Does the ARCA hoverboard violate known limits on small-diameter electric fans?
1) The max theoretical static thrust that can be obtained with an Electric Ducted Fan characterized by: Diameter = 120 mm and Power = 272 hp / 36 = 5.63 kW is:
(1.2 kg/m^3 x (5.63 kW)^2 x pi x (120 mm)^2/2)^(1/3) = 9.7 kgf
(I used the formula that gives the max possible static thrust as a function of power and the diameter of the propeller. The overall efficiency is considered 100%. For realistic efficiencies, smaller than 1, the Power is not 5.63 kW but 5.63 x efficiency)
As you see, 36 fans, that draw a total of 272 hp, can lift in theory 9.7 kg x 36 = 349 kg, well above the 192 kg of ArcaBoard (including the weight of the pilot). No limit is violated.
However, the configuration with 36, 120 mm diameter, rotors is bad because the same formula I used above says that a single 26 inch propeller powered by a 5.63 kW motor generates:
(1.2 kg/m^3 x (5.63 kW)^2 x pi x (26 inch)^2/2)^(1/3) = 30 kgf
In consequence, eight 5.63 kW motors, turning 26 inch propellers, will draw only 45 kW (60.4 hp) and lift 240 kg, more than the max mass of ArcaBoard in flight.
Small diameter propellers are simply inefficient for generating static thrust. This is the reason helicopters have large rotors. Hovering boards like ArcaBoard, also perfectly realizable, have no future because they waste an enormous amount of power.
2) A well designed and built electric hoverboard was made by C. A. Duru. It requires considerably less power than ArcaBoard and flies much better.
A comparison between the hoverboard of Catalin Alexandru Duru (see: the video) and that made by Dumitru Popescu from ARCA.
Video: C.A. Duru flying
Catalin Alexandru Duru's hoverboard
- 8 rotors, 4.5 kW each
- Total Power: 36 kW = 48.3 hp
- Payload: 1 person
Dumitru Popescu's hoverboard
- 36 rotors, 5.63 kW each
- Total power: 203 kW = 272 hp
- Payload: 1 person
In conclusion, ArcaBoard is nothing else but a badly designed hoverboard that requires an enormous power, 272 hp, to carry a man while 48.3 hp are enough for such a job, as demonstrated by C. A. Duru.
Source: A multicopter with 36 propellers that carries a man