How scaled up or down could a jet fighter be made and still fly?

Factual Questions
1

Inspired by a silly and random thought I had today.

If you took a fighter plane (for example the F-15E Strike Eagle McDonnell Douglas F-15E Strike Eagle - Wikipedia) and were able to scale it up or down at what point would it be too large or too small to fly under its own power and without adding or removing anything from the standard design? (assuming it is being flown remotely of course).

Without using new materials, just making them large or smaller as appropriate. I assume for example at some point the increasingly large engines or small engines can no longer lift the airframe etc?

Thanks in advance! :slight_smile:

2

Aircraft are finely tuned for the size of the components. A jet engine twice as large may not spin as fast. But you doubled the size of the jet engine - did you just double every component, or use a new engine engineered to be that size? For fancy jet engine you probably still need the tolerances; can you just double the fuel injection nozzles? The blades cannot spin at the same speed as the smaller version, do they have the strength to stand up to 8 times the weight and twice the centrifugal force? and so on…

The key issue is the square-cube law. Lift would be a function of wing area (and speed, etc.) so square-based. Weight is a function of volume, so cube-based. Double the dimensions of an F15 and it has 4 times the wing are, but weighs 8 times as much. And if the engines can’t produce enough thrust, you’re not going too fast… and to fly with smaller lift area for weight, you need to go faster.

The wild card is the jet engine. then you get into safety issues. The less wing lift, the higher the stall speed, so the faster you have to go to take off or land - and the longer the runway you need. the space shuttle was basically a flying brick - it landed so fast, about 220mph, needed a 3-mile runway even with a drag chute (you could not see one end from the other end of the landing strip due to the earth’s curvature. )

So it depend on your definition of “fly”. Strap a solid fuel booster on and almost anything will get up in the air. you just may not want to be in it.

Since I’m not an aeronautical engineer and I’ve only flown 2- and 4-seat prop planes, I’m going to make a rough guess that beyond 50% larger you are going to have too many problems for it to be practical. Look at the various sizes of aircraft and their configurations. fighters tend to be close to the same size. A similar craft that’s much bigger, would be the B1 bomber, then the Concorde (which is not as big as you think. You can walk through one at the the Intrepid museum in NYC) . beyond that, they all tend to look like the airliners with big long wings and supersonic is not practical. It takes a helluva lot of power to punch through the sound barrier.

(One stat I read was it took eight times the power to double the speed of an aircraft, and that was subsonic.)

3

that goes for pretty much any vehicle. the force from drag goes up with the square of the speed, and the power required to overcome it goes up with the cube of the speed.

4

md2000, if you double the dimensions of the F-15, you also have 4 times the drag but 8 times as much internal space for fuel and engines. And it does not weight 8 times as much - a jet fighter is not like a living creature. Internal cavities are not required to be filled with tissue, they can just be empty. Most aircraft are actually hollow shells, lined with internal ribs.

Because of the extra space for fuel, the up-sized F-15 would probably fly faster with more range. However, these internal rib supports would now be longer, and thus more vulnerable to stress, so ‘dogfighting’ might be less practical in one.

But you could possibly upsize a jet fighter, making it the size of a bomber, with even greater speed and more range. It would need a 360 degree laser turret, used to shoot down missiles and swat enemy fighters that try to approach it from ‘behind’.

The problem with such a design, the reason why jet fighters are small, I think are :

a. A larger aircraft is much easier to see on radar, and easier to hit with a SAM. Bigger target means that Soviet era SAMs can be less accurate and still get a solid hit.

b. A much larger aircraft can’t be carried on a carrier. This means that you can’t reuse designs - you would need a completely different aircraft for the ‘carrier variant’ for the aircraft.

c. Apparently, the much bigger supersonic capable-engines you’d need for a larger aircraft are much more complex and expensive to develop at larger sizes.

d. A larger aircraft like this would guzzle fuel. It would cost more to operate and more to construct, meaning less could be made for a given amount of defense spending.

e. 360 degree laser turrets are just now approaching feasibility. There’s only a handful of such weapons deployed, and they are not yet megawatt class. Current jet fighters were designed at least 15 years ago, if not longer.

f. War is about attrition. Lose a bigger, pricier aircraft in combat, and your losses are bigger. This is why the optimal air superiority fighter is probably the opposite. Probably you want to downscale and develop a drone aircraft that is supersonic that is the minimum size and cost to complete the mission. Then build a bunch of them.

**g. Stealth is a function of size. Stealth coatings and aircraft shape only reduce radar cross section from it’s original cross section, they don’t eliminate it. So the bigger the aircraft, the less effective any efforts to make it stealthy will be. This is probably the biggest factor, actually, as stealth is something the U.S. military has used to great effect in the last 30 years.
**

But, if cost were no object and you wanted to make the most awesome single fighter aircraft feasible, flown by 1-2 crew, you’d build bigger. Concorde size. Multiple laser turrets, higher speed and range than anything we have now. It would be able to burn enemy aircraft out of the sky at 150 kilometers away and would deal with SAMs by just shooting them all down. You’d fly these things in squadrons, their laser fire being used to protect each other.

5

Remember that wing area (and all other areas) scale with the square of the linear dimension, while mass scales with the cube. Engines surprisingly linearly photo-scale just fine with everything working properly aerodynamically, although various mechanical issues come into play. So thrust will scale with exhaust area, or by the square of the linear dimension.

Going smaller in size means at some point that you can’t get enough lift or enough thrust to create lift at least equal to mass. Details vary, but for an F-15 you have to reach that point not much below 1:1. Things look better aerodynamically if you scale up, but various stress and deflection problems as the thing gets softer and flappier all over mean you can’t get much above 1:1 either.

6

Structural considerations also have scaling issues. The stiffness and bending strength of a component scale with the cube of its thickness in the direction of bending; if you reduce the height of a beam by 1/2, it will have 1/8 the rigidity and 1/8 the bending strength of the original-sized component. This matters for all sorts of things, including compressor/turbine blades, the metal skin of the airframe and the overall G-tolerance of the aircraft. Whereas flutter may have been carefully eliminated from the original-scale aircraft with considered application of mass and rigidity, but in a scaled-up/down design, the mass, rigidity, and aerodynamic properties may reintroduce flutter within the desired operating envelope.

Airfoils (the shape of the wing’s cross section) behave differently at different scales, too. If you scale a plane up/down without changing the basic airfoil shape, you may find that the center of lift is in an unexpected location, which might just require extra downforce from the horizontal stabilizer to keep the nose up, or it might render the new plane completely unstable.

7

Isn’t this all easier to understand when you know what all scale model builders understand?

Air, water & gravity do not scale so aircraft do not 1:1 scale

Neither do boats.

Neither do floor joists.

At least not on my scales. Yours might work better. :wink:

8

They do make scale model RC jet fighters that are arm sized. They won’t be piece for piece actual shrunken designs, but that is because of cost and no real need to do so.

Dennis

9

The OP was pretty specific:

So no design changes, no new materials. Every linear dimension of every component gets scaled to the scale of the new aircraft, e.g. plane is 2X original size means skin is twice as thick, engines are twice the diameter.

if OP meant something different, or wants to relax the constraints, he should chime in here.

10

That’s irrelevant – a hollow shell that’s twice the linear size of another hollow shell still weighs 8 times as much, assuming everything remains in proportion, including the thickness of the shell.

11

Scaling up or down would fail very quickly because of electronic components. It doesn’t take very much change, microns really, for a solid state device to suddenly not operate if, for example, a capacitance value inside a circuit on a microchip is changed. Jet fighters won’t work without their electrical/computing systems.

12

Exactly. If we assume just take the drawings and specs and multiply by X% - the yes the square-cube law applies. But then so do the secondary effects as mentioned. Double - The weight cubes, 8 times, but the wing main spars cross section is only 4 times as large, so the strength for pulling high turns - you cannot pull as many G’s. The skin will be twice as thick, but twice as far between the wing spars front to back…

The problem is that everything has been fine-tuned for the selected size - "It’s this big, therefore it’s this heavy, therefore it has this wind resistance and this weight and the spars have to be this thick, at this speed the skin has to be this thick, and the engine has to put out this much power to go this fast, and will so consume this much fuel so for optimum flight profile need this big a fuel tank, which we can squeeze into here… Change anything significantly and the whole result cascades or performance gets much worse quickly.

I remember seeing something about some mechanics shoe-horning a Ford V8 into an old Volkswagen Beetle - of course, the transaxle wasn’t designed for it, accelerate too fast and you may just strip the gears. The front will lift up like a drag racer (which may have been an intended result). Need new shocks to handle the rear weight. And so on…

Each design decision is predicated on the parameters provided. As I said, if you want to scale up the geometry but re-engineer - there’s a reason why the Concorde or B1 or Vulcan does not look like a scaled up fighter. (Note wing area is significantly larger as a proportion of body on those…)

13

It’s more complicated than that. Bending resistance is proportional to the width of a beam’s cross-section, but it’s proportional to the cube of the height of the cross section. So if you double every linear dimension of a beam’s cross-section, the bending strength increases by a factor of 16.

But the bending moment arm (in this case, the lateral distance between a wing’s center of lift and the wing root) is also doubled, doubling the bending moment (assuming a fixed value of G).

And the aircraft’s weight has increased by a factor of eight, increasing the bending moment a further eight-fold (again, assuming a fixed value of G).

So the 2X wing spar has 16X the strength of the original, but for a given G it also has 16X the bending moment. which neatly cancels out.

14

Not quite true for fighters.

Yes, a transport or bomber has a lot of empty space inside the shell. Because the whole and entire purpose of the machine is to put stuff in that empty space and carry that stuff someplace.

The empty space inside a normal sized fighter is measured in low numbers of cubic inches. Everything *is *jammed in there nearly as tightly as your own viscera. The advent of enclosed missile / bomb bays for stealth has injected some empty space, but even then the bays are designed to just barely enclose the munitions. And subsequent munitions are designed to use all the empty space.

The only bulk area inside a fighter skin that’s not full of equipment is either fuel tankage that starts out full of fuel, or air intake tunnel that’s full of air. Both of which are designed to be as small as possible to accomplish the mission.

15

Yes, thank you - as I said in the beginning, third-order complexity considerations begin to dominate the design equations. Nothing is simple. Every piece of the design is a result of the factors from other pieces of the design.

Consider for example, scaling up a V8 engine. double everything, yes the cylinder size goes up by 8, the compression is the same - but the fuel injection nozzles only have 4 times the area; the fuel pressure is the same. Will you get enough fuel into the cylinders in time? Will it spread/vaporize fast enough to give a full combustion and produce twice to 8 times the power? Would piston rods with 4 times the cross section area handle double the piston driving force per square inch? (I knew a budding mechanic who shaved his cylinder heads to improve vehicle performance by increasing compression - within a month he’d put a rod through the block.)

Every design is a compromise of need versus capability. Those tiny drones work just fine; the square-cube law makes it very difficult to scale them up to passenger size. I can drop a mouse from 10 times its height (length) and it just walks (runs) away; humans, not so much…

16

Agree completely with your point. Which you made very thoroughly up-thread as well as just now. I didn’t try to rehash that since it seemed well-covered by you and others.

My quibble was entirely with SamuelA’s blithe assumption that there’s lots of empty space inside a current full-scale fighter and therefore that brute mass wouldn’t scale at square-cube. I should have trimmed my snip a little shorter to better isolate what I was aiming at.

17

Thank you for the answers everyone, its really interesting reading!

18

Yes exactly. I don’t know why he said that. Even sheet metal or pipe - double ALL dimensions and you octuple total volume and weight. Selectively only double SOME dimensions, (i.e. not sheet metal thickness) and now you are re-engineering and anything goes.

19

That was the first thing that came to mind for me: even a tiny scaling is going to screw up the microchips. 10% larger and your signals take >10% longer to get anywhere. 10% smaller and leakage current may kill you.

Which sorta leads into another problem: how far down to we go? Modern microchips are at a scale where atoms matter. You can’t scale those down. For example, the gate dielectric layer on a modern chip is perhaps 6 atoms thick. Which means it’s actually impossible to scale down by, say, 10%. And scaling by 50% would prevent the chip from functioning.

20

For scaling down, keep in mind the purpose of these vehicles is not simply to fly fast, but to deliver ammunition to a target. Make them smaller and they will hold less ammunition, and here the square-cube thing is working against you. Even if you had pure energy weapons, the batteries to store that energy take up space.