# How plausible is the claim about a 200 kW battery solution?

Following this question posted on Aviation:SE:

which is related to a hovering board described on the vendor site:

(source)

I would like to assess the claim this device really exists. In particular I wonder if it is possible to use the batteries to deliver 200 kW as claimed. I'm not trying to evaluate the aerodynamic aspects.

I don't see what technology could be used other than Li-ion cells. Assuming this is true, would this solution be compatible with the claimed characteristics:

• Power delivered: 200 kW,
• Running time: 3 min for a 110 kg user, to 6 min for a 82 kg user,
• Charging time: 6 hours, reduced to 35 min using a docking station.

Taking into consideration the Li-ion characteristics with the knowledge of an electrical engineer, is there any aspect that would prevent this solution to work, e.g:

• Weight, volume of the batteries (the board measures 145×76×15 cm),
• Wires size (there is little room available in the box),
• Current for charging (is this feasible to charge in 35 min),
• Discharge time (would cells allow to be discharged in 3 to 6 min),
• Cost (replacement of batteries is offered at $6,840). No speculation please, but known facts that would definitely contradict or support the possibility of the solution. For instance, I think these deductions are correct: • For a 3 min hovering, with 200 kW, about 10 kWh are used. • Due to specific energy and density for Li-ion, this means 40 kg and 14 dm3 for the batteries. • Price of the batteries: With an optimistic 0.40$ / Wh, this would be $4,000. • Charging 10 kWh in half an hour requires a 20 kW charger. • Assuming cos φ = 1, this would mean 91 A for 220V (well past what is usually found at home), and 5,000 A for the Li-ion cell voltage (this would require large wires that are not visible in the picture). • That goes past the speculation line, IMO. – Matt Young Dec 27 '15 at 4:00 • @MattYoung: It seems to me that determining the weight or the volume of the cells able to deliver 200 kW is very practical. Same for assessing if the cells can be discharged in 6 minutes. Which aspect bothers you? – mins Dec 27 '15 at 4:08 • You're basically asking "Would safety be plausible". What do you mean by that? And how is anyone here supposed to be able to know about the battery price that two companies negotiate? – pipe Dec 27 '15 at 4:14 • Oh, and another thing, I wouldn't want to even try answering this question unless you actually put the figures in the question. It will become pointless if the manufacturer changes the specs or removes the product. – pipe Dec 27 '15 at 4:16 • @pipe: Maybe you can be a bit positive and suggest improvements, isn't this site supposed to provide support rather than criticism? – mins Dec 27 '15 at 4:23 ## 2 Answers 203kW / 36 fans = 5.6kW per fan. Working voltage of 38V implies 10S Lipo (3.8V per cell). 5.6kW / 38V = 150A. We want 3 minutes at full power. At half power it will draw 75A for 6 minutes (max duration). A battery capacity of greater than 150*(3/60) or 75*(6/60) = 7.5Ah per fan will be required. Can it be done? Looks like 120mm diameter fans will fit in the space provided. Here's a 120mm fan that weighs 1kg and produces 7.5kg thrust on 12S:- 120mm 11 Blade Alloy EDF 700kv - 7000watt On 10S it would draw about 30% less power and produce about 15% less thrust, so let's say 5kW and 6.5kg (the fans they are using may have different motors, but we can expect similar performance at the same power level). And here's a 10S 4Ah battery that weighs 905g:- ZIPPY Compact 4000mAh 10S 25C Lipo Pack The board appears to use a total of 72 batteries - two batteries per fan. 2 x 4Ah = 8Ah, close to our required capacity. Max discharge rate is 4 x 25C = 100A per battery or 200A per parallel pair (and we 'only' need 150A!). Max charge rate is 5C, well above the 2C rate required for a 35 minute charge. At$67 per pack the total battery cost is \$4824.

Our 72 batteries weigh 905g x 72 = 65kg. The 36 fans weigh 36kg. Add another 10% for ESCs, wiring and support structure, and we get a total board weight of ~110kg. This board should generate 6.5kg x 36 = 234kg thrust in free air. At half power thrust would be reduced to about 75%, but could be boosted by ground effect - so perhaps 210kg of 'duration' hovering thrust. Take away the weight of the board and you have a payload capacity of 100kg.

Looks possible!

• Put a skirt on it... that will work.... and last way longer ...lol – Spoon Dec 27 '15 at 9:51
• You very well constructed answer has been useful to @Peter Kämpf to assess aerodynamic aspects on Aviation:SE. Thanks a lot Bruce. – mins Dec 27 '15 at 11:01
• Looks possible, but how about the 10kW charger? How would that look like? – John Dvorak Dec 27 '15 at 12:43
• 10kW chargers are available. However I would split the battery into 2 or more modules that can be removed from the board for charging, and use a smaller charger that can run off normal mains power. I would also increase the 'fast' charging time to 1hr (standard Lipo charge rate). – Bruce Abbott Dec 27 '15 at 17:43

I would like to assess the claim this device really exists. In particular I wonder if it is possible to use the batteries to deliver 200 kW as claimed.

1) The weight of the battery pack necessary to power ArcaBoard for 2.4 minutes is realistic. For example, if we use batteries of the type Tattu 22.2V, 22Ah, 488.4Wh, 25C, weight = 5.8 lbs we get 43.7 kg for the total mass of the pack necessary to generate 272 hp for 60 min / 25 = 2.4 min (close to those 3 min claimed by ARCA):

2 x 5.8 lbs x 272 hp / (22 A x 44.4 V x 25) = 43.7 kg

Even considering 38 V instead of 44.4 V the total mass of the pack will rise from 43.7 kg to 51 kg which leaves another 31 kg for the weight of the board, ducted fans and other accessories (ArcaBoard weights 82 kg). The main issue is not the weight of batteries but the enormous inefficiency of the Ducted Fans used by ARCA. They are totally unsuitable for the Arca board as explained at point (2).

2) 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.

3) 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.

Catalin Alexandru Duru's hoverboard

• 8 rotors, 4.5 kW each
• Total Power: 36 kW = 48.3 hp