1-1.5,
7.7-0 40.7G 69.4G 7.7S
now apogee
USR G25= .01-6.25, .3-9.06, .4-7.81, 1.2-8.28, 2-8.28, 2.4-7.66, 4-
1.56, 5-0 62.5G 105G 5.0S

On the same theory, here is a helpful dataset.
Altitude Pressure Ave.Temp. Less Air Greater Thrust
(ft) (in. Hg) (F.) Density
0 29.92 59.0 0. 0% 0.0%
5,000 24.89 41.2 16.8% 2.7%
10,000 20.57 23.3 31.3% 3.9%
15,000 16.88 5.5 43.6% 5.8%
20,000 13.74 -12.3 54.1% 7.0%
25,000 11.10 -30.15 62.9% 8.2%
30,000 8.89 -47.98 70.3% 9.3%
Revel in the tech post!
Jerry

--
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>

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:
http://www.apogeerockets.com/smartsim.asp
Ken

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

Hi, Alan.
Figured you'd tie into this thread. It is hard to
explain why one should be concerned with FM
equations these days, but for those of us who go
back... well we understand.
Would remark that one can get digital dirivatives
for optimization, but that finite interval sizes defeat
simple search mechanisms for optimal points. A
simple way around the problem, in vertical
simulations, is to do an FM integral over the last
fraction of an interval. That makes the time or
altitude from the digital solution continuous.
That, of course, is a coast phase integral, which
(I believe) is due to neither Fehskens nor Malewicki.
I used to love the Commodore 64 too. The real
trick, as far as I'm concerned, is to keep one
running for more than two years.
Best Regards,
-Larry C.

F-M is GREAT for coast phase if compute time is an issue. It sure would
be cool to make a version that at least factored in air density so it
could be used as well on high alt flights.

PDP-11-70 :)

--
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>

You posted that just for me, didn't you :-)
From my personal collection:

http://eisner.encompasserve.org/~kaplow_r/photos/computers/pdp-1170console.jpg
Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD"
>>> To reply, remove the TRABoD! <<<
Kaplow Klips & Baffle: http://nira-rocketry.org/LeadingEdge/Phantom4000.pdf
www.encompasserve.org/~kaplow_r/ www.nira-rocketry.org www.nar.org
You [should] not examine legislation in the light of the
benefits it will convey if properly administered, but in the
light of the wrongs it would do and the harm it would cause if
improperly administered -- Lyndon Johnson, former President of
the U.S.

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