Estimate the peak altitude of my rocket

[phyrox_eh]

Hi!

I have a simple question: How can I calculate the max altitude that my rocket will reach? It seems a simple question but I haven't found any post in the forum neither in the Wiki that computes this altitude (neither the max velocity the rocket will achieve).

I tried to compute it using several of formulas (this,this and this) but they do not consider the drag caused by the atmosphere...

Some pointer or guideline would be appreciated. Thanks!

[DBT85]

max altitude or max orbit it can achieve?

[UmbralRaptor]

For max altitude of a suborbital rocket? This would be the Goddard Problem, and because of drag is not amenable to analytic solutions. I'd lean towards finding some rule of thumb designs or messing around with numeric simulations.

Some previous discussions.

[qazsedcft]

Why do you want to calculate max altitude? Unless you just want to throw stuff up and see it fall down the max altitude isn't very useful at all. The following might be useful https://what-if.xkcd.com/58/.

If you mean to calculate the max orbit that you can achieve you need to use the rocket equation to find out the delta-v of your rocket. The main problem with that is that it doesn't take atmospheric drag into effect and calculating drag is really complicated.

Once you know the delta-v you can see what kind of orbit is achievable by calculating the specific orbital energy of the orbit. It depends on both the distance and the shape of the desired orbit.

Usually, this is done in reverse, first find out which orbit you want, calculate the delta-v required and then build a rocket to achieve that.

Links:

http://en.wikipedia.org/wiki/Specific_orbital_energy

http://en.wikipedia.org/wiki/Rocket_equation

[GoatRider]

In real life you just use a simulation. The game is a simulation. So just hit quicksave, and launch it. Hit quickload when you have your answer.

[phyrox_eh]

Wow! Thanks for your answers! I actually want to know the max altitude not the max orbit.

I think this is useful now in "First Contract". I want to optimize my rockets in order to perform different experiments in the same launch. To this end, I want to calculate the aproximate altitude (and velocity) of each stage so I can perform these experiments on different stages.

Edited August 1, 2014 by phyrox_eh

[Wanderfound]

Mechjeb will give you TWR, delta-V and burn time for each stage. Combine these values with some experimenting and you should be able to get an approximate idea. Keep TWR below 2 if you want to minimise drag losses.

As others have mentioned, the variability of atmospheric drag makes it pretty much impossible to calculate an exact answer.

[Pecan]

Wow! Thanks for your answers! I actually want to know the max altitude not the max orbit.

I think this is useful now in "First Contract". I want to optimize my rockets in order to perform different experiments in the same launch. To this end, I wanted to calculate the aproximate altitude and velocity of each stage so I can perform these experiments on different stages.

Good luck with that. The easy part is working out your straight-line thrust and acceleration - calculus will let you go straight up and back down, even with gravity and drag. Before you start though you'll need to determine exactly what your throttle setting, control-inputs and heading will be at each (fraction of) a second. That'll affect the accumulated velocity vector, which will determine your energy losses from gravity, steering errors and drag. Unless you fail to fly an exactly duplicated mission each time of course, in which case you'll get different results every time. Oh - and if you stage, jettison anything or reveal/conceal parts that affect your drag you'll have to work everything out independently for each of those events as well. You will time them to the second, with identical AoA, altitude, velocity and other flight characteristics, won't you?

TL;DR - straight up and back down can be calculated, but is worthless; you're unlikely to get contracts that specify an altitude without a velocity or other flight characteristics as well. Any more complicated flight through atmosphere can only be calculated within such a broad approximation it's also probably worthless; you're better-off having fun.

[GoSlash27]

The easy way to do this IMO would to launch a test rocket and "map" the DV vs. altitude. AFAIK nobody's bothered doing this yet.

You note the fuel mass and dry mass of the rocket and launch it. Every 5km altitude, you note the percentage of fuel used. The rocket equation will tell you how much DV it required to attain the altitude.

If you keep the acceleration within reasonable bounds, these results will be repeatable for any future rocket you send up, regardless of mass.

Best,

-Slashy

[Pecan]

Oh, you might find this NASA site useful, it came up in another discussion: http://exploration.grc.nasa.gov/education/rocket/flteqs.html

[mhoram]

During KSP 0.16 there was a challenge for exactly this problem.

If I remember correctly, the best solution for solving this Goddard Problem during the challenge was an autopilot that adjusted the ships velocity to match the terminal velocity.

I played around in Career mode with different combinations of Altitudes/Velocities/Items to test.

The craziest combination I had to try several times in oder to get the flight path right in a single launch - so try and error is another approach to solving this problem ;-)

[Drew Kerman]

The Ascent Komputron will do this for you, but currently only if you're running stock everything

[Pecan]

The Ascent Komputron will do this for you, but currently only if you're running stock everything

Probably a false positive but Chrome is reporting the .zip download as malicious. Let's all be careful out there.

[Claw]

The easy way to do this IMO would to launch a test rocket and "map" the DV vs. altitude. AFAIK nobody's bothered doing this yet.

I have created exactly this plot and will repost it when I get back to my computer (in maybe a couple hours). I posted it previously but I think there was no interest, so it's lost somewhere.

I use it for exactly what you are asking: when designing a rocket to reach a specific altitude/airspeed for a test. It's also somewhat easy to compensate for airspeed requirements, though there is a little bit of pilotage that's needed.

-Claw

EDIT:

Here you go. Not the best, but it works well enough for what I need. Gravity and drag losses are included so you can see that it's nearly a terminal velocity ascent.

If you need speed in excess of terminal velocity, you can just add the m/s that you need in excess of Vt. To figure out additional drag loss at that speed, you can eyeball it based on the slope of the drag loss curve below.

Edited August 1, 2014 by Claw

[GoSlash27]

Claw,

Excellent work! This should be extremely useful for testing contracts. How did you determine drag losses vs. gravity losses?

Thanks,

-Slashy

Edited August 1, 2014 by GoSlash27

[Pecan]

I have created exactly this plot ...

Maybe it's because it's 4am and I'm falling asleep but this gives the burn-out altitude, doesn't it? Peak altitude would need apoapsis including coasting above the indicated heights.

[Claw]

Claw,

Excellent work! This should be extremely useful for testing contracts. How did you determine drag losses vs. gravity losses?

Thanks,

-Slashy

Thanks.

Losses were calculated by MechJeb. I did the run several times and the numbers it gave me generally made sense, so I didn't go back and verify them in any distinctly mathematical way. I also flew to minimize flight path losses.

Maybe it's because it's 4am and I'm falling asleep but this gives the burn-out altitude, doesn't it? Peak altitude would need apoapsis including coasting above the indicated heights.

Yes, I suppose you're right. It doesn't give the coasted AP height but rather the dV needed to get to that altitude at Vt. I built this for testing, and it's typically at some speed above zero. I then calculate actual dV needs by adding or subtracting the differential between test speed and terminal velocity.

For example, if I need to test a component at 20,000m (+/- some tolerance), then I need roughly 2,500 m/s of dV to get there. I'm in the flatter range of gravity loss, so not much change in loss there (remember, the slope relates to loss rate). The atmospheric loss is still a bit steep, so I might need to think about adding some dV pad if my test requires a speed a lot higher than terminal velocity. But I don't want to remove too much dV if my speed is less than terminal velocity because the atmosphere will still drag it off.

This particular chart is done with a what I would consider a fairly standard "basic" profile without regard to doing one long continuous burn to altitude (I'm not necessarily worried about getting to orbit). I chose this one because it seems to be a reaonably common launch profile for most mid level users who would ask this question, and it seems to work pretty well for me. So this isn't quite an "optimum" climb to orbit, but one that follows close to terminal velocity (so maybe not too sub-optimum either). The reason the burn stops is that the craft reaches a point where the apoapsis is in orbit, so you coast to AP and complete insertion (again, assuming you were aiming for orbit).

If you want a chart that is one continuous burn, then this won't be it. I thought this one was most useful for those "test component X at YY,YYY altitude and ZZZ speed" designs. (This is a "test at altitude" chart more than a "get to orbit" chart.)

Which now reminds me, I probably ought to post a terminal velocity chart too. I was maybe assuming poorly that it was handy for everyone.

So while this isn't exactly what the OP asked for, hopefully it answers the real question about testing components at speed, at a specific altitude.

Hopefully that helps a bit,

~Claw

Edited August 1, 2014 by Claw

[Elington]

Probably a false positive but Chrome is reporting the .zip download as malicious. Let's all be careful out there.

Hi Pecan,

For the record the PC used to build that thing is protected by a genuine and up-to-date KAV 14.0.0.4651 (current build). And I always check the files explicitely before release. Anyway you're definitely right that every one should always be very careful!

Cheers,

David

[Tortoise]

You can't determine that from the ground unless you actually have some tool to simulate your launch because it all depends on how efficient your flight profile is, and the apoapsis will be even higher if you're using FAR.

[phyrox_eh]

Hopefully that helps a bit

Yes, this helps a lot! One question: Can you plot the terminal velocity plot you've mentioned?

It is clear that this is a Goddard problem and it is not easy to solve analitically. So I will check Pecan's NASA link and Elington's software, but I feel that Claw's graph is enough for the game.

Cheers!

Edited August 1, 2014 by phyrox_eh
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[fr33soul]

On 8/1/2014 at 4:15 AM, Claw said:

I have created exactly this plot and will repost it when I get back to my computer (in maybe a couple hours). I posted it previously but I think there was no interest, so it's lost somewhere.

I use it for exactly what you are asking: when designing a rocket to reach a specific altitude/airspeed for a test. It's also somewhat easy to compensate for airspeed requirements, though there is a little bit of pilotage that's needed.

-Claw

EDIT:

Here you go. Not the best, but it works well enough for what I need. Gravity and drag losses are included so you can see that it's nearly a terminal velocity ascent.

If you need speed in excess of terminal velocity, you can just add the m/s that you need in excess of Vt. To figure out additional drag loss at that speed, you can eyeball it based on the slope of the drag loss curve below.

how did you calculate this?

[Duck McFuddle]

I don't know the algorithm, but you can always just test it. If it's career mode/you have revert flight turned off then there are a few mods that let you do a simulation launch.

[Snark]

Note that the question is from well over four years ago-- the original question has long since been asked and answered, and folks have moved on.

Also, @fr33soul, you'll note that the person you quoted hasn't logged on to the forum since 2016, so your question is unlikely to get an answer at this point.

Also, note that the original discussion was from so long ago that it was before KSP 1.0 arrived, meaning that the game had a completely different aerodynamic model.  Therefore any graphs you see are likely to be practically irrelevant today, and any answer to your question would be moot.

Accordingly, locking the thread to prevent further confusion.  If anyone has a current question about rocket performance, feel free to spin up a new thread. 

Thank you for your understanding.