# Does the ARCA hoverboard violate known limits on small-diameter electric fans?

The ARCA board is being hawked as achieving 430 pounds of lift from 36 electric fan motors for six minutes of 'flight.'

To my uneducated eye, getting 12 pounds of static thrust from each of the small fan motors (430 pounds / 36 motors) seems unreasonable and perhaps impossible. The engineer says that it has 272 horsepower, so that would be 7.56 horsepower or 5.6kW per motor, which seems on the high side.

What are the a) theoretical and b) realistic amounts of thrust that one can assume from what looks like a 10-15cm diameter fan?

• Thanks mins, you caught my math mistake on the horsepower. – RoboKaren Dec 27 '15 at 6:30
• I've opened a side question related to the batteries on EE.SE. – mins Dec 27 '15 at 6:34

The key is that the Arca board only works in ground effect. Therefore, the pressure difference over the area of the board is the key for calculating its power needs.

From the video I would estimate the size to be 0.6 x 1.2 m thanks to @mins more thorough research we know that the board measures 1.45 x 0.76 m for an area of 1.1 m². To lift both the occupant and the board itself it claims to create 430 pounds of force, equivalent to 195 kg of mass in Earth's gravity, so the pressure increase between top and bottom is 1740 N/m² or just 1.7% of atmospheric pressure. This is not much when you consider that a turbofan compressor stage can create a pressure differential of 1.7, albeit at much higher speeds.

The concept is basically the same as the Hiller flying platforms of the 1950s, the first of which was powered by two 44 HP engines. Since the intake geometry of the Arca board is - how should I say - less than optimum, it can not fly as high as the Hiller vehicles and I find the claimed 272 HP hard to believe and the high power draw is due to the low efficiency of 36 closely coupled blowers.

Hiller VZ-1 Pawnee (picture source)

To calculate the exact amount of power needed I would need to calculate the mass flow from below the board at the given pressure, which depends nonlinearly on altitude. Then I would need to calculate the power to produce this mass flow at the known pressure differential with 36 small blowers. Sorry, but even my Hoerner books do not cover this. What is certain is that the thrust from the 36 blowers is not nearly sufficient to lift the 195 kg when out of ground effect. The board only works at very little altitude when the outflow cross section around the board is restricted. This gives it an automatic altitude limit of a few centimeters and makes it self-stabilizing in pitch and yaw.

It takes some thick skin to watch the full length of this platitude-filled piece of marketing for an obvious gimmick. The camera angles were chosen to make it look fly higher than it actually can, and in the one shot where it does fly higher you cannot see who or what is standing on top. Anybody spending 20 grand on this is going to regret it quite soon.

EDIT:

With the answer provided by Bruce Abbott to @mins' question on Electrical Engineering SE the question can be solved. Bruce approaches the problem from the electrical side and links to a 120 mm blower which creates 74 N thrust and consumes 7 kW of power. He calculates 65 kg for the batteries and 36 kg for the blowers, for an estimated mass of the board of 110 kg. However, in combination the thrust from closely coupled blowers will certainly be lower than that of an isolated blower with ideal flow conditions.

Conclusion: Looks possible, no limits are busted, but there is some potential for further optimization and badly needed mass savings on the board.

• Doesn't the Hiller flying platform gain some induced lift from the air traveling over the curved top surface of the air intake? – RoboKaren Dec 26 '15 at 23:30
• @RoboKaren Exactly right; the high flow speed creates suction. The Arca board neglects this, hence my "less than optimum" remark. – Peter Kämpf Dec 26 '15 at 23:33
• The Hiller flying platform gained some induced lift from the air traveling over the curved top surface of the air intake but the same curved surface righted up all the time the hoverboard as soon as the pilot wanted to travel in the forward direction. This is a serious drawback and one of the reasons the platform was abandoned as impractical. (see the explanations from here: rcgroups.com/forums/showpost.php?p=33605165&postcount=18) – Robert Werner Jan 2 '16 at 22:16

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

Dumitru Popescu's hoverboard

• 36 rotors, 5.63 kW each
• Total power: 203 kW = 272 hp