# Interesting Ball Trajectory Question

Hi All,
I am present using a kalman filter to predict the future motion of a ball that has been thrown. I have at present implemented a simple model of the
situation with gravity and air resistance. However, I have only modelled air resistance as directly proportional to speed.
1. I am tracking the ball (a cricket balls motion) over a distance of about 2.5m and want to predict a further 3-4m into the future. Will modelling the air resistance as proportional to speed squared make much difference to the accuracy of my prediction?
2. If I do go for a model with air resistance as proportional to speed squared, any suggestions how I can fit it to the kalman setup i.e.
X(t+1) = A.X(t)
where X(t+1) and X(t) are column vectors of x,x speed, y, y speed. and A is the relating matrix between the current state and the state at t+1 of the aformentioned variables. Maybe I need to have a different things in my column vectors? But they are the things I can calculate.
Note:- I have tracked the third dimension, but I am just trying to get the idea of all of this, so only considering 2d at the mo.
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Almost as long since I chucked a cricket ball as since I took high school physics, but I seem to remember wind resistance is proportional to the cube of velocity.
My two pennyworth
PeterS
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Unless the ball is going very fast or you need very high accuracy, I would just ignore it. Cricket balls are fairly heavy, so the effect of air resistance will be negligable over the kind of distances you are talking about.
- Daniel
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I need to be as accurate as possible. I know it seems a bit too much, but I want to predict the position of the ball to the best degree possible.

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You might want to think about starting with the dominant sources of position error in your system, and working back from there. I have done similar work where I tried make a model that accounts for the difference between the measured and predicted values. Here are some things other than wind resistance that you might want to take into account: does the elasticity of the ball change with temperature, is there any wear on the launching mechanism from run to run, how repeatable is the launching mechanism, is a cricket ball wooden (I have never seen one) and capable of changing mass with moisture content, will the density of the air be changing with altitude and humidity, is the elasticity of the ball surface uniform or does it have 'soft spots'? Given all this, if you can take repeated measurements that show a consistent error, you might just include an error constant in you calculation that improves the accuracy of the prediction.
- James B