Updated: Oct 11, 2020
DENSITY ALTITUDE (DA) - the height your aircraft 'thinks' it is at. Atmospheric conditions determine this. Your engine will behave accordingly. ALTITUDE with QNH set - your actual height above sea level. HEIGHT QFE - your height above ground level. This is specific to the actual spot where you set the QFE.
AMSL = Above Mean (average) Sea Level.
ISA = International Standard Atmosphere. This definition assumes the temperature at Sea Level is 15°C, and decreases by 2°C for every 1000 ft increase in our height above sea level, (we round up from 1.98°C - the maths is easier-).
WHY CALCULATE DENSITY ALTITUDE?
Because there are days that, although you and your aircraft are at, for example, 5500 ft AMLS, your aircraft will perform as though it is at 8500 ft, or higher, on take-off. Because there are days that, at Sea Level, your aircraft will behave as though it is already at 3000 ft on take-off. It's not the aircraft's fault. It's D-e-n-s-i-t-y A-l-t-i-t-u-d-e. I am going to keep this DA calculation very practical and user friendly. Of course there are different methods to do the same thing.
HOW TO CALCULATE DENSITY ALTITUDE:
Determine the Pressure Altitude:
Look in the aircraft, and set the Altimeter to the Standard setting, (QNE), 1013 hPa or 29.92 inches of Mercury . Read off the corresponding altitude on your Altimeter. This is the Pressure Altitude where you are, for today. Tomorrow the reading may be different. If there is a high pressure system around, your Altimeter will read a lower altitude than your actual height AMSL, if there is a low pressure system around, your altimeter will read as though you are higher than your actual height AMSL. It is possible for the PA to be the same as Standard, in which case your altimeter will read correctly. (1 hPa = 30ft)
If you have a modern dashboard, you may be able to read the Density Altitude on the screen, all worked out for you. No further effort required.
Work out the effect of Temperature:
Look at the Outside Air Temperature (OAT) There should be one somewhere in the cockpit. Calculate what ISA would deem as your actual ISA temperature at your current altitude AMSL. eg. at Sea Level in Richards Bay, it should be 15°C. Truth is, it usually isn't. Lets assume it is mid summer, and is 35°C outside, excluding the effect of the 80% humidity. Yes, it feels like a warming drawer, and every sane person is hiding inside a building with the air-con on full blast. So it should be 15°C but it is 35°C; a good 20°C hotter than ISA. The calculation to work out your DA is take the difference between the ISA temperature and the actual temperature, (in this case 20°C) and multiply that number by a constant 120 ft (we round up from 118.8 ft per °C to 120 ft for easier calculations... it's close enough and errs on the side of safety). 20 x 120 = 2400'
AltitudeTemperature - according to ISA
8000 ft --- -1°C
7000 ft --- 1°C
6000 ft --- 3°C
5000 ft --- 5°C
4000 ft --- 7°C
3000 ft --- 9°C
2000 ft --- 11°C
1000 ft --- 13°C
0 ft (Sea Level) --- 15°C
Put it all together:
Now add 2400' to your Pressure Altitude you got in step 1 above, and VOILA, you have the Density Altitude. Roughly. Please note, this calculation EXCLUDES the effect of humidity. I haven't been able to find a formula for humidity, but would recommend adding 20% to your take off distance if your humidity is 80%. Remember, when it is humid, water particles are taking up the space that would otherwise have been air particles, in effect making the air less dense, and giving your propeller less air to "bite" into, thereby reducing the performance, (both engine and aerodynamic), of your aircraft. It is always a good idea to make a quick density altitude calculation during your pre-flight.
One more example:
You are in Pietermaritzburg.
Your Elevation is 2500 ft. (Elevation is your height on the ground above Sea Level).
The PA is 1023hPa, - so the air is a bit thicker than ISA. (At ISA it would be 1013hPa).
The temperature is 30°C.
When you dial 1013 into your Altimeter, it will read, (give or take) 300 ft below your Elevation, 2200ft (1hPa = 30ft altitude).
Your temperature in Pietermaritzburg at 2500ft Altitude should be 10°C if ISA conditions prevailed.
You are now 20°C HOTTER than ISA (30°C - 10°C = 20°C HOTTER)
20 x 120 = 2400 ft thinner air = as if you are higher.
PA 2300 + 2400 ft apparent height increase = DA of 4700ft.
Your aircraft, taking off from 2500 ft physical height, is going to behave as though it is taking off from 4700 ft. If the runway has been baking in the sun, then the heat off the tar is going to thin the air even more just above the runway, increasing the DA on the runway even more.
Now you know why a runway below sea level in a desert is so very very very long.