Monday, March 8, 2010

Hoverboard Physics

Forget the flying cars, the coolest thing in Back to the Future II was the hoverboard.  I’m not sure what Marty and Doc Brown did to screw up the space-time continuum, but they better fix it because we’ve only got five years to invent to the necessary hover technology.  How much power would a hoverboard need to stay afloat?

I’m assuming that the hoverboard works like a conventional hovercraft, which floats by creating a cushion of highly pressurized air underneath it.  Marty’s hoverboard is about 30 cm (~1 ft) by 90 cm (~3 ft) and appears to have two circular propulsion doodads.1  I’ll assume the circles act like fans that push pressurized air down.  From the picture, it appears they each have about a 13 cm (~5 in) radius, leading to a total area of about 1100 cm2.  

In order for the board to hover, the pressure underneath must be large enough to lift the weight of the board plus Marty.  If the total mass of Marty and the board is 80 kg (~180 lbs), then the total force pushing down is,

force = (mass) · (gravitational acceleration)
= (80 kg) · (9.8 m/s2)
= 780 N.

This force is applied evenly over the area of the board, which is about 2700 cm2.  From this, we can calculate the extra pressure under the board that’s needed to make the craft hover,

pressure = (force) / (area)
= (780 N) / (2700 cm2)
= 2900 Pa.

In order to generate this extra pressure, air has to be pumped under the board through the circles.  We can estimate the speed of air flowing through the circles using Bernoulli’s equation2,

velocity  = [ 2 · (pressure) / (air density) ]1/2
= [ 2 · (2900 Pa) / (1.2 kg/m3) ]1/2
= 70 m/s.

In a previous problem, we estimated the power absorbed by a wind turbine.  The hoverboard is basically the same process in reverse, so we can use the same formula to estimate the power it takes to run the hoverboard,

power = (air density) · (area swept by the rotor) · (air speed)3 / 2
= (1.2 kg/m3) · (1100 cm2) · (70 m/s)3 / 2
= 23,000 W.

That’s roughly the amount of power needed to run 20 air conditioners.  If we were going to run this on 100% efficient solar power, we’d need a solar panel with a total area of about 18 m2.

[1] As you can see, I’m trying to impress you with my use of technical jargon.
[2] Rigorously speaking, Bernoulli’s equation doesn’t work here since air is compressible.  There are also some subtleties about the system not being enclosed, but this should be a reasonably good order of magnitude estimate.


  1. Cool idea. The compressibility of air only becomes non-negligible at around Mach 0.3. Below that point air can be assumed incompressible.

  2. What if you we able to find a power source, (or rechargeable battery) to insert instead of using solar (unless solar is used to charge the power source)? Plus what material would you use to build the board for this would save how much power or energy is used to get off of the ground?

  3. It's really a nice article ,
    Thanks for sharing with us,.
    hoverboard test

  4. I wanted to thank you for this great blog! I really enjoying every little bit of it and I have you bookmarked to check out new stuff you post.

  5. Skim away best organization for Hoverboards in Canada, you can Buy hoverboards online here effectively. Hoverboards in Toronto and hoverboards in Vancouver accessible furthermore hoverboards in Canada, purchase hoverboards on the web, hoverboards in Toronto, where would i be able to purchase a hoverboard in Canada, modest hoverboards online and hoverboards in Vancouver.

  6. You have some honest ideas here. I done a research on the issue and discovered most peoples will agree with your blog.
    self balance scooter

  7. awesome nice im feeling happy watch this videos i like it thanks for shareing kind information thanks but im looking for a Cheap limo hire in Sydney
    thank you so much

  8. This comment has been removed by the author.

  9. we are provide Cheap Hover boards in valuable price in your monthly income if you want to purchase this please contact us over this site UK Certified Hover boards

  10. I like your blog it's really cool and nice thank you for sharing this great information about the walmart hoverboard nice blog.
    walmart hoverboard

  11. This post is really very awesome and pretty impressive, thanks for the post and keep updating.
    Buy vedic gemstone online

  12. What i done like about hoverboards is that they dont actually hover, lol. I wish someone developed hoverboard which actually hovers one day. Floating board hoverboard shop

  13. Good information and great post. I like the website and am sure to keep returning. UL Certified Hoverboard

  14. Very interesting! This work is really satisfactory for us. Thanks Ul Certified Hoverboard

  15. Your website is really cool and this is a great inspiring article. all terrain hoverboards

  16. Interesting! I didn't see such a informative post about Hover Skateboard

    1. This comment has been removed by the author.

  17. This comment has been removed by the author.

  18. This is such a great post. I have learnt a lot.

  19. UK Hoverboard
    smart balance wheel for sale Brand new condition with all packaging Free carry case U.k certified and tested 12 months warranty ...

  20. Awesome article, it was exceptionally helpful! I simply began in this and I'm becoming more acquainted with it better! Cheers, keep doing awesome! top 10 cheap hoverboard

  21. It is good when we can get nice best hoverboards at good prices.

  22. Thanx for sharing this informatic article about Thanx for sharing this informatic article about hoverboard with us. I am waiting for your new post. with us. I am waiting for your new post.

  23. UK Segboards provides Professional Hoverboard Repair Service UK
    , Swegways repair service as well as Segways repairing services in the UK We have a dedicated Hoverboard repairing center with expert Technical Hoverboard engineers Team, that can fix your hoverboard problems. very easy and adjustable for kids and adults.

  24. Yes I’m agree with you,and I tried this too.i want to add a information regarding a best comanny that is SEGBO.SEGBO is now providing Certified Official Hoverboards UK. Now you can buy Cheap Hoverboards . At SEGBO, Chrome Hoverboards are also available.

  25. I want UK HoverboardsFor Sale So I was searching over the Google then I found your blog kindly quote me the best prices for Segways Hoverboard For Sale in uk


  26. capacity to get to goals with all common commercial center. Hoverboards UKavailable to be purchased travel accommodates a magnificent programming for those of you visionaries who appreciate to see an online certifiable repaired, whereby they find new, totally one of a kind, and motivating things like Segway.

  27. In the case of searching for Hoverboard Protective Cases to be purchased is done to simply fulfill the sheer delight of owning one, or even it is planned for down to earth substances that assistance inward city suburbanites, purchasing this item is a procedure that all cutting edge individuals would wish to understanding.

  28. The nuts and bolts are straight forward and it for the most part depends on liquid mechanics. Here is a full breakdown of how a
    Hoverboard Protective Cases functions so you can see how these sheets function.
    Controlled wind current: