Burn Time Estimator - Can someone check my maths?

[AlexinTokyo]

I'm making a tool to calculate the estimated burn time for a maneuver, because I'm sick of KSP not telling me when I set up a maneuver node. I jump around between ships a lot, and also deorbit boost stages, so I often can't get a reasonable estimate from the maneuver planner.

I'd just like to have someone check my understanding and my maths:

Inputs will be the current mass (m₀), the current stage I_sp, the current stage thrust, and the required ÃŽâ€v of the maneuver.

Start with the rocket equation:

ÃŽâ€v = g₀.I_sp.ln(m₀/m₁)

Rearrange to solve for m₁:

m₁ = m₀/e^(ÃŽâ€v/g₀.I_sp)

Find the difference in mass:

ÃŽâ€m = m0 - m1

The rate of consumption of reaction mass can be found by rearranging the formula for I_sp:

F_t = g₀.I_sp.m^bar (F_t being thrust an m^bar being the flow rate in kg/s)

m^bar = F_t/(g₀.I_sp)

Finally, dividing the mass difference by the flow rate gives the time to consume that mass:

t = ÃŽâ€m/m^bar

If my understanding is correct, that should give a reasonably accurate estimate of the burn time required.

Any thoughts would be appreciated.

Edited July 14, 2014 by AlexinTokyo

[cantab]

I've not checked to see if that works. Generally speaking if I'm not getting a burn prediction I just guesstimate it from my experience with the ship.

But earlier I had to do some small burns (50 m/s kind of stuff) on RCS, so I simply ignored the mass reduction and went by

F = ma

ÃŽâ€v = at

t = mÃŽâ€v/F

That was good enough for this purpose. I'm not sure how the accuracy falls off with increasing ÃŽâ€v. It will in any case always be an overestimate, so you can consider it "safe" to follow, and ease off the throttle a bit if you need to.

[Kryxal]

There's always KER and its report on your current vessel's TWR...

[Claw]

At face value the equations look right. I didn't dig in and test them out. Your best bet would be to go build a ship and try a series of short and long burns to try it out. Remember to grab the start mass, and maybe just use F5/F9 to make that part easy on yourself.

I'm sure there's a mod out there for this...

[AlexinTokyo]

Generally speaking if I'm not getting a burn prediction I just guesstimate it from my experience with the ship.

My guesstimates just consistently suck

Specifically, I almost always underestimate how long it will take, leaving me with not enough time to burn 50% before the actual node.

I didn't think of going back to Newton to get an estimate, to be honest, I just dived in with the rocket equation.

Looking at the difference in the results, it's about 0.6% for a 100 m/s ÃŽâ€v, 6.5% for 1,000 m/s, and 9.9% for 1,500 m/s. So, at the very least, it's a great sanity check for my numbers.

The difference also becomes more apparent with lower I_sp engines (the above are for 800 s, they drop to 1.3%, 13.6%, and 20.9% for an I_sp of 390 s).

Ninja1: I have KER, which I will use to get the inputs for this.

Ninja2: Yeah, I will test for accuracy when I get home this evening (unfortunately, I can't play KSP on my office PC )

[Drew Kerman]

already derived. I use this all the time. Perfectly accurate

But kudos for working to figure it out yourself. I couldn't even begin to

[MockKnizzle]

Assuming you're not using a large fraction of your propellant all at once, just divide your burn dV by your current acceleration and correct it by subtracting a small percentage based on the general magnitude of the burn in relation to how much dV your stage has. For a longer burn, your acceleration increases more significantly so the correction is larger.

Edit: Which, after reading the post linked above, is pretty much exactly what the math says, just in word-form

Edited July 14, 2014 by MockKnizzle

[AlexinTokyo]

Well, having run some simple tests I can say that this definitely gives accurate times.

Moreover, from the few simple tests I ran it looks like the navball's Estimated Burn indicator might use the simple F = ma derived estimation given by cantab above.

More exhaustive testing may be needed, but for now this is answered.