altitude record growth

Artifact of motors in the larger range being tailored mostly for larger rockets.

Lower power even if mis-tailored, are closer to optimum weight/thrust.

Optimal thurst/weight for an altitude attempt is usually a light, minimum diameter rocket with a long-burn motor. You don't find many long-burn motors in the M and N range, partly because of the heat issue and partly because of availability - most people want M and N motors to launch great big rockets, not minimum diameter altitude attempts.

I haven't thought this through yet - but it also may be a physical limitation because it takes a certain amount of initial thrust just to get an M or N motor's worth of propellant and casing going at a safe speed, which may reduce the relative possibility of a really long burn motor. I think Tom Binford made an EX M motor with a 17 second burn time, but I believe he launched a spool or something - not exactly an optimal design for an altitude attempt :-)

I imagine physics, or aerodynamics at least, has something to do with it. Drag goes up, to a first approximation, as the square of the surface area and as the square of velocity. Larger and faster rockets are operating in a much harsher drag environment with correspondingly greater airframe stresses.

I would guess the biggest factor is cost and accessibility. An average Joe can at least build a fairly competitive modroc and practice flying it. Lots of flyers leads to lots of innovations There is a long learning curve behind modern competition modrocs. The same is not true for envelope pushing HPR. Not many can afford to practice fly a lot of M motor altitude birds. Nor are the practice launch opportunities there as compared to a B motor altitude model. Flying a minimum diameter, optimal mass, N motor vehicle to maximum altitude is usually an "event", not a routine launch. I would guess that the HPR performance increments are increasing at a faster rate than are LPR/MPR but it will be a while longer before HPR competition "best practices" filter down to Joe Average, especially in the higher impulse levels.

But you do have me curious now. I need to go see what the K/L/M/N altitude records are.

A couple years ago I did a purely empirical curve fit to the altitude records, not limited to just single stage rockets.

For altitude in meters and newton-seconds impulse I got

H = 349*(I^0.38) +/- 12% for A - M motors

which corresponds fairly well to your results.

Later records in the higher impulse range will alter this somewhat.

I think the divergence at the lowest impulse levels is due to breakdown of motor selection and characteristics, i.e., partially filled casings and smaller L/d ratios, shorter burn times etc.

The other replies have addressed the upper end and other factors. Remember that for the big rockets decreasing air density becomes significant.

I was just amazed that such a simple equation was useful for obtaining first estimates of ultimate possible altitude over such a wide range of impulse.

I'm curious, did you look at motor class alone, or compare actual certified total impulse levels?

Remember that in the model rocket regime, motors are carefully designed to be close to the maximum total impulse limit for their respective class, with the exception of G motors that are restricted to 62.5 grams propellant weight and therefore fall at about the 50% G level.

With HPR motors however, there are few motor choices in each category that hover at the maximum total impulse for the class. From I to K you have altitude efficient SU motors designed to the total impulse limit such as the I65/J125/K250. But in the other classes and especially with reloadables motors are designed less for peak altitude as they are for effects, 62.5 g modularity, general purpose appeal, etc.

There are other long burn motors, currently there are motors certified up to about 14s burn time. The three I mentioned above are all long burners too.

Mike D.

For my study I just used motor class. Quick and dirty....

I didn't want to delve into details, just get a simple formula for a kind of rule-of-thumb rough estimate.

Then I tried to see if I could match the result with predictions from the Fehskins-Malewicki equations. Had a hard time getting Cd low enough to give meaningful results. Closer to 0.1 than the usual 0.7 for what I generally build. ;-)

I've found that CD for HPR rockets and certain model rockets are WELL below the established norm of 0.7... While I haven't encountered 0.1, I wouldn't say that it's not possible.

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

I would.

I don't have the motor or mass data to backtrack, but I'd be curious as to what the Cd works out to for a Super Loki Dart?

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