Airplane speed / efficiency curves, estimating between two curves.

hsmith

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Dec 20, 2011
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I have a couple of curves that describe the fuel efficiency of a plane at various speeds with two different gross weights.

The first curve is with the plane fully loaded 16000 lbs gross weight:

y = 0.0115x
2 - 3.0703x + 258.19

Where x is the speed and y is the MPG.

The other curve describes the speed versus MPG with a 9300 lbs gross weight:

y = 0.0093x
2 - 2.396x + 188.04

If I want to estimate the efficiency at an arbitrary gross weight (say at 12000 lbs), is there an accurate way to do this easily?

I was thinking about just performing a linear estimation between the two (~40% between the 16000 and 9300 y values for 12000lbs).

Is there a better way to do this?

Thank you in advance.


 
Try interpolation with each of the coefficients.

You could also build a model that includes the Gross Weight. What sort of data have you?
 
Data

The source data is pretty limited, it only specifies the MPG versus the GPH at various gross weights of the plane.


MPH 16000# 12900# 9300#
130 52.75 40 34.25
140 53.5 42 35.5
150 56 45.5 38.5
160 60.5 50.75 43.5
170 67.5 57.25 50.5
180 77.5 65 59

Thanks.
 
interpolation with each of the coefficients

Try interpolation with each of the coefficients.

You could also build a model that includes the Gross Weight. What sort of data have you?

I tried that, the results were poor.

Thanks.
 
I tried that, the results were poor.

Thanks.

Most often, poor results are the end product of poor effort. It's not really your fault, except that perhaps you really do not understand the power mathematics brings for an overwhelmingly wide range of problems.

Try this:

If F = Fuel Load, and
If M = MPH

0.00492668*F - 0.473651*M + 0.00375344*(M^2) - 0.0000146752*(M*F) = Efficiency(M,F)

Is this any better than your poor results? The average deviation from your empirical results is 1.69. Is that too big? The greatest deviation from your data is 4.58. Indeed, this may be too large, but it's just a first or second pass at a useful model. We can do a lot with it.
 
Thank you for taking a look at it. When I said that the results were poor attempting to interpolate the constants, I meant that they accuracy was poor even tested against several tested data points. The linear estimation between the two curves proved to be more accurate. I am looking for a worst case of < 5% due to the nature of the problem.

Unfortunately the problem requires a high degree of precision and I believe that attacking the problem with the limited amount of data that I presented is not possible. In order to produce a better estimate there will be other factors such as engine horse power, RPM, and perhaps altitude that will need to be taken in to account later.

Again, thank you for taking the time to look at it.
 
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