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I recently viewed on Youtube many videos of small and giant models of airplanes. In some cases they are small (for example an A330, 1 meter long) and in others they are huge (for example an A380, 5 meters long).

As far as I can see, the smallest ones seem to have electric engines (maybe fake jet engines in which fans act as propellers?) but the bigger ones seem to have internal combustion engines, even if I don't know how they run.

Anyway, the general impression is that even from a great distance it's obvious that they are models and not real aircraft. They are all too quick, too agile, make very short takeoffs, have very low inertia, make quick turns and so on.

Can you tell me why these handling differences exist in models that otherwise tend to simulate with great precision every other detail of the real aircraft (lights, shape, colors, fine details, landing gear, etc.)?

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    $\begingroup$ Very relevant discussion on Space.SE: Can a miniature Saturn V get to the moon and back? $\endgroup$ – dotancohen Feb 20 '17 at 17:35
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    $\begingroup$ tl,dr; Cube-Square law in effect. $\endgroup$ – RBarryYoung Feb 20 '17 at 18:08
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    $\begingroup$ Ask Reynold, if you have his number. $\endgroup$ – copper.hat Feb 20 '17 at 22:15
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    $\begingroup$ Another factor: If you're going to scale everything you should also scale your camera. Watch your model in slow motion and it will be more realistic. $\endgroup$ – Loren Pechtel Feb 22 '17 at 2:05
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    $\begingroup$ ^ If you watch model aircraft videos in slow motion they definitely tend to look more like the real thing. Also for real aircraft that kinda look like the way models fly check out some ultralight/stunt plane videos (and be amazed!) $\endgroup$ – Jason C Feb 22 '17 at 4:22
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It's partly inherent in the way things scale.

If you double the length of the model, then the wing area (length times width) increases by a factor of 4, but the weight and volume (length times width times height) will increase by a factor of 8 ... so doubling the size means halving the weight-to-lift ratio.

In the most extreme cases, a tiny model will blow away on a puff of wind, and a huge model (bigger than the real plane) can't take off at all.

I suppose you might theoretically try to make small models harder to fly, by adding extra weight.


The above is theoretically true but maybe nonsense in practice: it assumes that structural materials become thinner when the model is scaled, in reality the structure isn't even the same material.

So let's look at it another way:

  • A full-scale A380 weighs let's say 500 tons, length about 70 metres.

  • Decrease that to 1 metre model and the surface area has decreased by (70x70=) 5000.

  • So for the model to have the same weight-to-area as the full-scale plane, it would need to weigh (500 tons / 5000 =) 100 kg.

Your 1 metre model presumably weighs much less than 100 kg, therefore it has much less weight-to-area ratio. QED.


It's also important to consider the Reynolds number, which depends on the air's viscosity and density, and on the size and speed of the model. The Reynolds number affects turbulence, which is very important to a wing's lift (for an example of how even a tiny change has a large effect, see Can a sandpaper-thick layer of ice reduce lift by 30 percent and increase drag up to 40 percent?).

To get the right Reynolds number for a small model you must increase the density (e.g. pressure) of the air, or increase its speed. But given the ordinary speed of aircraft, you couldn't increase (scale up) the air speed because it would become super-sonic, which would change the scenario.

Based on this answer to 'Understanding the Reynolds-number scaling problem', and the comments below it, I think that a 1-metre model of a 70-metre A380 (so a scale of 70:1) might behave like the full-scale model if it were flown under the following conditions:

  • air density is scaled up, so 70 atmospheres of air pressure
  • lift and drag are scaled down, so:
    • weight of the model is 7 tons (instead of 500 tons)
    • thrust of the model is 4,000 lb (instead of 300,000 lbs), i.e. about 2 tons
  • air speed is realistic (e.g. 150 knots to take off)

Obviously this would be quite unusual for a model airplane1.

1Air liquifies at 60 atmospheres; and the model would need a specific density of about 100, i.e. 5 times heavier than gold or uranium).

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    $\begingroup$ I am wondering ... wouldn't it be necessary to flight "real" airspeeds if one would make model with increased weight and real wing loading? $\endgroup$ – Martin Feb 20 '17 at 12:32
  • $\begingroup$ Actually the Reynolds Number is the key to this question and it affects every body moving in a fluid, including boats in water (Hydrodynamics) as well as aircraft in the air (Aerodynamics). $\endgroup$ – Charles Bretana Dec 25 '17 at 23:14
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Model aircraft are generally built with much lower wing loading and much higher power to weight ratios. This can be done partially because they have no real payload, and do not have to fly for long durations.

Having a plane that is more lightly loaded and has more power results in the traits you mention. Also, being lighter means wind gusts and other turbulence will have a greater impact and result in more rapid directional changes.

I should also note that the extra power and lower wing loading is desirable in a model because a remote pilot does not have the same instrumentation and physical sensory input that is gained by being in the plane and helps to safely fly closer to the limits of the aircraft.

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The laws of physics are not scale invariant.

Area scales with the square of dimension while volume scales with the cube of dimension. Aerodynamic effects roughly scale with area. Mass roughly scales with volume. Inertial scales with mass. Moment of inertia scales with mass times dimension.

The end result of this is that the models have far stronger aerodynamic effects compared to their inertia. This makes them far more nimble than their real-world counterparts. OTOH the real-world aircraft are generally able to fly faster and further and have a better fuel consumption per ton-mile.

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    $\begingroup$ Not to mention that material strength usually roughly depends on area as well, so you can use much lighter supports that are needed in the full-scale plane. Most model airplanes are much lighter than a down-scaled plane would be, further reducing inertia and increasing lift. $\endgroup$ – Luaan Feb 22 '17 at 15:08
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    $\begingroup$ You might want to add that time scales inversely with the square root of linear scale. A quarter-scale aircraft performs its manoeuvres at twice the speed. $\endgroup$ – Peter Kämpf Feb 22 '17 at 21:35
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I'm not sure whether you are asking only about the physics involved, so hopefully this isn't too tangential - but one factor that's not really been touched on much is pilot input.

In addition to dealing with the disruptive influences that people have already mentioned, the pilot of a model would have to ignore its actual maneouvering capability and use a lot of restraint - very, very small and precise control inputs, unneccesarily slow acceleration, and so on - to achieve convincing scale flight behaviour.

With that approach (and in super-calm conditions) I think you'd be surprised at what can be achieved with large models - you've probably seen radio-controlled model work in movies without realising it. However outside of applications like that, there must be a strong tempation just to wang the model around, because flying is fun!

Of course you're unlikely to see much model flying in films now, since flying machines are one of the things that it's quite easy to render convincingly using CGI. But for a bit of historical context, there's a small but interesting gallery here featuring some of the model aircraft from the movie The Battle of Britain, which was noted for its outstanding model work (considering it was made in the sixties).

http://www.daveswarbirds.com/bob/models.htm

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  • $\begingroup$ Interesting alternative point of view. Thanks Mike! :-) $\endgroup$ – Luca Detomi Feb 23 '17 at 14:07
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It depends on the pilot, too. I have seen a guy fly a 5-foot wingspan model of Piper Cub just as if it were the real thing. Much longer than necessary (for the model) takeoff run with lifted tail, held back on the throttle to simulate scale speed, flew the pattern for the landing, and rolled it out. Very pretty flight. But he could have hot-dogged it like the OP's description.

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    $\begingroup$ Excellent point -- being able to maneuver quickly doesn't mean that the model has to maneuver like that. The physics & aerodynamics described in the other answers explain what the model is able to do, but the pilot is still, presumably, in control of what it actually does. Nice answer, and welcome to aviation.se! $\endgroup$ – Ralph J Feb 20 '17 at 23:35
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See this very relevant discussion on Space.SE: Can a miniature Saturn V get to the moon and back?

The square-cube scaling problem was already mentioned in other answers, but another important factor will be that the Reynolds number of the air does not scale with the model. You can think of this as the air being more viscous from the smaller scaled craft's point of view, which increases drag without providing any additional lift (Thanks to Vladimir F in the comments for corrections).

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  • $\begingroup$ First, "Reynolds number of the air" is a very strange formulation. There is no such thing as Reynolds number of the air. There is a Reynolds number which describes some physical problem, but it is not a property of the fluid, it is a scaling parameter of some configuration! $\endgroup$ – Vladimir F Feb 21 '17 at 13:09
  • $\begingroup$ Second, it is quite wrong to describe the effect of smaller Reynolds number as making the air thicker. Larger kinematic viscosity maybe, but not higher density! Perhaps higher density would help flying by increasing the lift and the drag at the same time, but increasing viscosity just increases the drag. And indeed at lower Reynolds numbers we will see much higher drag. I tried to explain this confusion already in aviation.stackexchange.com/a/21156/3189 The xkcd comic is not really relevant here. Even worse, it is misleading to point to it. $\endgroup$ – Vladimir F Feb 21 '17 at 13:12
  • $\begingroup$ @VladimirF: Thank you for your clarifications. Note that the OP is clearly not an AE, therefore I submit that in context, discussing kinematic viscosity would be no more lucid than saying simply "thicker". $\endgroup$ – dotancohen Feb 22 '17 at 8:10
  • $\begingroup$ My point with density-viscosity is because your link to XKCD which is highly misleading. The XKCD comic is about density. Higher density does help flying. That's why there is service ceiling. You cannot fly too high because the density of air is too low at certain height. However, viscosity (and Reynolds number is all about viscosity) does not help anything, especially at low Reynolds numbers. It just causes drag. (let's not complicate things with Kutta condition and viscosity) $\endgroup$ – Vladimir F Feb 22 '17 at 10:02
  • $\begingroup$ You're right, and I'm going to edit my answer. The scaled craft will see increased drag, but no increase in lift. I was completely thinking backwards. Thank you. $\endgroup$ – dotancohen Feb 22 '17 at 12:14
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Most of the precedent answers are right, I'm just trying to put this in laymen's words.

The construction of an airplane requires fine tuning of shape, material composition, volumes, masses, areas of various elements such as body, wings, control surfaces, engines etc. Now think of all these elements being optimized for the real scale plane, so that it can fly perfectly in the aerodynamical conditons it is designed for, namely airspeed (which involves distance), air density (which involves volume), lift, drag (which involves area) and weight (which involves mass). All this is the result of aeronautical engineering and the equations of fluid mechanics.

Now, as pointed out previously, when you scale distance, then areas, volumes and masses scale differently. Notably area goes with distance^2, volume with distance^3. Mass goes roughly with volume, but depends on what materials the model plane will be made of, which are likely different than those the real plane is made of.

So it becomes obvious that the reduced model plane operates in completely different aerodynamical conditions than the real plane. Hence the radically different handling characteristics.

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    $\begingroup$ Don't overlook how time scales: Inversely with the square root of size. A quarter scale aircraft will "look" as if time "flies" at twice its normal speed. $\endgroup$ – Peter Kämpf Feb 22 '17 at 21:39
  • $\begingroup$ @PeterKämpf: I know what you mean. The problem is that time should scale in order to accommodate for the change of scales of the other dimensions and still fulfill the same fluid dynamic equations. But it doesnt. Time is the same for model aircraft and the real. Thus even though the model plane certainly flies at much lower absolute airspeed than the real plane, it looks like it is flying too fast compared to its size. $\endgroup$ – Scrontch Feb 23 '17 at 8:06
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The scaled model is flying at its full potential but whereas the actual one is following global airline standards for safety and flying and manoeuvring in its safety zones.

We don't want our airline pilot to take sharp turns just because the plane could , Do we?

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hoehne and Swapnil already noted that when the model is capable of the outstanding maneouvres doesn't mean the pilot must perform them.

Models, whatever they ale model of, are more agile thanks to higher power to weight ratio and more agile engines. Delays between idling and full throttle for real craft are much longer than delays for model engines.

Another difference is in volume(mass)-area ratio, it is not constant. This allows the model plane to fly with slower velocities.

Also the flaps and rudder effective area is different for model and real craft. And their deflection angles are higher for model planes than for real ones.

To build a fyable model you must alter the position of the centre of mass. If you scale everything down, the plane won't be able to fly at all.

Modelling, in the scientific way, is real and nontrivial problem and one must be super-cautious to extrapolate (downscaled) model data to real (upscaled) problems. And hydrodynamics and aerodynamics are the most difficult ones of all.

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