Hoverboard Design

Propeller choices:
To minimize area, it is desired to use propellers in an inline axial configuration. One will have a lower pitch and the next one will have about double the pitch.
To stay within reasonable bounds, propeller diameter should not exceed 24 inches.
Regular 2-blade propellers in the range 20-24 inch diameter are expected to operate at about 8500 RPM and draw about 10 HP = 7.5 kW. They should provide about 25 lb thrust. I looked for the biggest pusher propeller on apcprop.com, and based on that picked a matching diameter tractor prop. Right now a promising-looking combination is a 20x10P pusher motor and a 20x16 tractor motor from apcprop:
https://www.apcprop.com/product/20x10p/
https://www.apcprop.com/product/20x16/
Though the 20x18 might be something to consider as well: https://www.apcprop.com/product/20x18f1-gt/

Based on the calculated performance files at https://www.apcprop.com/technical-information/performance-data/ for the above 2 propellers, and the RPM limits of 9500RPM based on https://www.apcprop.com/technical-information/rpm-limits/ I estimate a working max speed of 0-30 mph before noticeable loss of thrust, and a thrust of at least 25 lb per propeller, and a max power draw of 7.5 kW at 8500-9000 RPM. Assuming a 0→30 mph air acceleration by the first 20x10 propeller, the second 20x16 propeller will operate well in the speed range 60-90 mph corresponding to a vehicle speed of 0-30 mph, so the axial arrangement should more or less work out.

Two motors have been chosen as suitable for this size application: the 80100 series (80 mm diameter, 100 mm height) and the 10850 series (108 mm diameter, 50 mm height). The 10850 motor is preferable due to its lower profile, as it will make a slimmer craft and reduce propeller sway side-to-side. Neither has an appropriate kV: the 80100 is kv130, which means it has a max speed of ~8000 rpm at 16S=64V, but the max power output occurs at half speed. A desired kv would be 250. The 10850 is even worse at kv50. The 10850 is also not rated as high for power output, 5kW rather than 7kW for the 80100. I will contact manufacturer on alibaba.com to ask if they can make custom kv or power rating, as I definitely like the shape of the 10850. I contacted this seller:
https://www.alibaba.com/product-detail/CA80100-Type-7000-W-sensorless-bldc_60613785294.html
They claim 15kg thrust with the 80100 and 25kg thrust with the 10850 (?) but when I asked what propeller or RPM, they did not give a firm answer. I suspect they use quite big propeller to get that much thrust at low RPM (or they just guess some number).

I assume either motor with mounting will weigh around 2kg = 4.4lb, and say 1lb for propeller. A power output of 7.5kW, meaning 11kW electrical with inefficiencies, for 8 minutes results in 5.28 MJ, and at 16S or a runtime-average of 59.2V (3.7 V/cell), this is 25Amp-hours of battery requirement per motor.

Looking at some hobbyking batteries, it looks like a 4S/5Ah battery will weigh a bit under 500g. At 4S, I need 20C to supply 15kW to the ESC. Consider this battery: 4S/8Ah at 740gram weight
https://hobbyking.com/en_us/zippy-flightmax-8000mah-4s1p-30c-xt90.html

I would need 4 of above batteries for voltage requirement and 3 for amp-hour requirement, totaling 12 batteries per motor. This adds an extra 0.74*12 = 9 kg = 20 lb considering all the wires and connectors. This is way too much. Even with a crazy 12 motors, I need an excess thrust of about 190 lb / 12 = ~15  lb per motor. This assumes some bit of frame weight, clothes, and my own weight.
This leaves about 5lb battery weight per motor, with 12 motors. This will translate to ¼ of the above calculation, or 3 batteries per motor (on average, since I need 4 in series to get correct voltage: say 12 per 4 motors split as 16S3P). And a corresponding flight time of 2 minutes. Still worth a try!

With 3 batteries per motor and 12 motors, I will need to fit 36 batteries in some type of backpack. They will weigh 5*12 = 60 lb; a hefty bit but reasonable, like a backpacking pack. The above 4S/8Ah battery is 170x70x30 mm, and a custom pack could be designed to hold 3 high * 4 wide * 3 deep, for an outer minimal size of 51x21x9 cm, which is quite reasonable but will go up when wires and connectors are included. At that point I could even pack the batteries within the craft, for better cooling (more exposed surface area) and easier riding/lower CG/easier to test unmanned performance.

Motor+ESC cost estimated from above listing is $310. Battery cost is $68.50. Propeller cost is $27.00. For a 12-motor setup this adds up to 12*(310+27)+36*68.50 = 4044 + 2466 = $6510.

At this point it would be very useful to look for bigger propellers, as this can drastically increase thrust, perhaps reducing the motor requirement to a more reasonable 8, while also lowering required propeller RPM for that thrust. Going up to 24 inches may even be enough, and this is still quite a reasonable size to handle. Having 8 motors instead of 12 also makes the craft easier to move around by hand/carry, and makes it safer to fall forward/back. Based on the apcprop site, despite the lower RPM limit of 8630RPM on the 22-inch propeller, the thrust for that will easily be 30 lb and at a lower hp, definitely extending flight time. The 24-inch propeller, limited to 7900RPM, will still produce up to 40 lb of thrust and at slightly lower hp.

With 8 motors, I would need an excess thrust of about 190 lb / 8 = 23.75 lb per motor. This is 8.75 lb more than the 12-motor requirement, and if the apcprop data is to be trusted, the thrust gain for moving from 20 to 24 inches is just about as much. Thus I expect with a set of 24-inch propellers of similar pitch, I can get the same thrust with only 8 motors. This is good, as it drives down cost and frame weight. For a 8-motor setup this adds up to 8*(310+27)+24*68.50 = 2696 + 1644 = $4340. That’s much easier to think about than the 12-motor figure, and gives room for frame materials while staying within $5k.

Seeing as this seems reasonable, the next steps should be finding suppliers for 24-inch propellers and looking to get higher kv on the motor (perhaps 200kv will be adequate with the larger propeller). Since likely both will be custom, make a calculation to match the propeller pitch to the motor kv. Next order a set of 2 motors/propellers to set up a single axial unit, and test the electrical power draw and actual assembly thrust, to see whether it is worth continuing to buy the next 7 units.

Doing a review of youtube hoverboards, I see many units use 12 motors and 8 motors, and flight times of 3 or 2 minutes, confirming my calculations. The only unexpected finding was the “omni hoverboard” which has 8 rotomax 1.60 motors running at 10s (based on what I could see of the setup), and by my calculations this shouldn’t be possible. Either he is overvolting the motors and running at 15s or 20s (?), or the motors are not rated properly on hobbyking; since he is using 20-inch propellers. He achieves a 1-min flight time which is in accord with the calculations above, assuming he really does run the motors well past their specs, that is the easiest explanation. I think doing this is risky though. What I did learn from his videos is: to test hovering by tying myself with a harness up to a tree/overhang, so as to test real hovering while still being able to fall down; to carry out test flights over water in case of motor failure so I can crash without injury; and to not use a flight controller as it is possible to use your body to control the flight direction. I am still shaky on this point though, as simply tilting the body will not control the spin axis. Perhaps he uses the snowboard-like approach, of ‘twisting’ the board so as to get a spin moment. Then I need to account for this in my design.

Note the following page which has software and manuals (under Downloads header) for the 16S 180A ESC that I am using: http://www.fliermodel.com/en/prc-show.asp?id=688 

Based on initial sizing considerations, the ESC to Motor wires should be about 6ft long. I will use this for the testing, so an accurate drop in voltage is in effect. It is recommended to lengthen ESC to Motor wires rather than Battery to ESC wires, due to induction effects, which is what I will do here. Even though ESC outputs are 8AWG wires, I will use 10AWG wires for now because there are 3 per motor vs 2 per battery, and they will be lighter. Pending testing of voltage drop and power draw, perhaps it will be worth to consider all 8AWG construction.

For the backpack design, the motors will need to be attached to some rigid structure. I propose using Aluminum square tube for this structure, as this is readily available, light, and easy to machine. Here I determine the tube dimensions required.
The tube length should be about 27 inches, which gives 3 inch space between propeller blade edges. The stress criterion should be that each tube end can handle twice the full load of the vehicle+pilot weight before yielding, which would allow it to handle a potential impact with the ground.
Assume the 27 inch tube is held fixed at one end and the other end loaded with twice the vehicle+pilot weight (say 500 lbs), the maximum stress should be below the yield stress.
The maximum stress for this load condition is S=W*L/Z where W=500 lb, L=27 inch, Z=section modulus as follows for square tube:
Z=(a^4-b^4)/(6*a) where a=outer dimension, b=inner dimension
Also we have the tube mass M:
M=(a^2-b^2)*L*rho
For Al-6061 the yield strength S=35000 PSI and rho=0.098 lb/in^3
For fiberglass (http://www.build-on-prince.com/fiber-reinforced-polymers.html) the tensile strength S=30000 PSI and rho=0.055 lb/in^3

Based on the analysis in the Tube Stress spreadsheet, the 1" OD tube will not have enough strength to handle this load. The 1.5" OD tube will require at least a 0.19 inch thick wall. The 2" OD tube on the other hand will require at least a 0.082 inch thick wall. The thinnest wall of 1/16 (0.0625) on McMaster  is only available in OD up to 1" so is not useful. Note that with such a thin wall the loading may be OK but the structural integrity of the tube itself (susceptibility to buckling) is quite poor at large OD, which is probably why they don't carry this. The next thinnest wall of 1/8 (0.125) on McMaster is available up to 5" OD but it makes no sense to use a larger OD than necessary to meet the above loading requirements as this adds extra mass. This means a 2" OD 1/8" wall thickness Al-6061 tube is a good choice. This gives a weight of 2.5 lb per tube, which is acceptable. The frame will then be around 10lb.

For Fiberglass, the 1" OD tube will not have enough strength to handle this load. The 1.5" OD tube will require at least a 0.25 inch thick wall. This size is not available on McMaster. The 2" OD tube will require at least a 0.1 inch thick wall. On McMaster a 1/8 (0.125) inch and 1/4 (0.25) inch wall thicknesses are available. A 2" OD 1/8" wall thickness FRP tube seems a usable choice. This gives a reduced weight of 1.4 lb per tube. Using a 1/4" wall thickness instead gives a weight of 2.6 lb per tube, which is worse than Al-6061 tube but gives the best safety factor of 2 (1.22 for 1/8" FRP, and 1.43 for 1/8" Aluminum). As a practical concern, the FRP tubes are available as 5-ft lengths, which makes it easy to cut into two 2.5-ft lengths, as opposed to the Al tubes which are sold as less convenient 3-ft lengths.

Doing a quick Inventor analysis of the above load case with an Al-6061 tube 2" OD 1/8" wall thickness confirms the above values. I get a safety factor of 1.64 and an end deflection of 0.6 inches.
Switching the material to GFRP (Glass Fiber Reinforced Plastic), I get a poorer prediction of safety factor 0.36 (to yield) and end deflection of 2.96 inches. Using instead ultimate tensile strength instead of yield, I get a safety factor of 0.81. So the 1/8" wall thick GFRP tube is unacceptable. Running this analysis with 1/4" wall thick GFRP tube gives safety factor of 1.46 (to UTS) and end deflection of 1.8 inches. Due to the higher weight of this tube, I do not see the advantage of using GFRP in this application and instead prefer the aluminum tube.

The McMaster part is 6546K23 – 2"OD, 1/8" wall thickness, 3ft length 6061 Aluminum rectangular tube. Propeller bolts are McMaster 91502A153. Motor mounting bolts are McMaster 91274A131. Washers for these bolts are McMaster 93501A027. Stock for test motor holder 8975K71 (but consider mounting directly to tube end!). Stock for prop washer I already have – 1/8" aluminum sheet. All have been ordered 4/19/2018.
Perhaps of interest is this attempt at a propeller-powered bike: https://www.lanemotormuseum.org/collection/motorcycles/item/peugeot-propeller-bicycle-1920