Calculate Burn-Time for a maneuver?

[Mazen]

Hello,

problem is: I set a maneuver for my craft, but I didn't fired the stage yet, so the Est. Burntime the maneuver gives me should be messed up?

How can I calculate this for myself? I'm using Kerbal Engineer, so I know how much DeltaV my stage can provide and I also know how long it takes to burn all fuel.

Example:

Needed DeltaV for maneuver: 917.3 m/s

DeltaV in Stage: 1765 m/s

'Time' in Stage: 4:31.5

So, I though: This is easy, I can do that...

4:31.5 equals 271,5 seconds. Now divide 271,5 dV by 1765 m/s and you get the time your ship needs for 1 m/s dV. Which equals 0,15382[...]. And finally take this times the deltaV needed for the maneuver: 917.3 * 0,15382[...] = 141,1 seconds.

But the past has shown that it doesn't work that way. Can anybody help me? I think this formula doesn't consider the fuel consumption?

[oktupol]

Your formula would be right, if the mass of the spacecraft doesn't change. But since you are burning fuel, it does. The accelleration gets higher the less fuel you have, so you need more time for a maneuver when your tanks are full.

There is a way to calculate this, but i don't know how...

Edited August 8, 2013 by oktupol

[Mazen]

Maybe I could add the ln()? I think this is also used to calculate your deltaV manually. So I think this would come in handy, but I don't know how to add the ln() to my formula :/

[capi3101]

The only way I know to do it is to brute force it; recalculate your acceleration every second based on the mass flow of the stage, and use the kinematic equations to figure out your final velocity after each second. When in aggregate the total change in velocity equals or exceeds the delta-V of the maneuver, you have your actual burn time. A LOT of math involved there...I'm pretty sure there's a less mass intensive method involving a differential equation, but then again that would involve a diff-eq...

Newton's second law...your mass has changed each second based on your mass flow rate. F=ma therefore a=F/m; if F (thrust is constant), your mass decreases by the flow rate every second, with a proportional increase in the acceleration every second.

[numerobis]

The Tsiokolvsky relation has almost everything you need: it relates mass change to deltaV. So you know how much mass you need to expel.

The other thing you need: mass flow is thrust / (Isp . g0). So you know how much mass you expel in a second.

(Or you could just integrate it, which is how you derive Tsiokolvsky anyway.)

[Mazen]

I don't really get what you want to tell me. I'm not that into this stuff :/

I think I'll just throttle up to 100% and set a new maneuver node.

[numerobis]

You know how much deltaV you need to produce, and the Isp, and the initial mass. So you can calculate the final mass, after you thrust:

mfinal = minitial * exp( - deltaV / (Isp * g0))

That tells you how much propellent you need to expel:

mpropellent = minitial - mfinal

You expel this much propellent per second:

mdot = thrust / (Isp * g0)

So your burn time is:

time = mpropellent / mdot

[annallia]

Not entirely sure I get what you are asking about here... There is no need to do the calculations yourself the games will be relatively accurate. A short burst (just tap shift, tap x) won't hurt anything as far as your orbit or trajectory goes and usually fixes an inaccurate burn time.

[Grizzlol]

You could also simply quicksave, create a node with the approximate dV you wish to burn, burn anywhere just to see the estimated burn time, quickload and then do a proper node and burn.