What is the optimal altitude for a TurboJet engine?

[Klopchuck]

Please, has anyone determined what is the optimal altitude for the TurboJet engine, when you take into account engine thrust, drag, etc.? I figure it's between 8,000-12,000 based on feel, but I haven't done any math or empirical study. Has anyone else? Thank you.

[Letum]

Depends on your thrust to drag ratio and the weight lift ratio of the wings.

The optimum altitude will change with different numbers of engines, different wing loading and different amounts of drag on the craft.

Also, do you want optimum fuel efficiency or speed?

[EndlessWaves]

You haven't specified what you're trying to optimise.

Are you asking what the maximum altitude is that you get full power at? If so then there isn't a single answer as thrust depends on both altitude and forward speed.

[Klopchuck]

I see now that my question was incomplete... I've just started to fly aircraft, rather than space launch vehicles. Specifically, I've been playing with some alternate designs for the polar challenge, which seeks to get from KSC to the north pole in the least amount of time using stock parts (and mechjeb) without going ballistic (i.e., fly).

In other words, I'm trying to optimize speed, but the amount of fuel is probably a factor too, since it increases weight and affects range.

Is this question better? "If two identical Turbojet-powered aircraft were racing, what altitude would be the fastest? Also, would the range be different?")

(Here's the reason I can't "help myself": I know where to go to get the maths for space (vis-via equation, etc.) but not flying. Where can I go to get the maths for figuring out thrust, fuel efficiency, and velocity?)

What's confusing for me, is when I fly in the 12k-14k range, just above the "thick" atmosphere, I notice the Efficiency of the TurboJet is notably lower, such as 0.62 at 14k. However, I seem to reach much faster speeds. I assume this is due to the thinner atmosphere reducing drag. Is this a a measure of thrust to fuel consumption?

Is atmosphere thickness in layers? I recall seeing that in a discussion on an earlier version, so I assume drag is a step-function. "Efficiency" as displayed when you right click the engine seems to be a linear function, so my current theory is the best altitude is probably just above the transition from one thickness to another.

(Other factors I assume will help performance in this challenge... I presume you want to arrive at the North Pole with zero fuel, since excess would be dry weight. I've also rigged an SRB for jet-assisted take-off (JATO) that is vectored to the North, so I don't have to waste fuel/time/speed launching east and vectoring my heading to the North)

[EndlessWaves]

Is this question better? "If two identical Turbojet-powered aircraft were racing, what altitude would be the fastest? Also, would the range be different?")

It would depend on the aircraft and altitudes, if the higher one had to be pointing almost vertical to sustain it's altitude then it would be a lot slower but if they were both cruising between 0° and 5° from horizontal then the higher one would be faster.

I think fuel consumption is fixed (assuming maximum throttle) rather than dependant on efficiency so faster is always better.

The meter is a bit misleading, atmospheric density is the continuous function 1.2223*exp(-alt(m)/5000) but I've not come across equations for drag, lift and jet engines airflow for 0.16, although it does seem to be generally agreed that drag is dependant on mass rather than cross section.

[cardgame]

I think 14.2km is the sweet spot, but I don't have any hard numbers to back me up.

[G Addict]

My default altitude is 12km, as this seems to work well for all sizes of plane. As a rule, light planes with a lot of wing area are best going high, while ones with less wing or more weight will prefer lower altitudes.

[Klopchuck]

Found some Maths:

http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node70.html

This will take me awhile to unpack. I'm not a physicist or engineer, but I spent last night at KSC.

[ferram4]

Klopchuck, that math would be good if not for the fact that lift in 0.16 goes with velocity instead of velocity squared, as well as mass erroneously appearing in the drag equation, so the range and endurance equations there won't work.

As to your earlier point about the efficiency, I think that that is the percentage of maximum thrust that the engine is putting out, and I believe fuel consumption is constant for a throttle setting. Which means that you want to go as fast as possible at full throttle, regardless of efficiency and altitude.

As for design ideas, I'd suggest these:

Start with only two engines. More engines suffer from diminishing returns, since you double fuel consumption but only increase velocity by a factor of 1.4.

Use more wing than you think. That helps in keeping a low angle of attack at cruise, which makes designing the engine attach angle easier.

Angle the engines so that they are horizontal in cruise. Any thrust pointing down doesn't increase speed, and the wings should be keeping the plane up.

With good design, you should be able to make it to the North Pole on ~6 Mk2 fuselage tanks and at ~450 - 500 m/s. Climb fast up to ~8k-10k, then reduce your climb rate and make sure that your engines don't asphyxiate up there.

Hope this helps, good luck with your design!