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Old August 26th 06, 12:47 AM posted to rec.aviation.piloting
Peter Duniho
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Posts: 774
Default Koch Chart Formula

"abripl" wrote in message
ups.com...
[...]
Does anybody know Mr. Koch? Surely somebody made the chart up
originally?


You could make such a chart from scratch fairly easily, using empirical
methods. For an airplane that has published performance figures for
different density altitudes, it's especially easy. For one that does not,
you'll have to do some flight testing to obtain those figures, but once you
have them, the process is the same.

If you know the *exact* performance characteristics of a given airplane, it
is possible to come up with some pretty precise formulae describing that
airplane's performance at various altitudes. But getting that data is
difficult, and unless you have access to a vast engineering database of
engines, prop and wing airfoils, drag coefficients, etc. you're unlikely to
be able to. But empirical data is relatively easy to come by. Fly the
plane, take notes, viola.

Of course, someone already did all that, and they made a chart out of it. I
gather from your previous post that your approach was to attempt to
parametrically combine all of the factors into a single equation, but I'm
not convinced that's the right approach, at least not initially. You
actually have a couple of equations, based on the same line-intersection
equation that can be based on the chart that's already published. But that
equation isn't going to take the form "(aT + bP + c)^d".

You've got a line equation defined by the two endpoints (temperature and
pressure altitude), intersecting with the vertical axis at some point. That
gives you a vertical coordinate that can be used logarithmically (takeoff
distance) or exponentially (climb rate reduction) to determine the actual
correct factor found on the chart. The actual Cartesian coordinates for the
graph and the base or exponent (as appropriate) are derivable from the
existing chart, simply by measuring the chart and mapping it back to the
original numbers. But you're not going to get an equation of the form "(aT
+ bP + c)^d"...you'll get one linear equation that gives you the point of
intersection, and then two other equations (one log, one exp) to map that to
the actual performance adjustments.

Of course, even after you do all that, all you've got is a mathematical
description of the Koch chart. It's not going to tell you the *actual*
performance variations for a given airplane. It's just going to give you
the same (generally conservative) rules of thumb that the Koch chart
provides.

Pete