Please Help! How to calculate distance and speed

[Ulrikbm]

Hello

Is there anyone WHO can help me find the distance and speed for my rocket in ksp.

My problem is that I want to know how high my rocket go by a single stage. I know how to calculate Delta v and TWR. But how is it possible to calculate how fast and how long a rocketengine is pushing my craft from the moment it is turned on.

I have an example:

The full weight of my craft is 4,7374

without fuel it is 1,4874

The Isp in atmos. is 225

The thrust is 250

the maxburn is around 15 units/sec

the amount of fuel is 433

Is there anyone who can help my with an explanation on how to find the distance for the rocket before it burn out of fuel. and what will the speed at burn-out time be. Is there any formula for this calculation.

Thanks for any help.

[Taki117]

The issue with rockets is that they are constantly accelerating. It is possible to calculate burn time, by looking at fuel usage vs fuel amount. (both are available in the editor) However, I am unsure how to translate that into altitude

[MajorThomas]

The problem can probably be simplified into a formula if you hold a few variables constant, and assume you're only traveling straight up. But realistically you've got other things changing such as drag force, which depends on altitude (density) and velocity, which combine to give you dynamic pressure. This is a very real force and has a strong effect on your performance, so it's best not to treat it as a constant.

Because of dynamic pressure, the max. height your first stage will carry you depends to a large extent on your throttle setting. Lower throttle may prevent you from going too fast (and wastefully) in the lower atmosphere, so your fuel is more efficiently used, and hence you go higher. On the other hand, with a very heavy upper stage and payload, you may need to be at full throttle so you minimize the time spent lifting the upper stage to altitude and staging velocity (because if you're going too slow, you're "hovering" and burning fuel against the never-ending force of gravity. You have a rocket not a helicopter). Somewhere in between these extremes of too slow and too fast, there is an optimum point where you get the most out of your first stage. This point will (wet finger in the air) probably be something close to 200-300 m/s at burnout, and let's say 10,000 m altitude. YMMV, but if you're going much faster or slower than this at the 10,000 m point, then you're probably not at the optimum point for your stage.

A more exact way to get answers to your questions would be to solve the rocket state equations numerically...but you needn't look very far, because by gum, this is what you get just by flying your ship in KSP. So I'd suggest trying out your design in sandbox mode so there's no penalty for flying the same ship multiple times as you tweak the design.

You could also try an add-on such as mechjeb, that can provide you with overall numbers for each stage, and somewhere inside mechjeb are calculations going on to ensure the right speed and trajectory to stay near the optimum for your rocket. Just watch mechjeb fly your ship, and you'll learn something about how it ought to be flown

Edited November 12, 2014 by MajorThomas

[Starman4308]

Is there anyone who can help my with an explanation on how to find the distance for the rocket before it burn out of fuel. and what will the speed at burn-out time be. Is there any formula for this calculation.

Well, you can numerically integrate several differential equations describing thrust, drag, and aerodynamic lift* to achieve approximate answers, though they are dependent on many variables, such as what pitch profile you want. There's several programs out there which help you do that: one of my favorites is called Kerbal Space Program.

To be helpful: what MajorThomas said. MechJeb will generally fly an okay gravity turn; you can probably optimize it, but it gives you a rough idea of what you should be doing (disclaimer: not valid for FAR/NEAR aerodynamics, which are much less forgiving of large pitch angles).

*Using realistic aerodynamics, as opposed to the stock souposphere. If you're wondering: the programs NASA uses are probably very similar to KSP's physics engine, except with much more realistic equations, and much more boring interfaces.

[LaytheAerospace]

The math on this is a lot hairier than you might expect. The rocket's performance is going to change pretty dramatically during the launch. When its tanks are nearly empty, acceleration will be several times higher than when full. Atmospheric drag has a very nonlinear relationship to altitude and velocity. Steering losses from your rocket wobble will factor in, too.

Best bet would be to just determine it empirically, and stick your rocket on the pad.

[Brotoro]

Yeah...because the rocket mass and air density and force of gravity are constantly changing, you get a set of diffferential equations to solve. So it's easier just to solve them numerically.

If you assume constant air density and constant gravitational force, the differential equations can be solved giving the Fehskens-Malewicki equations that model rocketeers used back in the days before we had simple simulation software...so here they are for your amusement:

[MajorThomas]

FWIW, Starman just mentioned "gravity turn" which TBH I can sense it when I'm flying it but don't know exactly what it is. However, I notice the following about gravity turns, which is the trajectory MechJeb apparently uses:

1. Start off flying basically straight up, and at some point typically between 7000 m and 10000 m altitude MechJeb will begin turning gently. So when I fly manually, at this altitude I start pitching over gently to the East.

2. Note that if you tried to fly pointed in the same direction after initiating the gravity turn, your actual path will be veering to the side more and more. This probably has something to do with the gravity turn concept.

3. However if you steer close to that path...which is curving more and more as you ascend...you'll have a low angle of attack with the air at all times, which is desirable. Minimizing AOA prevents undue stress on the airframe, undue drag, etc.

4. I find that you pretty much exit the atmosphere when your trajectory angle relative to the horizon is about 30 to 20 degrees. Above the atmosphere, it doesn't matter what your AOA is, if there's no air to cause drag or stress.

So yes, it's going to be hairy to calculate all this. Bro's great equations seem useful for vertical flight only, but realistically you're always going to be curving over until you're flying completely horizontal. Simplest and best way to "solve" such equations in a more immediate way is to use KSP.

Edited November 14, 2014 by MajorThomas

[Starman4308]

FWIW, Starman just mentioned "gravity turn" which TBH I can sense it when I'm flying it but don't know exactly what it is. However, I notice the following about gravity turns, which is the trajectory MechJeb apparently uses:

1. Start off flying basically straight up, and at some point typically between 7000 m and 10000 m altitude MechJeb will begin turning gently. So when I fly manually, at this altitude I start pitching over gently to the East.

2. Note that if you tried to fly pointed in the same direction after initiating the gravity turn, your actual path will be veering to the side more and more. This probably has something to do with the gravity turn concept.

3. However if you steer close to that path...which is curving more and more as you ascend...you'll have a low angle of attack with the air at all times, which is desirable. Minimizing AOA prevents undue stress on the airframe, undue drag, etc.

4. I find that you pretty much exit the atmosphere when your trajectory angle relative to the horizon is about 30 to 20 degrees. Above the atmosphere, it doesn't matter what your AOA is, if there's no air to cause drag or stress.

So yes, it's going to be hairy to calculate all this. Bro's great equations seem useful for vertical flight only, but realistically you're always going to be curving over until you're flying completely horizontal. Simplest and best way to "solve" such equations in a more immediate way is to use KSP.

Well, there's a stock "gravity turn" and then there's real gravity turns. What you do in stock is gradually tip over eastwards. In the absence of atmosphere, you want the absolute minimum amount of vertical thrust necessary to avoid uncomfortable encounters with terrain: you want to start going horizontal as much as possible from the moment of liftoff. This practice minimizes gravity drag (loss of dV to gravity). In the presence of stock souposphere, though, sea-level atmosphere is going to kill your velocity quickly (aero drag). As such, you want to burn vertical to get out of the thickest of the soup before starting your eastwards turn. This is what MechJeb is calibrated for: a pitch profile designed to balance aero and gravity drag in a stock drag environment. It has nothing to do with aerodynamic stresses or AoA, because stock aerodynamics acts equally an all parts and does not model body lift.

A real gravity turn can only really be done in FAR/NEAR. In these mods, you wait until you're going ~60-100 m/s (depending on rocket TWR profile), tip over 2-5 degrees east, wait for your prograde marker to catch up, and then say "Look Ma, no hands!". If CoL is properly behind CoM and your rocket is pointed reasonably close to prograde, aerodynamic stability will tend to keep your rocket pointed dead-prograde all the way through until you hit upper atmosphere. You need to do this (possibly plus or minus a few gentle control inputs), because any violent movements away from prograde will cause your rocket to flip from aerodynamic instability, and if you start your gravity turn too late, you will, A, run into difficulties trying to turn at high velocity, and B, waste lots of dV going upwards.

Once you've passed max-Q (maximum aerodynamic stress) and are in upper atmosphere, you can start to have your own ideas about what the proper orientation is. I would suggest trying to keep tAp (time to apoapsis) around 10-20s, which will describe a gentle ascent which is mostly going horizontal, minimizing gravity drag while slowly getting you out of atmosphere. This often has the advantage of keeping you in a good orientation to take advantage of body lift*, though that is dependent on your current stage's TWR and how close you are to orbital velocity.

*Go fast enough, and even a giant tube of rocket fuel gets aerodynamic lift in FAR/real-world physics.