I'm a Ib student who took HL Physics so I have to do my own lab and report(IA). For my ia i decided to measure the force of lift of a RC helicopter depending on its propeller radius my measuring mass difference on a scale before and after flying at max power. The results are quadratic in shape. I was able to come up with the equation F=ρπr2 v2 (proof at bottom). v being the initial velocity of air underneath the propeller using the assumption that the air pushed by the propellers are cylindrical in shape and have negligible initial velocity.
The problem is I want to be able to derrive an equation that represents the force in terms of radius. My initial thought was to use a power equation since power should be constant. However this didnt work and it concluded that force is proportional to radius2/3. I was able to come up with a power formula in terms of r as the only variable using torque and drag. So i'm thinking I just need another formula in terms of velocity only but cant really think of anything.
Any tips?
Proof: F=∆p/∆t =m∆v/∆t =ρVv/∆t =(ρπr2 hv)/∆t =(ρπr2 v2 ∆t)/∆t =ρπr2 v2
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