rocket delta-v

[LTR]

Hello,

is there an optimum impulse motor for a given rocket or is it just a case of fitting as powerful a motor as possible?

Logic tells me that excessive thrust would make a rocket aerodynamically unstable, but is that the case? Is there a way to calculate the cut off point in terms of impulse/thrust?

If maximum altitude were the goal, would a shorter or longer duration impulse of the same force be better? If a longer duration impulse yields a better altitude (which is my current belief), is there a way to calculate the "optimum" duration?

Presumably, knowing the CD of a given rocket would be necessary to calculate any "optimum" values - is there a way to calculate that for agiven rocket from practical flight measurements?

Sorry to be all "questions, questions, questions" - any help or advice at all would be very gratefully received

Thanks!

 

[boatgeek]

Hello,

is there an optimum impulse motor for a given rocket or is it just a case of fitting as powerful a motor as possible?

Logic tells me that excessive thrust would make a rocket aerodynamically unstable, but is that the case? Is there a way to calculate the cut off point in terms of impulse/thrust?

If maximum altitude were the goal, would a shorter or longer duration impulse of the same force be better? If a longer duration impulse yields a better altitude (which is my current belief), is there a way to calculate the "optimum" duration?

Presumably, knowing the CD of a given rocket would be necessary to calculate any "optimum" values - is there a way to calculate that for agiven rocket from practical flight measurements?

Sorry to be all "questions, questions, questions" - any help or advice at all would be very gratefully received

Thanks!

Welcome!

Taking the questions one at a time:
"Optimum" means lots of things to different people. Usually, people optimize for altitude, speed, or "looks cool". Altitude is discussed below. Optimizing for speed usually means a short burn, high-thrust motor for a given impulse. Optimizing for looking cool depends on what you like.

Excessive thrust doesn't make the rocket unstable unless one of the fins comes off or the rocket folds in half. That definitely makes it unstable. Stability through transonic and supersonic speeds gets weird, so you could have a rocket that was stable subsonic and unstable supersonic. That would also be messy.

Usually, people want longer-duration burns to get higher altitude. The reason is that drag varies by speed squared, so higher speed = a lot higher drag. Keeping the rocket at relatively low speed usually gives a higher altitude. Sometimes, you can also get to an optimum weight where making the rocket either lighter or heavier makes it lose altitude. There are many exceptions, so check assumptions with your simulations.

Which takes us to your fourth question. You can simulate performance with a few different programs. I use OpenRocket, which is open source and free. RockSim is also popular, as is RasAero, particularly for supersonic flights. Once you fly your rocket a few times with altimeters, you can adjust the simulation (especially surface finish) to dial the simulation in to how it behaves in flight. Then you can start dialing in motors that give you the performance you're looking for.

 

[Alan15578]

Hello,

is there an optimum impulse motor for a given rocket or is it just a case of fitting as powerful a motor as possible?

Logic tells me that excessive thrust would make a rocket aerodynamically unstable, but is that the case? Is there a way to calculate the cut off point in terms of impulse/thrust?

If maximum altitude were the goal, would a shorter or longer duration impulse of the same force be better? If a longer duration impulse yields a better altitude (which is my current belief), is there a way to calculate the "optimum" duration?

Presumably, knowing the CD of a given rocket would be necessary to calculate any "optimum" values - is there a way to calculate that for agiven rocket from practical flight measurements?

Sorry to be all "questions, questions, questions" - any help or advice at all would be very gratefully received

Thanks!

You pretty much want maximum total impulse. When specifying an optimization problem you need to be clear about your are optimizing, what your are varying to achieve the optimization , and what constraints or side conditions that you require. The typical problem of interest to sport rocketeers is known as the Goddard Problem: how to deliver thrust to maximize vertical altitude, with limited fuel (assuming a constant Isp, or simply limited total impulse.), typically starting on the ground at zero initial velocity. This is a well worked problem and you can do your own research to find some of the interesting variations. The solution is typically composed of three flight phases: Maximum thrust (ideally just an infinite thrust impulse), followed by a singular act phase until burn out, and then a coast to apogee. The singular arc phase is more interesting, but for MR it is nearly trust at twice weight, or trust to maintain drag equal to weight. Approximately calculating this optimum altitude can be done on the back of an envelope. First, calculate the velocity where drag equals weight. Calculate the total impulse required to accelerate to that velocity (velocity *mass). Subtract that impulse from your total impulse limit and then divide by the singular arc "cruse trust" to get the burn time to burnout. multiply this burn time by the velocity to get burnout altitude. Finally calculate (or look up) the coast altitude to apogee and add that to your burnout altitude. You can no doubt imagine some subtle improvements to the calculation as described. If your case is under powered you may not have a singular arc phase and just want maximum thrust untill burnout.

The reality is that Isp is not constant, and we cannot vary thrust optimally, and maximum trust is typically limited as well. The high thrust- low thrust dilemma is often best addressed with clustering or staging. Within a single solid rocket motor you are pretty mush limited to choosing an initial core or propellant geometry, and nozzle erosion etc. Furthermore, in MR you are limited to a finite choice of certified commercial rocket motors. Understanding optimal trust is helpful, but at the end of day you are back to running simulations to find the solution that works best for you.

"optimum duration" may be even simpler. It may be the distance to the recovery barrier (e.g a river, interstate highway, or forest) divided by the wind speed.
Alan

 

[LTR]

Hello both,

thanks very much for taking the time to reply and for such full explanations - very helpful indeed.

I use OpenRocket and find it very informative, but it's difficult to tell whether actual flights bear out the simulations without some more effective instrumentation, which is my current project.

Given that drag is proportional to velicity^2, is there a maximum/ideal velocity to aim for for a given rocket where a given impulse will achieve maximum altitude?

Thanks for your help

 

[Charles_McG]

I think it works out to be an 'ideal momentum' - you vary mass to vary velocity for a given motor/airframe combo. You can add a mass object in OpenRocket and vary it to see how it impacts the coast phase of the flight (and thus the altitude).

 

[LTR]

Thanks for your reply.

OpenRocket suggests less mass = greater altitude, but I suspect that's mainly down to the small sizes/thrusts I'm modelling (D9 motors and 100g payload).

Thanks for your help

 

[BDB]

Thanks for your reply.

OpenRocket suggests less mass = greater altitude, but I suspect that's mainly down to the small sizes/thrusts I'm modelling (D9 motors and 100g payload).

Thanks for your help

There are definitely scenarios with high thrust motors where added mass actually increases altitude. But the D9 likely won’t give you that kind of flight profile. Be sure to keep your velocity off the rod at or above 50 ft per second. Below that you start to get into flight profiles that vary from wonky to dangerous.

 

[LTR]

Wonky

OpenRocket says my rocket reaches 13.4 european metres per second (or about 44 of your US ft per sec) at 1m altitude, so I'm pretty much on the money in that respect, by the look of things - thanks for your advice

 

[Larry Curcio]

In a vertical flight, the equations seem to work out this way to maximize altitude:

Compute the terminal velocity in a vertical ascent at thrust=2*weight. (If you like, use a credible range of Cd’s and split the difference.)

Create an arbitrarily short bolus of impulse (i.e.; arbitrarily high thrust) to bring the rocket up to that speed. If the thrust duration is short enough, you can use the rocket equation to estimate how much propellant to burn this way, since the rocket should not move enough that gravity and drag will figure. (This is in theory, but in many cases, achieved speeds are close to theoretical outer space deltaV.)

Keep the thrust=2* weight for the rest of the flight.

The above is theory, but the result below (useful in LP) is practical:

It follows that, if the rocket equation gives you a deltaV of less than terminal velocity at thrust=2*weight (sufficient condition), just make the thrust as high and short as possible for maximum altitude.