# density altitude equation

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When using your calculated pressure altitude to figure out density altitude, where does the 120 come from?

Density Altitude in feet = Pressure Altitude in feet + (120 x ISA deviation)

Its not really important but I'm sick of hearing "it's magic"!!

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yeah my instructor has no idea what the 120 is or where it came from. it's bound to be a simple reason for conversion purposes but a hard answer would be nice.

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Where does the constant in any equation come from?

It simply is the accepted conversion for the increase in temperature above standard. A better question might be "Where does ISA come from?"

Maybe I'm missing the point, but you have to have a datum to reference, and this is how you quantify the deviation from standard. 120' is the difference you get for each difference in degree. No?

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I don't know if this helps simplify matters it's from wikipedia

Easy formula to calculate Density altitude from Pressure Altitude

This is an easier formula to calculate (with great approximation) Density altitude from Pressure Altitude and International Standard Atmosphere temperature deviation

Density Altitude in feet = Pressure Altitude in feet + (120 x ISA deviation)

Of course you'll need:

Outside Air Temperature

ISA temperature = 15°C - (1.98°C/1000ft x Altitude in feet)

Edited by helo08

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Lose 120 feet for every 1 degree of temp increase above standard.

This is what I use in Excel to make it quick.

B1 is pressure setting (29.93)

B2 is Temp C (5)

B6 is field elevation (2600)

with this pasted in cell B4

=((B2-(15-(B6*0.002)))*120)+(((29.92-B1)*1000)+B6)

Edited by IFLYEVERYTHING
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Helo08 was on the right track with the website. Take a look at the "simplified" equation towards the end:

where: DA = density altitude, feet

Pa = actual pressure (station pressure), inches Hg

Tr = temperature, deg R (deg F + 459.67)

Set Pa to 29.92 and hold it constant, then vary Tr by 1.8 degree F increments (equal to 1.0 degree C), starting at 59 degrees F.

What you will see is the density altitude changing in approximate 120 foot increments for each 1 degree change in temperature. However, it is only an approximation that (in this particular case) is only valid over a relatively small range of temperature (i.e., 52 -57 degrees). At 0 degrees F, the delta altitude per 1 degree temperature shift is actually 137 feet, whereas it is 108 feet at 100 degrees F.

Soooo... like your instructor said, "It's magic!" The "120" can't readily be inferred from the equation and besides, it's only a rule-of-thumb that isn't too accurate over the normal temperature range in which you might be expected to fly. In the summer, you may want to use "110" instead and "125" in the winter. Oh yeah, start factoring in the effect of humidity up DA and you'll have to work with the formulae at the top of the page.

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thanks charlie golf, you really cleared that up for us unfortunate students with simple instructors

Couldn't have said it better myself.

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Any chance you could email me that excel formula as an excel sheet? I would like to put it on my Treo.

Thanks!

Matt

matt@helicopterseminars.com

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Just to add what CofG said,

When you calculate Density Altitude using 'pressure altitude', 120' is a constant; a number to use as a substitute to a series of complex calculations (one of which is shown below).

120 is an approximation of the result of this formula. A more accuate vaule is therefore 118 (as found by my Excel calculation!)

OK, so now you ask, where do the 145442.16 and the 0.235 and 17.326 come from?!

Well, they are just constants too; results of calculations done by matheticians which evaluate factors such as sea level air density, vapour pressure, the effects of temperature on dry parcels of air etc..etc..ending up, I presume at something like Gas Constant, Gravitational Constant, and Pv =nRT. I'm not about to go into how they are derived. Some of that gets beyond my understanding to do justice here.

So yes, 120 is derived from values which have been emperically calculated or arbitarily agreed (ISA) to form a 'reference' so that when we see one set of conditions we can compare them to others, without having to do huge complex calculations each time.

http://wahiduddin.net/calc/density_altitude.htm

Hope that helps.

Joker

P.S.

Any chance you could email me that excel formula as an excel sheet?

For anyone who is interested in tinkering with spreadsheet formulae, then this is probably the best source of all sorts of aviation formuale by Ed. Williams

http://williams.best.vwh.net/avform.htm

Relationship of pressure and density altitude:

D_Alt=P_alt+(T_s/T_r)*(1.-(T_s/T)^0.2349690) (Standard temp T_s and actual temp T in Kelvin)

Edited by joker
##### Share on other sites Guess I always thought that the "120" was a rule of thumb type of calculation to use on the fly so to speak. Using the chart that most manufacturers, and the FAA like to use, a 1" change in pressure results in ~100' change in altitude... no?

But I'll admit that I'm "Old Skool" and tend to accept things for what they are.

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