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## Density Height Calculations

• lostinspace2011
• Topic Author

### lostinspace2011 created the topic: Density Height Calculations

In my preparation for the PPL theory exam I came across this question:

Altitute: 7000ft
QNH: 1003 hPA
OAT: -4 C

and I am being asked to calculate pressure height, density height

PH=Elevation + (1013-QNH) x 30
PH=7000 + 10x30 = 7300ft (So far no problem)

ISA Temp at PH=15-7.3*2=0.4
ISA Deviation = OAT - ISA Temp
ISA Deviation = -4 - 0.4 = - 4.4

DH=PH+ISA Deviation x 120
DH=7300+(-4.4x120)
DH=7300-528 = 6772ft

However the work book suggest the correct answer to be 6820ft. Working backwards (7300-6820=480=4 x 120) this assumes an ISA deviation of 4, which suggest that instead of using 7.3 (7300ft) for the PH 7.5 was used.

So my question is what is the recommended way to round up/off the elevation to calculate the ISA temperature.
Should I always round up to the neared 500ft ?

• michel@deprez.id.au
• • Offline
• Posts: 8

### michel@deprez.id.au replied the topic: Density Height Calculations

From the examples I have done with Bobs exams round up or down to the nearest 500ft when calculating the ISA Temp.
Regards, Michel.
The following user(s) said Thank You: lostinspace2011

• arc0717
• ### arc0717 replied the topic: Density Height Calculations

Hi

But then to reach DA of 6820', the calculation will be using PH 7300' and ISA Dev using PH of 7,500 as follows:

DA = 7300 + (120 x (-4 - (15 - (7.5 x 2)))
DA = 6820'

Why is that?

Azhar

• michel@deprez.id.au
• • Offline
• Posts: 8

### michel@deprez.id.au replied the topic: Density Height Calculations

I'll defer to the more educated ones....(@Bob or @Stuart)... but if I can hazard a guess, it's probably accurate enough for our simple calculations. If you are really at the peak of weight and density limits then you should probably not fly the aircraft unless you are 100% certain you are under the maxes.
I'm sure we have all seen that youtube clip of that guy who took off from a high elevation aerodrome and almost clipped the trees?

• bobtait
• • Offline
• Posts: 2103

### bobtait replied the topic: Density Height Calculations

This method is used is to avoid using fractions of a degree in the calculations. That would be perfectly acceptable in practice. (After all we don't use fractions of hectopascals for the QNH - that's always given to the nearest whole).

Therefore, if the pressure height is 7300 feet, for the sake of establishing an ISA temperature, we use 7500 feet which will give us a temperature to the nearest whole degree.

Therefore, the ISA temperature is (15 - 2 x 7.5 = 15) which is zero. Since the actual temperature given is -4°C, the ISA deviation is -4.

120 times -4 = -480. So the density height is the pressure height of 7300 - 480 = 6820.
(Note that we only use the rounded-up figure to establish the ISA temperature, but we apply the ISA Deviation correction to the pressure height as calculated previously).

Also, the actual aircraft performance data is usually given in the form of tables or graphs. That makes it impossible to use entry arguments calculated to a fraction of a degree. Do you know the weight of the aircraft to a fraction of a kilo? You'd be lucky to know the gross weight to the nearest 10kg. That's why there are margins built into the performance figures.
The following user(s) said Thank You: arc0717, michel@deprez.id.au