# Physics equation for air displacement? Answered

I want to make a fan powered go-kart, is there a formula I can use to calculate the minimum amount of air displacement to make it move?

Tags:

## Comments

The forums are retiring in 2021 and are now closed for new topics and comments.

Starting with <strong>Nacho</strong>': Newtonian mechanics give you F=MA meaning that Force = Mass x Acceleration. To rearrange this, the acceleration on the go-kart = the Force from your fan divided by the mass of the go-kart (and you). The force from the fan is best measured in pounds-thrust or equivalent.<br /> Mechanical friction needs to be weighed-in, then you have aerodynamic-drag to account for which is proportional to speed cubed and it's starting to get a bit complex...<br /> <br /> You'd need a fairly powerful engine and a <em>big</em> fan - what have you got?<br /> <br /> L<br />

Your best bet is probably to think of this as a <a href="http://en.wikipedia.org/wiki/Jet_engine#General_physical_principles">jet engine</a> problem, without any fuel. You're sucking some mass of air into and out of the fan. The difference in velocity (i.e., the fan blowing speed minus your cart's speed), together with the mass of air throughput per unit time, gives you the rate of change in momentum (force). The mass of your go-kart, together with that force, gets you the acceleration.<br /> <br /> Write down those equations, leaving the air mass-throughput as an unknown, and solve for it in terms of other things, like what acceleration or final speed you want.<br /> <br /> Most big fans quote the throughput as volume (cubic feet per minute [CFM], usually). To get from volume to mass, you need to know the density of air, which you can get from Wikipedia. So now you can compare what you want your go-kart to do, with what different fans can provide.<br /> <br />