Koch Chart Formula

Does anybody have the Koch Chart formula (equation)? Or know where to
find it?
I have a chart copy but want the function.

"abripl" wrote in message
ups.com...
Does anybody have the Koch Chart formula (equation)? Or know where to
find it?

I don't think there is an actual equation that works generally. As an
obvious counter-proof to the idea that there is one, consider that density
altitude affects airplanes with normally aspirated engines differently from
those with turbocharged engines. The same Koch chart would not work for
both types of airplanes.

I haven't done a lot of research on the origin of the Koch chart, but I
believe that it's to be used as a general guideline, not as a precise
determination of how airplane performance is affected by density altitude.

If you do want to implement the Koch chart mathematically somehow, I'd
suggest that your best bet (in terms of ease of implementation) would be to
manually read off a range of pressure altitude and temperature combinations
to create tables giving the performance adjustment, and then interpolate
between the values for specific input of pressure altitude and temperature.

You could more accurately describe a Koch chart mathematically by actually
reverse engineering it (the scales on the middle portion of the chart appear
to be logarithmic and exponential for the takeoff distance and climb rate
reduction, respectively, so you simply need to measure the scales and
determine the base and power for those functions, and the pressure altitude
and temperature graphs appear to be linear), but that may be more trouble
than it's worth. Given that the chart isn't a precise way to determine the
performance change anyway, you may find it's overkill to analyze the chart
that way.

Pete

Google found several "aviation Koch chart" links including
this one
http://wind-drifter.com/technical/technical.htm scroll
down the page. They have some calculators listed, but the
Koch Chart is just the graph. But any high school math
teacher should be able to walk you through the solution of
the algebra problem to find the system of equations.





"Peter Duniho" wrote in
message ...
| "abripl" wrote in message
|
ups.com...
| Does anybody have the Koch Chart formula (equation)? Or
know where to
| find it?
|
| I don't think there is an actual equation that works
generally. As an
| obvious counter-proof to the idea that there is one,
consider that density
| altitude affects airplanes with normally aspirated engines
differently from
| those with turbocharged engines. The same Koch chart
would not work for
| both types of airplanes.
|
| I haven't done a lot of research on the origin of the Koch
chart, but I
| believe that it's to be used as a general guideline, not
as a precise
| determination of how airplane performance is affected by
density altitude.
|
| If you do want to implement the Koch chart mathematically
somehow, I'd
| suggest that your best bet (in terms of ease of
implementation) would be to
| manually read off a range of pressure altitude and
temperature combinations
| to create tables giving the performance adjustment, and
then interpolate
| between the values for specific input of pressure altitude
and temperature.
|
| You could more accurately describe a Koch chart
mathematically by actually
| reverse engineering it (the scales on the middle portion
of the chart appear
| to be logarithmic and exponential for the takeoff distance
and climb rate
| reduction, respectively, so you simply need to measure the
scales and
| determine the base and power for those functions, and the
pressure altitude
| and temperature graphs appear to be linear), but that may
be more trouble
| than it's worth. Given that the chart isn't a precise way
to determine the
| performance change anyway, you may find it's overkill to
analyze the chart
| that way.
|
| Pete
|
|

"Jim Macklin" wrote in message
news:CGYGg.5789$SZ3.2892@dukeread04...
Google found several "aviation Koch chart" links including
this one
http://wind-drifter.com/technical/technical.htm scroll
down the page.

So what? No one was asking what a Koch chart is, and hopefully everyone
here knows how to use Google by now.

They have some calculators listed, but the
Koch Chart is just the graph.

There are no calculators to provide the information that the Koch chart
provides.

But any high school math
teacher should be able to walk you through the solution of
the algebra problem to find the system of equations.

Doubtful. There is no single "system of equations" that provides the
general answer that a Koch chart attempts to provide. The best you can do
is to show what the Koch chart itself shows, and that chart is based on
general rules of thumb, not actual mathematically derived functions based on
actual density altitude effects.

Pete

I'm sure you can combine equations as well as I, so ...


Variables: D=(density altitude) P=(pressure altitude)
T=(temperature in degrees celsius)


D = (145426 * (1- ((( 288.16 - P * .001981)

/288.16)^5.2563 / ((273.16 + T) / 288.16))^0.235))


APPROXIMATIONS:

For fixed pitch prop, increase sea level standard day takeoff distance 15%
for each 1000 foot increase in density altitude. Approximation good to 8000
feet density altitude

For constant speed prop, replace 15% with 13% in the above equation

For fixed pitch prop, decrease sea level standard day climb rate 7.5% for
each 1000 foot increase in density altitude.

For constant speed prop, replace 7.5% with 7% in the above equation.

(Equations and approximations from "Axioms of Flight", James Embree, Flight
Information Publications, St. Louis MO, 1984. ISBN 0-9601062-7-8)

Density altitude equation not independently verified. Use and report
results please.


Jim



"abripl" wrote in message
ups.com...
Does anybody have the Koch Chart formula (equation)? Or know where to
find it?
I have a chart copy but want the function.

On Wed, 23 Aug 2006 09:37:50 -0700, "Peter Duniho"
wrote in
:

There are no calculators to provide the information that the Koch chart
provides.

Although not what you were talking about, there is this:

http://www.mountainflying.com/apr_denalt.htm
The APR DENALT (DENsity ALTitude) Performance Computer
To solve the takeoff distance and rate of climb at any particular
density altitude, dial in the outside air temperature (degrees
Fahrenheit) and read the "takeoff factor" and "rate-of-climb
factor" to apply to the normal sea level values obtained from the
Pilot's Operating Handbook.

For those who care, you can save the Koch Chart as a picture
file to your computer. Then open it with PAINT or some
other photo editing program. Locate the x,y coordinates for
each part of the graphs and then use those numbers to solve
the algebra problem to get the formula for the system of
equations. Or just use the chart and add a cushion for
safety.



"Larry Dighera" wrote in message
...
| On Wed, 23 Aug 2006 09:37:50 -0700, "Peter Duniho"
| wrote in
| :
|
| There are no calculators to provide the information that
the Koch chart
| provides.
|
| Although not what you were talking about, there is this:
|
| http://www.mountainflying.com/apr_denalt.htm
| The APR DENALT (DENsity ALTitude) Performance Computer
| To solve the takeoff distance and rate of climb at any
particular
| density altitude, dial in the outside air temperature
(degrees
| Fahrenheit) and read the "takeoff factor" and
"rate-of-climb
| factor" to apply to the normal sea level values
obtained from the
| Pilot's Operating Handbook.

I tried a (aT + bP + c)^d type of exponential empirical function
fitting but so far not very exact.

In any case I revised the koch chart into more details with both F and
C temp units and with take off / climb "factors" from SL - easier to
use. Everybody is welcome to the chart at
http://www.abri.com/sq2000/Koch-Chart.gif

My experimental with my engine/prop combo does not have POH values for
takeoff-climb values with altitude and I have flown some over
mountains. Thats why the chart is important to me.

did you not get the exact equations I posted here two days ago?

Jim



"abripl" wrote in message
ps.com...
I tried a (aT + bP + c)^d type of exponential empirical function
fitting but so far not very exact.

In any case I revised the koch chart into more details with both F and
C temp units and with take off / climb "factors" from SL - easier to
use. Everybody is welcome to the chart at
http://www.abri.com/sq2000/Koch-Chart.gif

My experimental with my engine/prop combo does not have POH values for
takeoff-climb values with altitude and I have flown some over
mountains. Thats why the chart is important to me.

Your function was for Da = f(Pa, T) which in turn require various
approximations to get takeoff distance and climb performance - not a
finished product.

I may try again later to get a better empirical function - not
impossible.

RST Engineering wrote:
did you not get the exact equations I posted here two days ago?

Jim