How long to burn to exhaust x amount of dV?

[guitarxe]

I know how much dV I want to use up for a particular manoeuvre. Knowing what engine and mass I have, how do I calculate for how long to burn to exhaust a certain amount of dV?

Edited September 24, 2014 by guitarxe
changing to answered

[Pecan]

The amount of fuel required for a given deltaV can be found from a familiar equation:

Fuel Mass = EXP(dV_Required / (Isp * Gravity))

Since you know how much fuel your engine burns per second it's easy to work out how long it'll take to get through that much :-)

The 'Fuel Mass' here is a percentage of the total rocket mass. The equation comes from NASA:- http://exploration.grc.nasa.gov/education/rocket/rktpow.html

Edited September 25, 2014 by Pecan

[MegaFlop10]

Are you using manoeuvre nodes?

Also, the equation for burn time is:

M / q × [ 1 - 1 / e^{(DV / C)} ]

[guitarxe]

So, let's say I want to use up 676m/s. My engine is the LV-909, isp is 390, fuel consumption is 13.06kg/s

We get a Fuel Mass of 1.19. That's what, in tons? That's too small to be in kgs...

So then we calculate burn in seconds to get

1.19 * 1000 / 13.06 = 91.37sec of burn time.

(Times 1000 to convert to kg, since I am assuming the above Fuel Mass number is in tons).

Is that correct?

[guitarxe]

Are you using manoeuvre nodes?

Also, the equation for burn time is:

M / q × [ 1 - 1 / e^{(DV / C)} ]

What is the C in that equation, and what is q?

I am flying probes using Remote Tech 2, thus I use the semi-autopilot of RT2 to do my burns. And I don't like the imprecision of manoeuvre nodes combined with the imprecision of thrust control anyway. I want to get my probes into KEO orbits, and getting the orbital period exactly right using just your keyboard is quite impossible.

[dzikakulka]

I don't think Pecans equation works, first thing is that it doesn't take object mass as an input while it is a very important parameter (think how much fuel 1ton craft would require and how much 100ton craft would). Or I'm stupid or something, anyway you have all math required here:

http://forum.kerbalspaceprogram.com/threads/40053-Estimate-the-duration-of-a-burn

Edited September 24, 2014 by dzikakulka

[mhoram]

Use the Tsiolkovsky rocket equation

dV = v_e * ln(Mass Full / (Mass Full - Used Fuel Mass))

with v_e = I_SP * g₀

You get I_SP friom the description of the engine,

and g₀ = 9.82 m/s² according to http://wiki.kerbalspaceprogram.com/wiki/Specific_impulse#Conversion_factor

From all this you can calculate the Used Fuel Mass.

Edit: 13.06kg/s is consistent with my calculations

Edited September 24, 2014 by mhoram

[guitarxe]

I don't think Pecans equation works, first thing is that it doesn't take object mass as an input while it is a very important parameter (think how much fuel 1ton craft would require and how much 100ton craft would). Or I'm stupid or something, anyway you have all math required here:

http://forum.kerbalspaceprogram.com/threads/40053-Estimate-the-duration-of-a-burn

The step that comes before this calculation, to find the dV that I want to expend, takes mass into consideration

But thanks for that link!

[MegaFlop10]

What is the C in that equation, and what is q?

I am flying probes using Remote Tech 2, thus I use the semi-autopilot of RT2 to do my burns. And I don't like the imprecision of manoeuvre nodes combined with the imprecision of thrust control anyway. I want to get my probes into KEO orbits, and getting the orbital period exactly right using just your keyboard is quite impossible.

I got the equation from this website, in the propulsion section.

q is fuel consumption, and C is effective exhaust gas velocity.

C can also be rewritten as V_e.

Sorry about that.

_Edit:

_{I think Kerbal Engineer Redux also has the total burn time for a stage, you could use the right-click menu in the VAB and change the fuel in the tank to the dV you need, find the burn time, and put it back.}

Edited September 24, 2014 by MegaFlop10
Adding a bit of information.

[Empiro]

How exact do you want to be? For small burns like this (as in the the total dV is relatively small compared to ISP * 9.8), you can also approximate by assuming a constant mass to make things really simple. Take take thrust in kN divide by mass in tons, that's your acceleration in m/s^2. Then, divide dV by your acceleration to get an approximate time of burn. You can shave off a bit because you will be accelerating faster toward the end, but I find that this is usually pretty close because I often will throttle back toward the end of a burn so I don't overshoot.

[cantab]

Agreed with Empiro's suggestion. That will be fine for almost all purposes, especially as it strictly overestimates the time needed. It's what the game uses when it displays the burn time. Only if you're doing something extreme like a 5 km/s ejection or insertion burn are the errors likely to matter.