# Can the Arcaboard fly?

Recently, BBC news had a video that claimed to show a "real" hoverboard:

As far as I can tell, there are 36 small fans on this device, and it seems to be flying just a few inches off the ground. But in other shots, it gets considerably higher.

So I started wondering about the physics of it all - the energy required, the wind velocities achieved - to see if this could be debunked. Could such a board really fly?

• From an engineering perspective, that seems like too many, too small fans. As a general rule larger rotors generate lower power requirements at identical thrust. That's why human powered rotorwings have such whopping big rotors. – dmckee --- ex-moderator kitten Jan 5 '16 at 0:49

For an ordinary helicopter, the thrust achieved can be estimated from the density of the air, the area of the blades, and the velocity imparted. If you have an area $A$, density $\rho$ and velocity $v$, then the thrust can be computed by conservation of momentum (mass flow $v\rho A$ times velocity $v$):

$$F_t = (v\rho A) v = \rho A v^2$$

In what follows, I used the specifications I found on the techtimes site and I round shamelessly:

dimensions 57x30x6 inches = 1.45 x 0.75 x 0.15 m
weight 180 lbs = 80 kg
power 272 hp = 200 kW
max load 243 lbs = 110 kg
max speed 20 km/hr

In this case, there are 36 small fans (approximately 10 cm across based on the fact there are 10 in line, with some space, along the 145 cm length) for a total fan area of 0.28 m$^2$. For a 110 kg rider the total load is 190 kg, requiring a thrust of 1900 N.

With air density $\rho$ of 1.2 kg/m$^3$ $A=0.28 m^2$, that would require an air velocity of 75 m/s or 170 mph. Not only would it be hard to have fans generating such velocity, you would have enormous difficulty drawing that much air into the fans, and the wind and noise would be insufferable. Finally, the power needed to move that much air is the force times velocity, or 142 kW. This is close to the power spec of the board.

But looking more closely, we see that the board is quite close to the ground. This means that, like a hovercraft, it might be sufficient to create and maintain a pressure differential: if the air under the board is at an elevated pressure, it will provide a lot of lift. In this case, the area under consideration is the full area under the board - roughly 1.2 * 0.6 = 0.7 m$^2$. That means we need a pressure difference of just 1 kPa average across the entire board; but as the board hovers higher, it will require a lot more power. But then it can only get up to 30 cm - so this "ground effect" is probably a key to its flight.

So I conclude that, based on the specs given, it is indeed possible that such a board could fly. Would it be loud? I imagine 36 fans blowing 75 m/s wind would be very noisy! Is it power hungry? Oh yes - if it's using 150 kW of power to move at 20 km/h, we can estimate the equivalent "miles per gallon" using the EPA conversion factor of 33.7 kWh / gallon to get 5 gallons for one hour of "flight", or 2.5 miles per gallon. Finally - the thing only flies for 6 minutes before needing recharging - so you only ever fly 2 km on a charge.

Oh - and since it weighs 180 lbs, good luck popping it into the trunk of your car.

• Ah! Power consumption figures suggest I'm right about the fan geometry. – dmckee --- ex-moderator kitten Jan 5 '16 at 0:51
• I suspect that in the test flights that have been shown for PR purposes that the board may have actually been powered by means of an electrical cable rather than on-board batteries because of the heavy power consumption and the weight of the batteries. Also, I don't see anything that looks like force-sensitive pads under the rider's feet for maneuvering, which makes me think that the board may have been controlled remotely and not by the rider. – user93237 Jan 5 '16 at 0:52
• @SamuelWeir: I'm skeptical too, but control does not look to me like an issue. You can just tilt it with your feet, to turn it or let it accelerate horizontally. – Mike Dunlavey Jan 5 '16 at 1:28
• I expect there is some significant gyro control - at one point the rider gets on and the board just sits there. But yes, for things like height control etc you would need a control mechanism that is not shown - likely remote control for now. – Floris Jan 5 '16 at 1:34
• @dmckee yes the fan geometry is VERY unfavorable for power consumption. But if the technical info I found is correct they have insanely strong motors in each fan - about 5 kW apiece to get to 200 kW total with 36 fans. – Floris Jan 5 '16 at 1:37

If the bottom had tiny holes like the ones on the air hockey games and the floor was smooth, it may slide quite easily just off the floor on the cushion of air.

• Yes - as long as it stays VERY close to the smooth ground: that is how a hovercraft works. You don't need "tiny" holes - just a snug fit so that not much air escapes. Then you can maintain a little bit of pressure. That's all you need... – Floris Apr 25 '16 at 5:16
• The tiny holes allow you to use a smaller blower and increase the velocity of the air coming out of the bottom. Smaller blower equals less power consumption and less total mass of board. – waychow May 2 '16 at 2:52