Why don't scale models fly at scale weights?

Can anyone please explain to me in lay persons terms why we can scale our planes to 1/4 the size but not 1/4 the weight of the full scale versions? In example, if a full scale Piper Cub, theoretically weighs 1200 lbs, why wouldn't the 1/4 scale version be able to fly at 300 lbs? Your input would be appreciated.

From : Don Stackhouse

Stan, there are a number of factors at work here.

1. Lengths scale linearly with scale factor, but areas (like wing area and the cross-sectional area of structural members) scale with the square of the scale factor, and volumes (which determine weight) scale with the cube of the scale factor. All this assumes we're duplicating the same structural design and materials, if we change any of those it gets more complicated.

In plain english, this means that if it's half as big, it will have 1/4 the wing area and 1/8 the weight. Sounds good so far, but now for #2:

2. Reynolds number, a.k.a. "Scale effect". Length times velocity times air density, divided by air viscosity. In the millions for an airliner's wing, 1 to 3 million for a Cessna 152 wing, 30,000 to 100,000 for an R/C hand-launched glider. Air molecules don't scale down when we scale the model down. If air molecules look like ping pong balls to the full scale, they look more like basketballs to the model. The job of forcing yourself through a mass of ping pong balls is quite different from tunneling through a pile of basketballs.

From the model's point of view, the airfoil on the model will have proportionately higher drag and less lift in most cases than the full scale airfoil. Also, things like boundary layers (that thin layer of air next to the skin where the air is transitioning from the speed of the skin to the speed of the "freestream" outside of the boundary layer) behave dramatically differently.

A large aircraft will tend to have what's called a "turbulent" boundary layer over most of the skin. This means that the air within the boundary layer is constantly stirring and mixing itself. This creates quite a bit of "scrubbing" action against the skin (increasing skin friction), but it helps the flow stay attached to the aircraft's surface. Full scale airfoils are designed with this type of boundary layer in mind.

A full scale sailplane or smaller, slower aircraft will tend to have large parts of its boundary layers flowing in what's called "laminar" fashion; nice smooth layers without any mixing between them. This can reduce drag if properly managed.

A model tends to have laminar flow too, but it tends to separate easily, leading to big globs of stagnant flow being dragged along under the separated boundary layer. Even behind the propeller, even if you put "turbulators" on the wing, for smaller models the flow will tend to be laminar, and try to go back to laminar if you turbulate it. It would rather be laminar and separated than turbulent and attached. This separation if it occurs dramatically increases drag and reduces lift. Full scale airfoils used on model-sized aircraft are especially bad in this regard. In general, the relatively bigger air molecules will put up with less "muscling around" from a model than they will from a full scale aircraft, so the model has to do less of this, and with more finesse. When you're not as big and powerful, you have to rely more on diplomacy.

3. If you want a 1/2-size model to "look" like it's going the same apparent speed (same number of fuselage lengths per second) it has to have half the actual speed. This means that the "dynamic pressure" ( the force of the air against the model, from which comes lift and drag) is only 1/4 as much. Since the wing area is also only 1/4 as much, the total lift making ability of the wing (even if we ignore Reynolds number effects) is only 1/16 as much!

By the way, if we're only going 1/2 as fast with something 1/2 the size, the Reynolds numbers are only 1/4 as high, so the #2 problem just got even worse!

4. The atmosphere doesn't scale down when we shrink the model. A 20 mph gust for a model is a lot more serious than a 20 mph gust for its full scale counterpart. We can limit some of the effects of this by only flying on calmer days, but the smaller gusts still exhibit this effect.

5. The model isn't flown as precisely as the full scale aircraft. Since you aren't actually in it, you can't see as precisely what it's doing. This means that you can't keep it flying as closely to the optimum angle of attack, yaw angle, etc. as the full scale. This costs a bit of performance, which must be compensated for by larger performance margins in the original design of the model.

With all this against them, it's kind of remarkable that our models fly as well as they do!

Don Stackhouse @ DJ Aerotech