FWIW: Refinement to Fehskens-Malewicki - New Equivalent MAss

Gosh! I wouldn't want to jeopardize national security by flying a pop bottle rocket... And to think I have three stored in my refrigerator!
-Larry (Hah! They'll never take me alive!!!!!)C.

http://nira-rocketry.org/LeadingEdge/Phantom4000.pdf
www.nar.org
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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 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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Bob Kaplow wrote:

Only if launched into "Controlled Airspace"...
-dave w
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
On 5 Mar 2005 14:05:35 -0600, kaplow snipped-for-privacy@encompasserve.org.TRABoD (Bob Kaplow) wrote:

don't you mean FAA notification for over 1 lb?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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! <<< Kaplow Klips & Baffle:    http://nira-rocketry.org/LeadingEdge/Phantom4000.pdf www.encompasserve.org/~kaplow_r/ www.nira-rocketry.org www.nar.org
"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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Bob,
I've been off the scene for some years now, so forgive me if I'm not up to date. This is a mid D motor. Doesn't that exempt it?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
writes:

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 www.encompasserve.org/~kaplow_r/ www.nira-rocketry.org www.nar.org
"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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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:

http://nira-rocketry.org/LeadingEdge/Phantom4000.pdf
www.nar.org
attainable
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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.
--
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Yup. I figure about 4.5 lb*sec/lb. Micrograin beats it by ten fold :-)

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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.

--
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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>
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
wrote:

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

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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>
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
wrote:

Jerry, buy a clue.

Alan
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
On Sun, 6 Mar 2005 21:14:49 -0500, "Ken Karbon"

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

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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>
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.