Quandaries and Queries

I am a farmer in Ontario. It has been almost 20 years since high school. I am toying with making a windmill. The output chart for the the old generator I have is shown below. Before I tear it appart I would like to develop a formula from the chart that can predict the output at various speeds.

Thank you very much for your time,
Matthew

 Rpm x100 kWatts 6 0.28 9 1.15 12 2.61 15 5.13 18 8.93 21 14.24 24 19.13 27 19.92 28 19.73 29 18.69

Hi Matthew,

I plotted your data and got

which is roughly what I expected. The output in kWatts increases slowly at first, then rises rapidly with increased rmp and then flattens out. The fact that the last two points drop off is probably from increased experimental error near the limits of your equipment.

To me this looks like a logistic growth model, that is a function of the form

I used the nonlinear fit procedure in the computer program Mathematica to estimate a, b and c and got the function

I then plotted this function on top of your data points to get

This is quite a good fit so I would feel confident in using the equation above to estimate the output from the generator. I have two cautions however. First it is an estimate and I don't have error bounds to give you. The second caution is that your data values for rmp range from 600 to 2900, so you should only use the function estimation with rpm values in the same range.

Penny

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