Hello I've been using Tracker for some time with students and the first thing we do is analyse projectile motion and get a value of g (ay) to show it's downwards and always about the same. I tell them to use high frame rates for the video and a blank background for auto tracking. We have a video with 240fps that's nice and smooth but the autotracker seems to be giving enough variation between matches on each frame to create very poor acceleration vectors compared to a 30fps video.
Re: Problems with high frame rate and autotracker -
Douglas Brown
450 Posts
Assuming the absolute uncertainties dx in the position measurements are the same, then higher frame rates, which give smaller displacements per step ("disp"), will automatically result in larger relative uncertainties (dx/disp). This is why the velocities and accelerations have more noise.
> I've been using Tracker for some time with > students and the first thing we do is analyse projectile > motion and get a value of g (ay) to show it's downwards > and always about the same. I tell them to use high > frame rates for the video and a blank background for > auto tracking. We have a video with 240fps that's > nice and smooth but the autotracker seems to be giving > enough variation between matches on each frame to > create very poor acceleration vectors compared to > a 30fps video.
Re: Problems with high frame rate and autotracker -
Bob Roach
2 Posts
Well this problem was mentioned a couple of years ago, but a solution was not really proffered. May I suggest an alternative that we have found quite successful. Start with the displacement data. Try to place an accurate regression line through it. If you have data from a gravity experiment, then use at least a cubic for the regression, or better yet, use a function arising from integrating Newton's 2nd law. Once a good regression formula for the displacement is found, This can be differentiated to get a smooth curve for the velocity and differentiated once again for the acceleration. Alternatively, one can start a regression with the velocity data from tracker. For example, if one assumes a constant drag coefficient, then Newton's 2nd law can be integrated for the velocity. The function is typically a hyperbolic tangent for problems involving objects falling in a gravitational field. This make an excellent regression formula (do allow time to be shifted slightly since one never gets to start at (0,0)). Further, the coefficient in front of the tanh function is exactly the terminal velocity. Hence one can get the terminal velocity without the object actually reaching it. For the more advanced, one can recognize that for most objects, the drag coefficient is not really constant at the lowest Reynolds numbers. But above about 1000 to about 300,000 (which is where most of the data is for school projects), the CD is fairly constant. So ignore data outside the Reynolds number range and the results will be quite accurate.
