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How to scale the weight of a RC model aircraft?

If the scale of an model aircraft is 1/4, what should the scaled weight be?

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    $\begingroup$ Check the chord and speed of the model (Reynolds number) compared to the original. Models, generally smaller and slower, are usually only a small fraction of the weight of the original. $\endgroup$ Mar 13 at 18:29
  • $\begingroup$ Does this answer your question? $\endgroup$ Mar 13 at 19:01
  • $\begingroup$ (coments converted to answer) $\endgroup$ Mar 14 at 15:09
  • $\begingroup$ If you have a large enough room you can always play around with fluid viscosity. And if you have an extremely large wallet, you can play around with gravity ;) $\endgroup$
    – EarlGrey
    Mar 15 at 10:40

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About 4% to 5% of the original mass.

Scaling laws tell us that area grows with the square and volume with the cube of length. However, this is too simple for two reasons:

  1. Airplanes are not solid but have some hollow space inside. Therefore, their mass grows with something between square and cube.
  2. Wing loading, flight speed and loads grow with increasing size. Therefore, smaller airplanes get away with a lighter structure.

Practical results of the exponent of length to describe mass growth are between 2.2 and 2.3. For a quarter scale model this means that mass will reduce to 0.252.2 = 0.0474 to 0.252.3 = 0.0412 of the original mass.

If design parameters like range (relative to size, of course), payload or maximum load factor change between original and model, the mass will also not strictly follow scaling laws.

In order to know how to scale speed we need to understand which parameters change and which will stay constant. Since we intend to fly the model here on Earth, gravity and air density must stay the same. Gravitational acceleration is length divided by time squared. If length scales linearly, so must time squared. Ergo, time scales with the square root of length. Smaller models fly more slowly but faster relative to length.

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  • $\begingroup$ What do you mean by it flies faster relative to length? Unfortunately I'm forced to use a longer chord to get at least half the Re. Unfortunately that means the distance between the wing and tail is shorter. The reason I'm asking about scaled weight is to get a scaled Ixyz that will resemble the flight characteristics of the full scale aircraft as much as possible. $\endgroup$
    – Fred
    Mar 19 at 17:09
  • $\begingroup$ @Fred Speed is distance over time. Now scale that distance with your length change and compare actual speed with that length-scaled speed. $\endgroup$ Mar 20 at 7:24
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In addition to Peter Kämpf's answer, scaling down also allows a wider range of materials and engines to be used, therefore a vast range of wing loading to play with depending on the flight characteristics that are aimed for.

This being also related to the fact that RC planes don't have that imposed payload consisting of carrying at least one to-scale human body.

As an example here are two videos of 1:4 scale RC F4U corsair.

First is an indoor 4kg electric model, second is five or six times heavier, (probably <25kg) powered by one 250cc radial engine.

first example

second example

This somehow also asks how flight speed scales down and relative to what.

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This is an example of the square-cube law.

The square-cube law states that for three-dimensional objects, scaling linear dimensions results in the surface area varying proportionally to the square of the change in linear dimensions, and the volume varying proportionally to the cube of the linear dimensions.

So, for a model aircraft 1/4 the size of the original, its surface area should be 1/16th that of the original, and its volume (and mass) should be 1/64th that of the original, 16 being 4 squared and 64 being 4 cubed.

However, the support members of a 1/4 scale model aircraft need not be as strong as that of the full sized model due to the same square-cube law due to their only needing to support 1/64th of the original mass yet being 1/4 the size. That's why mice and insects seem to have sticklike limbs compared to elephants.

So, a 1/4 scale model would likely be less than 1/64th of the weight, or might carry a significantly larger payload.

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  • $\begingroup$ Peter's answer shows how for this application, the square-cube law is a good approximation but we can do better. $\endgroup$ Mar 14 at 15:14
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What is your basic purpose for trying to scale the weight? Wouldn't the lightest possible model you can possibly build always fly best? After all, you can always fly it faster than the actual minimum stall speed, if it suits your purposes for looking more scale-like.

Keep in mind too that there are two different contradictory issues as to what sort of flying speed looks the most "scale like". On the one hand, we can think of the time needed to cover one fuselage-length and scale that to match the real thing. That will always result in slower speeds than you might tend to expect. On, the other hand we can think of the degrees of turn per second generated at a given bank angle, say 45 degrees. To match that to the original, you'll have to fly fully as fast as the original.

So if you slow down enough to satisfy the first criteria, your turn rate for any given bank angle will look way too fast. So the best airspeed to fly for the most "scale-like" appearance is somewhat ambiguous.

(Yet another alternative would be to fly at an airspeed that scales the turn radius at any given bank angle to the full-scale airplane.)

But since a light model can always fly faster than its stall speed, but a heavier model cannot fly slower than its stall speed, it would seem that there would be no advantage to building heavy rather than light, as far as presenting a scale-light appearance in flight is concerned. So we're back to asking, what is your basic purpose behind trying to "scale" the weight to match the original in some way?

(Some of the answers already posted appear to address the likely weight of the model, rather than the ideal weight of the model.)

The basic answer to your question appears to be "it's best to build the model as light as you reasonably can."

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  • $\begingroup$ Lightest isn't always "best," even full scale. For instance, sailplanes both big and small carry ballast. But apart from that, they are indeed built as light as can be. $\endgroup$ Mar 14 at 15:12
  • $\begingroup$ @CamilleGoudeseune -- well, sailplane flight dynamics are rather different than powered airplane flight dynamics, as you know doubt know. But I'm sure there is some weight below which the flight just wouldn't look quite right-- hard to articulate exactly why though. $\endgroup$ Mar 14 at 15:15
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    $\begingroup$ @CamilleGoudeseune -- yeah you are probably on to something, in that you probably want the power-off or power-idle gliding speed that yields the best glide angle, not to be unreasonably low, for scale-looking landing approaches. For reasons noted in the answer, it would seem to be hard to pick one single ideal speed and thus one single particular ideal weight, to make said power-off or power-idle approaches look as scale-like as possible. It depends on what criteria you are most interested in. $\endgroup$ Mar 14 at 15:23

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