more confusion on cessna performance chart

A little while ago I started a thread about why a Cessna landing
peformance chart showed a climb wt limit that was pressure altitude
rather than density altitude dependant. Well now I am similarly
confused by a different performance table ( not a chart this time)
which shows the take off distance required for a C172N. This table
shows the distance required as a function of pressure altitude form 0
to 8000 ft ( in steps of 1000 ft) and temperature of 0 to 40 deg C in
steps of 10 deg C. This table comes from the flight manual of the
aircraft.

Now I thought it would be a useful addition to my Excel flight fomulas
to convert all this data into a graph of distance required vs density
altitude and fit an equation to it, so then I could just enter density
altitude and the program would calculate distance required ( with
corrections for wind etc)
Well the problem is that where the density altitude ranges overlap for
the different temperatures the distance required differs with the
lower the temp, the higher the distance required for the same density
altitude.

At around 8000 ft density altitude the difference was like 300 ft
between 0 and 40 deg C which is quite significant. I am pretty sure I
know how to calculate density altitude, but just in case here is how I
do it,

Take the pressure altitude and correct for temperature as follows.
eg for 3000 ft pressure altitude and 30 deg C. ISA temp would be
(15-3x2)=+9 C, so we are 21 C over ISA temp. 21*120 =2520 +3000
=5520 ft density altitude

So why would the takeoff distance required vary with temperature at
the same density altitude?, it goes against everything I understood
about peformance being a function of the air density.

Any help appreciated.
Terry
PPL downunder

Rolling resistance of tires?

Hard to say what Cessna's assumptions are, especially when they didn't
include their formula, just a data set.

On Mon, 14 Jan 2008 12:56:46 -0800 (PST), terry wrote:

So why would the takeoff distance required vary with temperature at
the same density altitude?

I confess that I'm lazy today and didn't read what you said for
comprehension, but I will address the above statement.

DA mantra:
Density altitude is pressure altitude corrected for non-standard
temperature.

Ok, so if DA has been corrected for temperature, then we're done.

The "vary with temperature" part of your statement doesn't make any sense
if you are using DA, the temperature factor has been applied already. You
wouldn't apply temperature again to come up with an answer.

The statement above would make sense if you said: The takeoff distance
required will vary with temperature at the same "pressure altitude".


--
Dallas

Your PA-to-DA calculations clearly differ from Cessna's, probably
because they used a different standard atmosphere. There are plenty
to choose from: International SA, U.S. SA, ICAO SA (all revised over
the years) and some others, some of which are no longer used. You'd
need to find out which SA was used by Cessna when the 172N was built.
Good luck with that project. I would just plot some points from the
POH and draw a smooth curve connecting them; I'd be conservative in my
choices of data points and call that good enough.

On Jan 15, 9:49*am, Dallas wrote:
On Mon, 14 Jan 2008 12:56:46 -0800 (PST), terry wrote:
So why would the takeoff distance required vary with temperature at
the same density altitude?

I confess that I'm lazy today and didn't read what you said for
comprehension, but I will address the above statement.

DA mantra:
Density altitude is pressure altitude corrected for non-standard
temperature.

I agree
Ok, so if DA has been corrected for temperature, then we're done. *

The "vary with temperature" part of your statement doesn't make any sense
if you are using DA, the temperature factor has been applied already. *You
wouldn't apply temperature again to come up with an answer.

No I havent corrected twice, the point of the post was that after
correcting pressure altitude for temperature to get density altitude,
different combinations of pressure altitude and temperature which
result in the same calculated density altitude give different
performance figures.

The statement above would make sense if you said: *The takeoff distance
required will vary with temperature at the same "pressure altitude".

yes it would make sense but then I would have had no need post the
problem, which is that the same density altitude calculated using
different combinations of pressure altitude and temperature do not
give the same performance. For example, Dallas if the presssure
altitude as 5000 ft and temp was 10 dec C, that would be a density
altitude of 5520 ft.
Now I could get the same density altitude of 5520 ft if I had a
pressure altitude of 3000 feet and a temperature of 30 C . Do we
agree on that? I I would then expect that the takeoff distance
required for either of these 2 scenarios would be the same. The point
of the post being that this not the case with the data set in the
table.

I could have explained it a lot better with graphs but I dont think
you can do that on usenet.

Terry

On Jan 15, 10:24*am, quietguy wrote:
Your PA-to-DA calculations clearly differ from Cessna's, probably
because they used a different standard atmosphere. *There are plenty
to choose from: International SA, U.S. SA, ICAO SA (all revised over
the years) and some others, some of which are no longer used. *You'd
need to find out which SA was used by Cessna when the 172N was built.
Good luck with that project. *I would just plot some points from the
POH and draw a smooth curve connecting them; I'd be conservative in my
choices of data points and call that good enough.

Good point , perhaps that is the issue,the data I have do not specifiy
what standard atmosphere.

Thanks
Terry

On Mon, 14 Jan 2008 16:20:34 -0800 (PST), terry wrote:

I could have explained it a lot better with graphs but I dont think
you can do that on usenet.

I've been known to use graphics to ask questions here.. like this:

http://img.photobucket.com/albums/v1...ofileChart.jpg

--------------
Oh, and this might interest you... as mentioned in an other post, the
algorithms to determine DA are not "fixed" they are a black art of sorts.
Here's a good example, two of the same model but different editions of an
electronic E6B with the same values entered yield two different answers for
DA & PA.

http://img.photobucket.com/albums/v1...SportysE6B.jpg

Go figure.
--
Dallas

So why would the takeoff distance required vary with temperature at
the same density altitude?, it goes against everything I understood
about peformance being a function of the air density.

Any help appreciated.
Terry
PPL downunder

I wonder if Cessna used formulas at all. I would think rather not.
They probably measured all of those values during the certification
process. I don't see how any aircraft could get its performance info
certificated based solely on mathematical calculations. You have to
test the plane for realiable data.

If I'm right and all those data points come from actual flight data
(and an average of that, too), then it's not a big surprise that
simple calculations regarding density altitude don't seem to make
sense.

Also density altitude calculations that consider only temperature are
at best approximations -- good enough ones for most conditions,
probably. But density altitude is also dependent on moisture content
of the air, which is perhaps even less known in a given air parcel
than temperature.

Has anyone on the list ever worked with or for Cessna who might know
how they generate their performance charts? Experimental measurement
-- or calculated "guess"?

On Jan 15, 11:20*am, terry wrote:

*For example, Dallas if the presssure
altitude as 5000 ft and temp was 10 dec C, that would be a density
altitude of *5520 ft.

DOH not a good example that should have been 5000 ft and 9.3 deg C to
give 5520 ft

Now I could get the same density altitude of 5520 ft if I had a
pressure altitude of * 3000 *feet and a temperature of 30 C . Do we
agree on that? *I I would then expect that the takeoff distance
required for either of these 2 scenarios would be the same. *The point
of the post being that this not the case with the data set in the
table.

I could have explained it a lot better with graphs but I dont think
you can do that on usenet.

Terry

Has anyone on the list ever worked with or for Cessna who might know
how they generate their performance charts? Experimental measurement
-- or calculated "guess"?

To answer my own question: in the USA FAR part 23 describes in
excruciating detail how these data charts have to be created and I
excerpt for GA (a bit wily nily):

Sec. 23.45

General.

(a) Unless otherwise prescribed, the performance requirements of this
part must be met for--
(1) Still air and standard atmosphere; ...

(b) Performance data must be determined over not less than the
following ranges of conditions--
(1) Airport altitudes from sea level to 10,000 feet; and
(2) For reciprocating engine-powered airplanes of 6,000 pounds, or
less, maximum weight, temperature from standard to 30° C above
standard; ...

(f) Unless otherwise prescribed, in determining the takeoff and
landing distances, changes in the airplane's configuration, speed, and
power must be made in accordance with procedures established by the
applicant for operation in service. These procedures must be able to
be executed consistently by pilots of average skill in atmospheric
conditions reasonably expected to be encountered in service.

(g) The following, as applicable, must be determined on a smooth, dry,
hard-surfaced runway--
(1) Takeoff distance of Sec. 23.53(b);
(2) Accelerate-stop distance of Sec. 23.55;
(3) Takeoff distance and takeoff run of Sec. 23.59; and
(4) Landing distance of Sec. 23.75.
NOTE: The effect on these distances of operation on other types of
surfaces (for example, grass, gravel) when dry, may be determined or
derived and these surfaces listed in the Airplane Flight Manual in
accordance with Sec. 23.1583(p).

Note the word "determined", not "calculated" or "derived" for all
except the bit about types of surfaces, where "derivation" is allowed.

There are a LOT of variables in those rules that don't lend themselves
to mathematical expressions. My conclusion is that there is no simple
formula available to apply in an Excel spreadsheet that will reliably
predict the numbers from the chart, thus your calculations seem to
have contradictory results (eg, different performance for same density
altitude).

Of course, someone with more experience in aircraft certification /
performance data generation will probably post something right away
showing I don't know a damned thing and my conclusions are completely
wrong.