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While calculating takeoff distance for Cessna 172, POH need to be used. POH charts has pressure altitude and temperature and then distance for those two known parameters.

Does this mean if we have pressure altitude and temperature then we don't have to worry about density altitude in our calculation? Why would we want to calculate density altitude if we only need to know pressure altitude and temperature?

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    $\begingroup$ Is density altitude not calculated from pressure altitude and temperature? $\endgroup$ – TomMcW Nov 4 '16 at 21:24
  • $\begingroup$ @TomMcW Yes, those are two of the primary variables in calculating density altitude. Depending on what you read, some formulas allow you to use only those two variables. Others also—more accurately—include humidity or dewpoint as a variable. $\endgroup$ – J Walters Nov 4 '16 at 21:28
  • $\begingroup$ The thing with Cessna POH data is that if you analyze it, the pressure altitude and temperature do not seem to correspond very accurately to density altitude. If you try to convert the given pressure altitude and temperature data into density altitude, the results are non-proportional. In other words, it is hard to reverse engineer the data to develop a table or formula that is based instead on density altitude. $\endgroup$ – J Walters Nov 4 '16 at 21:31
  • $\begingroup$ Does it mean in Cessna POH charts, they have considered what density altitude going to be for a given pressure altitude and temperature? $\endgroup$ – PMoubed Nov 4 '16 at 21:39
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    $\begingroup$ I would imagine a bigger issue for this is that it's easy to measure pressure and temperature but less so density. Even though you can calculate density it'd easy to measure the others. $\endgroup$ – Notts90 Nov 4 '16 at 23:29
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I have analyzed this information before, and this is what the chart looks like with one line for each weight category if you convert the temperature and pressure altitudes to density altitudes and then chart that vs. the takeoff distance: enter image description here

You can see that I have drawn a sort of best-fit line for this information. I did not add humidity as a factor because the manufacturer's charts had no relevant data.

Clearly, the trend from the manufacturer's data, when converted to density altitude, does not appear perfectly linear if you follow the data points they jump up and then start lower again in chunks of similar density altitude.

The greatest variation here is about 400 feet from the highest point in any of those clusters to the lowest point in the same cluster. That would be the yellow line around 8,000 ft of density altitude.

To answer your question, maybe they didn't use density altitude in the POH because their data appears to be irregular.

With that small margin of error here, I am comfortable using these best-fit lines to quickly calculate my data because I wouldn't make a go descision for a takeoff with a calculated distance anywhere near being within 400 feet of acceptable runway length.

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    $\begingroup$ I almost wonder if my best-fit lines aren't more accurate to actual performance. $\endgroup$ – Ryan Mortensen Nov 5 '16 at 14:57

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