How to determine a polynomial from interpolating between 2 other polynomials

Hi,

Have a look at the attached image. This is an aircraft performance chart. When we use these charts, we plot differents parameters (altitude, temperature, etc..) and, with a pencil, follow these curves and determine the value we are seeking for (fuel, time, distance, etc.)

I would like to acheive the same programmatically so I determined the polymnomials from the kown curves. However, there can be an infinite number of curves and when the plot falls between 2, I must find a way to come up with a new equation based on the interpolation of 2 polynomials.

The attached image shows a dotted line down to a reference line, then the user follow the closest curve (red) down to the know Y axis value, then vertically down (orange) to the value we are seeking.

What would you suggest? Is there some kind of magic with Excel?

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It will not be magic, it will be math. I find that the first step is to understand and define the mathematics I will use.

Polynomials are often useful as empirical correlations, but sometimes they are not the best way. I often find that I prefer to understand the real math behind such a process and use those kind of equations rather than polynomials. In a case like this, usually the first thing I will do is try to find the mathematical equations that produced the graphic.

A basic approach to the problem you describe might look something like this:

1) Read off several data points from the chart and enter into the spreadsheet.
2) Using desired equation, perform regression to obtain parameters for the desired equation. If this regression proves to be "linear" (such as a polynomial or an exponential), then I can use the LINEST() function to perform the regression: https://support.office.com/en-us/art...a-fa7abf772b6d If the desired equation is non-linear, then I will need to use non-linear regression techniques and Excel's built in Solver.
3) With parameters for the desired equation, I can calculate the desired values based on given inputs.

@acheo

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