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#18
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Re: Ball Flight Model
Sorry for taking so long to reply. Unfortunately I had to take a brake from Robotics this weekend and do other work.
In regards to my last post about Force, I was trying to do a sanity check to see if the model was accurate. So one way to do it was to calculate the force required to impart on the ball to give it its initial velocity, but the numbers were too small in my opinion. I only spent 5 minutes on it and then I realized I was making the wrong assumption using Vf = Vi + at, because that assumes acceleration is constant, which is incorrect. So here is what I did which didn't work, and then below is what I did to fix it. (Incorrect Calculations) F = ma; Vf = vi + at; In the above equations, we know Vf, and m. Vi is 0 because ball is at rest, and t we can define based on how fast we want to shoot. So if we solve eq. 1 for a and plug into eq. 2 and solve for F we get. F = Vf*m / t lets say we defined t to be 0.5 seconds the above would yield force required, assuming acceleration is constant. But this is a wrong assumption because acceleration is not constant throughout the launch. So the better way to do it is use the Law of Conservation of Energy, and in this case for my team we were thinking about springs, so I wanted to calculate the spring force we would need. Kinectic Energy = 1/2 * m*v^2 Spring force = 1/2 * k * x^2 If we assume 100% energy transfer from spring to ball we can set these equations equal. we know m and v, and we can choose x based on our design. So lets say we only wanted to compress a spring 5 inches. We solve the below for k; 1/2 mv^2 = 1/2 kx^2 K = mv^2 / x^2 I have plotted the lb/in spring constants while varying the max displacement for the points I gave you. This should give an idea of the force required. The numbers do align with what I think they should be, so my sanity is back in check. Hope this helps, Kevin |
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