Ground Speed and Fuel Consumption Rate as a Function of Altitude?

[Feldhaus]

Hey!

Assuming I'm flying a plane in KSP with a constant weight horizontally at 100% thrust, is it possible to plot the ground speed or the fuel consumption rate (in units per second) as a function of the altitude?

I want to use Ground Speed because the "Surface Speed" is measured at the altitude of the aircraft and because of the curvature of Kerbin it is higher than actual Ground Speed. At 10,000m up the difference is about 1.6%. For a more accurate number we need to convert "Surface Speed" to the actual Ground Speed, I came up with this equation:

V

Ground

= ( V

"Surface"

* r

Kerbin

) / ( r

Kerbin

+ L

Altitude

)

The equation for fuel consumption in tonnes/s is this:

Fuel Rate (t/s) = Thrust / ( g * I_sp )

Fuel Units are measured in liters and the density is 5 kg/l so we get this Formula for Units/s:

Fuel Rate (Units/s) = ( Thrust / ( g * I_sp ) ) * ( 1000 / 5 )

or Fuel Rate (Units/s) = ( Thrust / ( g * I_sp ) ) * 200

That's as far as my knowledge goes, I hope you can help!

Thanks!

Edited June 23, 2014 by Feldhaus

[Red Iron Crown]

Assuming I'm flying a plane in KSP with a constant weight (using infinite fuel) horizontally at 100% thrust, is it possible to plot the ground speed or the fuel consumption rate (in units per second) as a function of the altitude?

If you're using infinite fuel your consumption rate is zero at all altitudes.

[Feldhaus]

If you're using infinite fuel your consumption rate is zero at all altitudes.

I know, I should say the fuel consumption rate if we assume the weight is constant or the initial fuel consumption rate at 100% Fuel.

I want to know what the initial fuel consumption rate and Ground speed is when I fly up to Altitude X with and then turn off infinite fuel

[Red Iron Crown]

Jet engines or rockets? It's a bit simpler with rockets, more complex with jets.

[Feldhaus]

Jet engines or rockets? It's a bit simpler with rockets, more complex with jets.

Jet Engines. In my specific case I'm using the Basic Jet Engine. I want to compare the fuel efficiency of a plane with different numbers of Engines in "Meters per Fuel Unit" which is Ground Speed (m/s) divided by Fuel Rate (Units/s).

I already made some manual measurements but I'm curious if this can be expressed as a function of the altitude.

These are my measurements:

"MFU" is Meters per Unit of Fuel (Ground Speed divided by Fuel Rate)

[Red Iron Crown]

It's going to be complicated to do theoretically rather than empirically, because thrust is going to vary based on the number of intakes at higher altitudes, and the drag of the aircraft is a factor, too.

There are some parameters in the part.cfg that should help with the calculation, for the standard jet engine they are:

	atmosphereCurve
 	{
		key = 0 1000
		key = 0.3 1800
		key = 1 2000
 	}
	velocityCurve
	{
		key = 1000 0 0 0
		key = 850 0.2 0 0
		key = 0 1 0 0

The atmosphere curve is used to determine Isp at differing altitudes, but I don't know the function that is used to derive it. I believe the velocity curve is used for the thrust calculation, but I'm not 100% sure of that.

[Laie]

I suspect you're about to recreate this work:

http://forum.kerbalspaceprogram.com/threads/82157-A-detailed-look-at-Kerbal-s-jet-engines

(nothing wrong with that, btw: it's a good idea to re-check the old lore from time to time.)

Edited June 23, 2014 by Laie

[Red Iron Crown]

^^ That's a great resource.

[Feldhaus]

It's going to be complicated to do theoretically rather than empirically, because thrust is going to vary based on the number of intakes at higher altitudes, and the drag of the aircraft is a factor, too.

There are some parameters in the part.cfg that should help with the calculation, for the standard jet engine they are:

	atmosphereCurve
 	{
		key = 0 1000
		key = 0.3 1800
		key = 1 2000
 	}
	velocityCurve
	{
		key = 1000 0 0 0
		key = 850 0.2 0 0
		key = 0 1 0 0

The atmosphere curve is used to determine Isp at differing altitudes, but I don't know the function that is used to derive it. I believe the velocity curve is used for the thrust calculation, but I'm not 100% sure of that.

Thanks for the clue! Yes, I assumed that the function would depend on some constants like mass, air drag and engines that are individual for the vessel, we just have to figure out how these constants relate to altitude.. Theoretically this should be possible, shouldn't it?

I suspect you're about to recreate this work:

http://forum.kerbalspaceprogram.com/threads/82157-A-detailed-look-at-Kerbal-s-jet-engines

Well I want a function to describe one of those graphs, "Fuel flow relative to altitude", and those are empirical measurements, not the theoretical results of a function..

[Red Iron Crown]

Intake air is going to be a factor, too. At the link Laie posted I saw this gem:

The fuel flow is only relative to altitude. That means that a fully spooled up Turbo Jet at maximum throttle at a certain altitude always uses the same amount of fuel per second, no matter how much thrust it produces.

It should be possible to calculate what you're looking for algorithmically, after all, that's what the game itself is doing.

[Laie]

Intake air is going to be a factor, too.

[Red Iron Crown]

I don't think so. One of my spaceplanes starts snapping for air at 28km, yet thanks to Kasuhas work regarding fuel and air flow, it will keep going without flameout for much longer. Fuel consumption per second increases slightly even while the engine is being starved down to 50% it's desired air.

That's sort of my point, when it's starved for intake air the fuel consumption remains the same while the thrust (and presumably speed) drops off.

[mhoram]

You can also find some info in this thread. Warning: contains physics and code.