What is the minimum speed for a scale-model of a modern commercial aircraft to fly?

Question

Suppose a commercial jetliner (say an Airbus A320 or Boeing 737) were scaled down into a remote-controlled drone, so that its wingspan were two feet wide. My questions regarding this scale-model are:

1) Would jet engines work if scaled-down to such proportions?

2) Would the wings, tailplane, ailerons, flaps etc. work if exactly scaled down in the same ratio as the fuselage?

3) At what velocity should the scale-model taxi in order to take off?

4) At what speeds should the scale-model fly to achieve stable flight, if the length and breadth of the wings etc. are made correctly to scale?

5) Is it possible that the flight speed of a scale model of a commercial airliner can be scaled down to the extent that it can realistically be remote-controlled by a person on the ground in a city environment, such as a park?

6) One of the things I am asking here is: can the plane shown in this video be genuine? Or is it necessarily a hoax, made with computer graphics?

Answer 1

If you scale down the structure of a modern airplane, it would work nicely. Since volume scales with the third power of length, but area scales with the second power, the wing loading would decrease with the scaling factor. Therefore, the dynamic pressure required to fly would also decrease with the scaling factor, as would all aerodynamic pressures. This means that all stresses within the structure will also come down, so the structural safety margin increases with the scaling factor.

What scales less nicely are the flow phenomena. The Reynolds number will come down with the 1.5th power of the scaling factor (1 power for the length and 0.5 power for the reduced speed), so the boundary layer would be relatively thicker. This would reduce the maximum lift coefficient and would make the gaps between the high lift devices of the wings (slats, flaps) too small to work properly. A simple logarithmic scaling law works well only over small changes and can not be applied here. After all, the scaling factor is close to 60. I would guess that the maximum lift coefficient is only half of what it is for the real aircraft, so the take-off speed is reduced by a factor of $\sqrt{0.5\cdot scaling\;factor}$. If the take-off speed of the original is 260 km/h, the model could take off at maybe 45 or 50 km/h.

This is quite a bit lower than the speed of the original aircraft, but still too high to fly it comfortably in a park. A wide open field would be more suitable.

At the same time, the relatively thicker boundary layer means the drag of the scaled aircraft is relatively higher, so the L/D of the aircraft comes down. Unfortunately, the flow inside the scaled gas turbines will also be negatively affected by the Reynolds number, so they will produce little thrust. In all, I am quite sure that the scaled Airbus or Boeing would not be able to accelerate to the required take-off speed since both drag increase and thrust loss due to scaling will make this impossible.

I saved the hardest part for the end. The flow in the tiny hydraulic lines would be thick as honey (but you could increase the hydraulic pressure by the scaling factor before the lines burst!), and scaling all control circuitry would result in electronic components which would cease to work completely.

In the end, my answer would be a clear no. It will require a lot of adaptions, and only then a scale model could be made to fly.