How far can my plane fly?

[Streetwind]

I'm intimately familiar with rocketry, but planes have always been something I found profoundly unintuitive. I suppose I'm just not a plane person. Still, occasionally I end up making an effort to poke at them, and yesterday was such a day.

While doing a few test flights, it occurred to me: how do I figure out how far my plane can fly? I have KER's dV readout, and that's fine for a rocket, but a plane doesn't really work that way, does it. For instance, I could fly at a higher altitude and lose 40% of my engine's Isp, but reach twice the airspeed - so even though the dV readout just crumbled, my total distance covered will actually be higher in this regime!

This is obviously a complex problem that's highly dependant on the specific conditions, so I'm not asking for mathematically precise solutions or anything. I'm just curious how the "plane pros" go about estimating the cruising range of their aircraft. For instance, if you have the Fine Print addon installed, you can get contracts to fly past a number of waypoints on Kerbin's surface at specific altitudes. These waypoints are not always close to KSC, or even to each other, so having a way to at least roughly eyeball the atmospheric cruise range of your aircraft could be very useful.

Edited November 25, 2014 by Streetwind
Marked as Answered

[The_Rocketeer]

I don't think I'd describe myself as a "plane pro", but I do have a few relevant thoughts.

In rocketry (in vacuum), the formula for calculating delta-V is fairly straightforward - you have a fixed amount of thrust per fuel (ISP), a fixed amount of dry mass and a variable amount of fuel mass. Calculating delta-V is just a matter of those 3 variables (only one of which really varies during a flight). Even delta-V for an atmospheric launch is fairly easy to calculate because only the slowest, lowest part of the ascent will be affected significantly by atmosphere, and assuming a terminal velocity ascent it's not too hard to work out how much drag you'll experience for how long. In other words, ascent delta-V doesn't vary very much, on the grand scale, from craft to craft.

For an aircraft, though, you aren't flying straight up to space, and therefore quickly escaping the delta-V cost of ascent. Instead, you're flying through the atmosphere, always experiencing drag to greater or lesser extent. You also have an added variable - lift - which is dependent on speed, and therefore on the balance of thrust and drag. Lift works against mass, basically converting some of your thrust into negative mass (assuming you're flying straight and level). In vacuum, any delta-V you use is retained as orbital energy (unless you burn retrograde). In atmosphere, this is like having a retro-thruster with infinite fuel that burns harder against you the faster you go, so the more delta-V you spend, the more quickly it's dissipated.

Consequently, your atmospheric delta-V calculation becomes very much more complicated, and the answer changes rapidly depending on your situation - high and fast has far more delta-V than low and slow, but a climbing plane has less delta-V than a descending plane. Complicated, no? Therefore it doesn't really make any sense to use delta-V to calculate aircraft range, and you might as well just fall back on the old-fashioned measures:

Fuel-time: How long you can run your engines on full throttle before you run out of fuel.

Operational ceiling: How high can your plane fly without running out of lift or thrust (due to low air/intake pressure).

Maximum speed at ceiling: How fast can you fly at peak altitude. This will depend on your drag coefficient at the air pressure of your ceiling.

(Note: it is possible to design a plane that can overcome these limitations - this is the basic design principle of a jet-powered spaceplane.)

Maximum speed * maximum fueltime = maximum distance (usually called range).

This will always be an overestimate as it doesn't include fuel used to climb and accelerate (or descend and land). There are ways to calculate optimal climbrate and therefore climbing time and fuel consumption for a particular design, but realistically it's probably not worth it.

As an after-thought, a little under half of your maximum range there's what's called the Point of No Return (PNR). This is the point at which, if you're not already half way to target, you should turn back or else you won't make it to target on your remaining fuel. If you are trying a circumnavigation, if you get to the PNR and you're not half-way round yet, your plane isn't going to get all the way round!

Edited November 25, 2014 by The_Rocketeer

[steve_v]

If you're running FAR, it's calculated for you in the flight data window

[Streetwind]

Fuel-time: How long you can run your engines on full throttle before you run out of fuel.

Operational ceiling: How high can your plane fly without running out of lift or thrust (due to low air/intake pressure).

Maximum speed at ceiling: How fast can you fly at peak altitude. This will depend on your drag coefficient at the air pressure of your ceiling.

Maximum speed * maximum fueltime = maximum distance (usually called range).

This will always be an overestimate as it doesn't include fuel used to climb and accelerate (or descend and land). There are ways to calculate optimal climbrate and therefore climbing time and fuel consumption for a particular design, but realistically it's probably not worth it.

Hmmm... putting it that way, that does make sense. Using engine runtime instead of dV is a great idea. It'll make a test flight necessary, but hey, that's what KCT's simulation mode is for

If I understand it right, then I need to find the altitude and throttle setting at which the product of speed and fuel time is the highest, since thrust (and by extension fuel throughput) varies with speed, and Isp (and by extension fuel throughput) varies with altitude. And that defines the probable maximum cruise range the design can manage. Or, if I have a prescribed altitude, such as for the contract waypoints, I can find out if the plane can make it while holding that altitude or if I need to experiment with the throttle or with climbing between waypoints.

That helped me improve my understanding of planes and jet engines, thanks!

If you're running FAR, it's calculated for you in the flight data window

I suppose I should start looking at that, shouldn't I. I keep forgetting that FAR has a UI of its own.

[Wanderfound]

Engine runtime doesn't really do it either, though. If you want to travel long distance on Kerbin, the quickest and most fuel efficient way to do it is as a suborbital hop, with the engines shut down for a significant portion of the trip.

Once you've got some speed and altitude built up, it's not too hard to glide around Kerbin with no thrust at all. You bounce off the lower atmosphere like a rock skimming over a pond.

In FAR, anyway; stock aero planes glide more like bricks.

[The_Rocketeer]

That helped me improve my understanding of planes and jet engines, thanks!

Truthfully I'm relieved it even made sense - I've been up all night writing up a uni assignment! Still, glad to be of service

Engine runtime doesn't really do it either, though. If you want to travel long distance on Kerbin, the quickest and most fuel efficient way to do it is as a suborbital hop, with the engines shut down for a significant portion of the trip.

This is technically true, and in practice it is what I've done when using a turbojet aircraft. However, it does assume that you have the thrust and/or air-intakes to break atmosphere, or even continue to ascend much at all above thrust cut-off. Constantly speeding up and slowing down is more costly than maintaining an optimal speed, unless you can cut power just right to coast all the way back in.

Edited November 25, 2014 by The_Rocketeer

[Wanderfound]

This is technically true, and in practice it is what I've done when using a turbojet aircraft. However, it does assume that you have the thrust and/or air-intakes to break atmosphere, or even continue to ascend much at all above thrust cut-off. Constantly speeding up and slowing down is more costly than maintaining an optimal speed, unless you can cut power just right to coast all the way back in.

Quibbling rather than disagreeing (), but you don't actually need to reach space. The higher the altitude the better, but you can start the "stone-skimming" technique from as low as 40,000m. The friction is low enough up there that there is very little speed lost to drag, especially if you keep your AoA minimised.

It's basically the technique that the Silbervogel was designed to use: http://en.m.wikipedia.org/wiki/Silbervogel

You do want to be up around Mach 5 at the start, though.

Edited November 25, 2014 by Wanderfound

[Jovus]

For me, it's basically binary.

Basic jet engine - don't leave the home continent, and you'll be lucky to reach the farther edges of it.

Turbojet - circumnavigate Kerbin. Possibly multiple times.

[The_Rocketeer]

It's basically the technique that the Silbervogel was designed to use: http://en.m.wikipedia.org/wiki/Silbervogel

Appropriately for KSP, a craft that would have exploded if it had ever been tested. ()

But yes, you're describing the same effect that allows fish and dolphins to swim faster by leaping out of the water - they're still slower than a jetski though.

I think the optimal configuration is probably a compression-lift platform, such as the XB-70 was designed to utilise. This is more like a boat/jetski planing on the water than the dolphin leaping into and out of it. Of course, I'm talking hypothetically about a sustained flight - Kerbin is so small that truly sustained high-altitude flight just isn't necessary.