PPRuNe Forums - View Single Post - Mathematical functions in performance diagrams
Old 25th May 2021, 09:11
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Trim Stab
 
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You can achieve what you want (and very accurately too) by using multivariate regression, as I suggested in my earlier post.

You need to extract data points from the diagram, then put it into LINEST into a spreadsheet program to build a multi-order polynomial of your variables. This will use least-squares regression to solve the best fit multi-dimensional curve to fit the data.

I suggest you aim to create with a low-order polynomial such as:

D=aT + bT^2 + cM + dM^2 + eM^3 + fW +gW^2

Where D= roll distance, M=Mass, W=wind, abcdefg are constants.

You will then need to somewhat laboriously and tediously extract manual data points from the diagram. The more data points you extract, the better. But you MUST input data points at maximum and minimum values of T, M, and W that you will encounter (and combinations of them). This is because the best fit curve will be very accurate interpolating within your data limits, but wildly inaccurate when extrapolating outside your limits.

You then put all your data into a spreadsheet and use LINEST to solve the values of your contants abcdefg. You then have a mathematical formula for your roll distance.

The more data points you add, the more accurate it will be. You can also make a higher order polynomial if necessary.

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