FWIW: Refinement to Fehskens-Malewicki - New Equivalent MAss

Larry Curcio · 2005-03-05T16:21:55+00:00

I must be one of the few people who still uses the Fehskens-Malewickiequations.I have used them as refinements, in each interval, to digital calculations,andas A simple way to do drag coefficient and altitude backtracking in aspreadsheet.I discover that many individuals believe these equations to be much lessaccuratethan they actually are for standard model rockets. Here are the recognizedsourcesof inaccuracy, and the reasons why they don't matter for small rockets:1) They do not depreciate air density with altitude. For rockets withaltitudes less than about 1200 feet, the difference is trivial. Most home-brew (**Not**, for example, WRASP) digital routines out there have moreinaccuracy from digital error than is in this exact integral, which doesn't depreciate air density.2) They use flat thrust curves. In fact, if boost times and altitudes aresmall, the difference in total altitude and velocity are trivial. Indeed, for very short burning times, the differences are absent. (G. Harry Stine made a big deal of thrust curve shape in his _Handbook_. His calculations, there, arewrong.) In practice, model rocket thrust curves that deviate most from flat linesare also the shortest in duration. Problem? What problem?3) The boost phase equations use an average mass, equal to the dead massplus half the propellant mass. This approximation, while technically incorrect, makesvirtually no difference when propellant fractions are small, as they are in modelrockets. In fact, the differences are trivial for mass ratios (LaunchMass/BurnoutMass)up to about 2. No standard model rocket has a mass ratio anywhere near that.On the plus side, the coast phase integral is exact, given the constant airdensity assumption.Elementary digital programs frequently make the same assumption and theircomputations are notexact.I was happy with all of the above until I started playing with waterrockets.(Go ahead and laugh, Jerry :-). That's when I ran afoul of item 3). Asidefrom this item, waterrockets...

Mar 05, 2005 48 Replies

Rate this thread:

Larry Curcio 21 years ago

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.

Vote

Ken Karbon 21 years ago

Not RockSim, but wrasp. A fellow recently wrote the code for PDAs. It is called prasp, I believe. RockSim includes a heavy CAD package and contains a tremendous amount of overhead with part databases and such. The flight simulator portion is still simple and would run on calculators and PDAs.

Vote

Jerry Irvine 21 years ago

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 :)

Vote

Bob Kaplow 21 years ago

You posted that just for me, didn't you :-)

From my personal collection:

formatting link

Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD" >>> To reply, remove the TRABoD!

Vote

Jerry Irvine 21 years ago

Nope. For Chuck Rogers.

I sat there for HOURS/DAYS/WEEKS debugging, testing and improving the accuracy, I/O interface, and usefulness for task of the programs we co-wrote.

Hey Chuck, I still admit you did the math research. You after all, are a much bigger geek than me!

Jerry

Vote

Alan Jones 21 years ago

We post tidbits of wisdom in an open forum so that more rocketeers may understand.

There are several methods for finding optimal points without derivatives, they just are not as fast or accurate.

Time and rocket motion are continuous. Use of a digital (numerical) ODE solver does not alter that. The ODE solver can solve for any (continuous) altitude at any time that may be desired by the user or optimization algorithm.

I have done hybrid ODE/FM simulations. I used an ODE solver to get the maximum speed of a supersonic model rocket, and used the FM coast equations to finish the subsonic portion of the coast, but only to save computation time.

That is matter for Fehxkens to address. He pops into RMR occasionally. There was that old Ricatti guy, but Douglas Malewicki is the guy who really capitalized on it and brought it to attention of model rocketeers.

I've never had one fail, except for the original inadequate power supply. I do have one set aside that needs the keyboard cleaned.

I was actually hoping that you would discus the equations modeling the performance of the water rocket thrust.

Alan

Vote

Alan Jones 21 years ago

Well, I first used F-M on a PDP-8 in high school, but that was before I learned calculus and added all the magic bells and whistles.

The C-64 is a home computer that more people can relate to.

Alan

Vote

Jerry Irvine 21 years ago

Hence the term "Malewicki Chart" too.

Super-sucky?

Jerry

Vote

Larry Curcio 21 years ago

I was into that last summer. I have my notes and a spreadsheet, which uses the solver to optimize. Upon review, I have an error somewhere. Will discuss it within the next week or two. Was about to write it up anyway. That's why the FM stuff.

Regards,

-Larry

Vote

Join the Discussion

Have something to add? Share your thoughts — no account required.

Didn't find your answer?

Ask the community — no account required