Most efficient speed for jets?

[pincushionman]

Is there an engine setting which is most efficient to fly at, and how can it be determined? In the real world, aircraft don't cruise at engine redline for a number of aerodynamic and engine-performance reasons, and to allow flexibility for maneuvers. Is there a way to estimate the most efficient cruising speed for a jet in KSP?

[Hodo]

If you are running FAR and AJE you wouldnt cruise at 100%. Most of the time I cruise at 40-50% throttle in FAR when I am not trying to go into space.

Sometimes I don't even have that much throttle, on some of my combat fighter designs I cruise at 25% throttle because that will keep them at mach 1.5 pretty easily.

[MarvinKitFox]

Under stock KSP aero model:

Each jet engine type, and to a somewhat lesser extent each plane implementation of them, has a different optimal speed *and altitude* for best efficiency.

(efficiency defined here as most distance per fuel)

Based on recent experience with doing career temp/report missions all over Kerbin, using basic jet engines..

With heavy fuel load, optimal range was with TWR of about 0.4, at altitude of 8000m. Speed about 220m/s

With very low fuel load, optimal range was with TWR of about 0.25, at altitude of 10500m. speed about 315m/s

Anything under 6000m forces you to fly so slow that you may go grey before completing your mission.

Anything over ~16000m snuffs a basic jet. Actually, over 12000m they suffer bad ISP losses.

In short: Fly slower than terminal velocity, to reduce drag. Slower is more efficient, as long as you are using wing lift not vectored thrust to stay up.

Fly as high as your engines are comfortable, to reduce drag.

Use as low a throttle setting as you can possibly manage, and still maintain your altitude.

Take each of these to an extreme, and you end up with something that cruises at 12000m, at 35m/s, capable of circling the word 5 or more times.

[Laie]

First off, some data sheets:

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

Due to the peculiarities of stock aero, the most fuel-efficient way of moving about is always as fast as possible, as high as possible. You may burn twice as much fuel per second at 15km compared to 5km, but you'll also move at least three times as fast.

[KerikBalm]

flying at 2,000 m/s at 50km is basically in orbit, and you can go very very far with no fuel use.

KSP turbojets are most efficient at 1,000 m/s, due ot their velocity curve. They produce 2x as much thrust for the same fuel consumption relative to a velocity of 0.

Next is the ISP curve for atmosphere.... at low altitude, they have a horrible 800 ISP, going up to about 2500 ISP at something like 5 km, then back down to 1200 ISP as the air pressure decreases to vacuum conditions.

.... so the engine itslef is most efficient at 1,000 m/s at 5km... but the drag losses at that speed are extreme.

Its worth nothing that in Real Life - Lift/Drag remains relatively constant as velocity changes (until you get into higher mach numbers). This also means that L/D is pretty much constant across different air densities, as a lower air density just means you must travel faster. So for a given angle of attack and wing shape, your efficiency is the same regardless of what speed you travel at (but AoA changes do affect this, so to travel faster at the same AoA would require a different design with a higher wing loading - so for the same mass, just smaller wings)

- but not so in stock KSP aerodynamics, L/D gets arbitrarily low as velocity gets aribtrarily high, as drag follows a V^2 relationship, but lift is proprotional to V (not V^2).

Double your velocity, halve your L/D.

However, as I noted at the start... often, you don't really need much lift, because due to the small radius of Kerbin, you get very close to orbital velocity, and you don't need to generate that much lift at all.

ie, the karman line http://en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_line

is quite low:

around this altitude, the atmosphere becomes too thin to support aeronautical flight, because a vehicle at this altitude would have to travel faster than orbital velocity to derive sufficient aerodynamic lift to support itself (neglecting centrifugal force).

Since we can actually fly near this line in KSP (airbreathing engines don't work at those speeds and altitudes in real life), its actually most efficient to fly up around there.

But thats like saying the most fly efficient way to fly in terms of cumulative distance travelled, is to go into orbit.

But in KSP, for flights where "centrifugal force" does not significantly reduce the amount of lift needed, then the most efficient way to fly is to fly as slowly as possible because of the funky lift equation, which means you want the basic jet, and it will take absurdly long to get anywhere like that.

[numerobis]

- but not so in stock KSP aerodynamics, L/D gets arbitrarily low as velocity gets aribtrarily high, as drag follows a V^2 relationship, but lift is proprotional to V (not V^2).

Double your velocity, halve your L/D.

While true, your lift:drag ratio is greater than 1 for all wings, for all speeds below escape velocity.

I may spend lunch calculating, for a given plane:

for each altitude,
 for each angle of attack,
  for each throttle setting,
   find the speed we reach at equilibrium between drag and thrust.
   is vertical velocity zero under those conditions?  If so, store this data point.
among all data points we stored, which one has the least fuel consumption per distance?

My gut is that the best cruising altitude will be high and fast, even for basic jets. And it will increase as you burn off fuel.

[numerobis]

It took me longer than lunch, but I implemented the pseudocode above. So now I can write the following incantation -- and you can too if you download the KSP-scripts

from planeDesigner import plane, part
import lift, jets
p = plane(   
        # cockpit
        part(None, Cd=0.008, extraMass = 1),  
        # two short fuel tanks, two-thirds empty (1.5t capacity each)
        part(lift.mk2FuselageShort, n=2, extraMass = 0.5),
        # intake and jet
        part(jets.ramAirIntake), 
        part(jets.turbojet),
        # wings and control surfaces
        part(lift.deltaDeluxe, 2),
        part(lift.avr8, 2),
        part(lift.deltaDeluxe, 2, AoAdegrees = 60),
        # vertical stabilizer; it's a delta-deluxe but edge-on, so there's no lift or drag
        part(None, Cd = 0, extraMass = lift.deltaDeluxe.mass),
        )
p.optimizeFuelConsumption(verbose = True)

All but the last line are about defining my plane: two short Mk2 fuselages with fuel (here I look at how the plane works when it's consumed two thirds of its fuel), the lowest-drag cockpit, a ram air intake up front and a turbojet in the back. I use a pair of AV-R8 for elevators at the back, a pair of delta-deluxe at the center of mass for roll, and a second pair of delta-deluxe at the top of the fuselage, tilted to have a 60-degree angle of attack so they generate a lot of lift. Then there's a delta-deluxe for a vertical stabilizer (I turn off all its controls).

The last line recommends what altitude, pitch, and throttle setting to fly at. My code ensures that the plane will be level with those settings (i.e. net forces are zero), and it chooses the combination that minimizes fuel consumption per distance.

What it looks like is a long computation that slowly spits out lines one by one, such as:

Testing altitude 8000, best so far is 6000 with (28, 0.05438232421875, 88.11264038085938, 0.000353374694661201)

This line says that the best solution it's found so far is to fly at 6,000m at a pitch of 28 degrees with throttle at 5.4%. Then you'll be going 88 m/s and you'll consume 0.000 kg per m you travel. It helps to rewrite it as something like 35 kg per 100 km.

After crunching for a while it will output something more legible like:

Fly at 25500 m altitude, pitch 46 degrees, throttle 0.146, to achieve 1192.61 m/s using 0.0286144 U/km

So there you go -- with turbojets you should fly high and steep. At that altitude, I think 14.6% is full throttle.

What's interesting with the turbojet planes I've tried is that there's an ideal point around 6km to 6.5km at very low throttle, then performance falls until about 15km. After that, performance rises again, and basically it's all about going as high as you possibly can, even if it requires pitching up steeply to maintain that altitude.

My code assumes you want to stay level. I'm doubtful that's this is actually optimal -- instead, you could bob up and down. That way you put out a lot of thrust at low altitude with marginally better Isp, then you punch through to high altitude where the air is thin. But it's certainly more restful to just stay at a fixed altitude.

- - - Updated - - -

Oh, and if you replace the turbojet with a basicjet you get the advice:

Fly at 3000 m altitude, pitch 30 degrees, throttle 0.020, to achieve 46.91 m/s using 0.0417307 U/km

So the basic jet is much slower *and* burns rather more fuel -- at least on this plane.

[Anquietas314]

numberobis: A possibly more efficient strategy with turbojets (particularly with a small, high TWR plane) is to launch the plane out of the atmosphere into a suborbital hop to cover very large distances (using the turbos). It's not quite what OP was after, but in my experience it uses way less fuel than flying through the atmosphere to get there, although admittedly precision's a bit of a tricky issue because of the spin up/down times on the jets.

[numerobis]

The forum merged my update for the basic jets, which obscures my last paragraph that says basically that -- level flight is what my code assumes, but that isn't necessarily the most efficient.

[Anquietas314]

The forum merged my update for the basic jets, which obscures my last paragraph that says basically that -- level flight is what my code assumes, but that isn't necessarily the most efficient.

Oh I did see that, it's just that your suggestion was a little different; I'm saying you should (in my experience) punch through not only to high altitude, but completely out of the atmosphere (i.e. > 70km)

[numerobis]

Ah, OK, sure. I'm sure there's an analyzable tradeoff between the energy to push yourself way high versus the savings from the lack of air.

For the OP: if you want to fly level, seems that the most efficient at low altitude is very low throttle -- just enough to just barely stay aloft. This makes you go agonizingly slowly. On the plus side, that makes you very maneuverable.

For turbojets, you do better yet by flying as high and fast as possible. You're still at low throttle, but that's because you're low on air. But then your turning radius gets huge.

[Anquietas314]

For turbojets, you do better yet by flying as high and fast as possible. You're still at low throttle, but that's because you're low on air. But then your turning radius gets huge.

For OP's sake it's worth mentioning that with a pretty reasonable number of intakes (more than in your code) you can fly quite a bit higher than 25km while maintaining (actual) full throttle. My cargo plane has 10 of the structural ones per engine (not terribly efficient, but it's meant to look good) and it lasts until about 35km before it needs to start throttling back - but by then you usually want to be using the engines in rocket mode (rapiers for easy design...) to get out of the atmosphere quickly anyway.

[numerobis]

Yeah, I'll need to track down exactly the specifics of how the air-starved engines work. You get more thrust by being at full throttle and air-starved, but you can stave off flame-out by throttle back; it's confusing to me.

[Anquietas314]

Yeah, I'll need to track down exactly the specifics of how the air-starved engines work. You get more thrust by being at full throttle and air-starved, but you can stave off flame-out by throttle back; it's confusing to me.

Going by KER's readout (for one engine - it derps badly for multiple ones), turbojets hit flameout at 1000% intake air usage - that is, trying to use 10 times more than is actually available; for rapiers it's more like 350%. Not sure if that helps at all. Usually my designs are very close to the speed limit of both engines before they actually reach those figures though, so naturally the thrust readouts can't really be compared in any useful way without knowing exactly how speed (at a fixed altitude) maps to thrust :/. Not to mention KER's thrust readout for jets is way off at high altitude.

[numerobis]

At full throttle and full thrust limiter, flameout occurs at 0.1 for turbojets, meaning they're getting 10% of the air they request (it's in the cfg file). That's about the only thing I understand.

It's the interaction between the throttle, thrust limiter, and air availability that confuses me. What happens when you pull back throttle *and* you don't have enough air to be at full throttle? How should you set things up to have maximum thrust? Those aren't clear to me.

The 'throttle' that my simulation talks about is based on a simpler model: what fraction of maximum fuel flow should you aim for? Then it's up to you how to do that with the throttle and thrust limiter.

Anyway, to answer your question I added two radial scoops to my example and got the following readout:

Fly at 28000 m altitude, pitch 59 degrees, throttle 0.147, to achieve 1265.70 m/s using 0.0273117 U/km

Really does seem to be that turbojets are all about flying high and steep. Can you imagine if your airliner was pitched up 60 degrees?

[Anquietas314]

Really does seem to be that turbojets are all about flying high and steep. Can you imagine if your airliner was pitched up 60 degrees?

In fairness, (RL) airliners don't fly at mach 15 (~half orbital velocity) either . Or mach 3 for that matter, though I think concord might have been able to back in the day.

[numerobis]

Indeed. I wrote most of this code while bumbling about at 10km at about 300 m/s. If only I could have been going 1200 m/s instead. I'd have been home in time to catch the bus rather than needing to hail a cab from the airport!

That does remind me that I assumed you're at the equator going due East -- unlike what was the case with my flight. Any other latitude and heading will have less of a boost from sidereal rotation.

Edited January 4, 2015 by numerobis