Landing/Takeoff Considerations, Part IV: Density Altitude 

“Some people change their ways when they see

 the light; others when they feel the heat.”

--Caroline Schoeder--

Density altitude, pressure altitude corrected for temperature and humidity, is a very interesting and important reality for pilots. It defines the atmospheric reality, the performance reality, within which an aircraft operates.

For normal people—non pilots—air is air. It may be wet or dry, warm or cold, but its condition does not significantly affect how people operate within it unless things are quite extreme. We can walk just as quickly or slowly in cold air as we can in warm air. Moist air does not affect our ability to speak or gesture any differently than dry air.

To a pilot, however, density altitude has immediate and significant implications for aircraft performance. It directly affects takeoff and landing distances, rate of climb, and any of the myriad other aspects of performance involving lift.

Remember the formula for lift? Lift = 1/2C_LPV²S where C_L represents the angle of attack combined with the shape of airfoil, P (Rho) represents air density, V represents velocity and S represents the surface area of the aircraft’s wing. If we change any of the factors involved in lift, we change the lift produced: lower the air density, reduce the lift; increase the air density, increase the lift.

Air density is a factor in every performance aspect of flight involving lift. The only time we are not concerned with lift production is when we are securely tied to the ground and, even then, we may have concern about unwanted lift produced by brisk winds that may threaten the security of our little machine on the ground.

Normally, when we speak of density altitude, we refer to the result of correcting pressure altitude for temperature. In fact, there are four variables that combine to produce density altitude: altitude, pressure, temperature, and humidity.

Altitude is the height ASL. If we are on the ground, we refer to altitude as station altitude. If we are in the air, we refer to altitude as height above sea level (ASL).  Out here on the coast, we are pretty much talking about sea level for station altitude and often forget to include this factor. For those poor people who must fly out on the prairies or in other difficult regions, the altitude of their airport can be a significant factor. Just sitting on the ground at Calgary/Springbank (CYBW), for example, puts us at an altitude of 3939’.

Pressure is derived from the standard baseline: pressure altitude. Altitude and pressure combined are used to obtain pressure altitude. If you are in the aircraft, you can determine pressure altitude by simply setting your altimeter to standard pressure, 29.92” Hg, and reading the result.

If you are on the ground sitting at your desk, you can combine the altimeter setting for a given reporting station with the station altitude. Take the station pressure in inches of mercury, subtract it from the standard, 29.92, multiply the result by 1000—each 1.0 inch of mercury is equivalent to 1000’; each 0.1 inches is equivalent to 100’; each 0.01’ is equivalent to 10’—and add the difference to the station altitude.

For example, let’s take a look at a METAR for Calgary/Springbank.

METAR CYBW 302200Z 35006KT 25SM FEW052 SCT070 SCT120 24/11 A3005 RMK CU1AC3AC1 CB EMBD N + E SLP172=

The METAR tells us the altimeter is 30.05 inches of mercury, somewhat above standard. To determine the pressure altitude at YBW we would subtract the station reading from standard, 29.92 – 30.05 = - 0.13, multiply by 1000, - 0.13 x 1000 = - 130, add the result to the station altitude, - 130’ + 3939’ = 3809’, and there we are. The pressure altitude at the time of the METAR is 3809’. The higher than standard pressure indicated by the altimeter setting gives us a lower than standard pressure altitude.

For those of you who enjoy equations, we could say: PA = H + PA V, where H represents station elevation and PA V represents pressure altitude variation approximation, i.e. 29.92 minus the current altimeter setting times 1000 (1).

If we want to get tricky and use an electronic pressure altitude calculator we would come up with a slightly more accurate number, 3814’ (2).

To derive the density altitude, we now must factor in temperature and humidity. From the METAR we learn the temperature is 24 degrees C, somewhat higher than standard. ICAO standard temperature for sea level is 15 degrees C. Standard for 3939’—using the standard lapse rate of 1.98 degrees C per 1000’—would be approximately 8 (7.799) degrees C, 16 degrees C above standard.

Placing the pressure altitude, 3809’, under the temperature, 24 degrees C, in the airspeed correction window of our little E6B Flight Computer gives us a density altitude of just under 5000’. My old eyes simply don’t give me much better resolution (3).

What does this mean? Just sitting on the ground at YBW at the time and day of the METAR, our little aircraft will perform as though it were flying at 5000’ on a standard day.

Humidity is the last factor and one we don’t normally consider because it affects engine performance more than lift performance, although it does decrease lift. Wet air is less dense than dry air and we can expect a decrease in performance as a result. An easy Rule of Thumb is to add 10% to our computed takeoff distance on days of high humidity. This covers both the loss of engine power and the decrease in lift we might anticipate (4).

If we want to get really accurate we can use an electronic density altitude calculator, which includes both temperature and humidity, and determine the density altitude is 5023’ (1084’ + 3939’ = 5023’) (5).

A more rough and ready Rule of Thumb for calculating density altitude is to say that for each 10 degrees F. or 6 degrees C. above or below standard we would add or subtract 600’ to or from field elevation (6).

Using our example at YBW, the temperature is 16 degrees above standard, so we subtract 960’ (24 – 8 = 16; 16/10 = 1.6; 1.6 x 600’= 960’) giving us a density altitude of 4899’ (3939’ + 960’ = 4899’), not too far off what we found with the E6B method or our electronic flight computer.

So, what does all that mean in terms of takeoff and landing performance? Simply this: high density altitude reduces performance; low density altitude increases performance. Density altitude is the performance altitude of the aircraft, the altitude at which the little machine thinks it is operating.

Most Pilot Operating Handbooks will allow you to compute the required takeoff and landing roll figures so you can make an intelligent decision whether or not to takeoff or land. We also have a couple of Rules of Thumb that can be helpful.

For takeoff, to the sea level performance figure, add 12 percent for each 1000’ of density altitude up to 8000’; add an additional 20 percent for each additional 1000’ density altitude above 8000’.

Taking our day at YBW, for example, a C-172 which requires about 900’ for takeoff at sea level on a standard day, would require just over 1400’, an increase of almost 60% (4889’/1000’ = 4.899; 4.899 x 0.12 = 0.58788; 1.58788 x 900’ = 1429.092’).

If we added a high level of humidity to this scenario, increasing our takeoff distance by an additional 10% to 1540’ (1400’ x 1.1 = 1540’), unless we have runway to spare we might want to consider waiting until early morning when the temperature is, hopefully, much lower. The 1200’ runway that seemed just fine at sea level simply won’t do under these new conditions.

Our rate of climb is also sadly reduced by high density altitude. A Rule of Thumb for quick estimates is that our rate of climb is reduced by approximately 7% for each thousand feet of density altitude up to 8500’ and 8% for each thousand feet above 8500’.

With our little C-172, which can produce a rate of climb of about 680’/min at sea level on a standard day (according to the POH, always somewhat optimistic), at YBW on the day and time of the METAR we might expect something closer to 450’/min. (4899’/1000’ = 4.899; 4.899 x 0.07 = 0.34293; 1 – 0.34293 = 0.65707; 900’ x 0.65707 = 446.8076). Not quite as exciting as we might hope, particularly if there are any obstacles in our path.

Density altitude has a very significant effect on aircraft performance. Runway lengths are fixed, but the distance we require for takeoff or landing is a function of the performance environment with which we are working. Out here on the coast we tend to become spoiled and lazy. Most of the airports are pretty close to sea level and the marine environment moderates temperatures. This is all to the good.

It is important to remember, however, the rest of the world is not always quite so forgiving. Understanding how to calculate density altitude, its effects on aircraft performance and how to accurately use the performance tables provided with your aircraft can contribute in a very positive manner to both your enjoyment of flight and safety.

Notes:

1. http://www.tpub.com/content/aerographer/14269/css/14269_72.htm

2. http://www.hqjmtc.army.mil/weather/stnpresspa.html

3. For the full meal deal check out: http://en.wikipedia.org/wiki/Density_altitude

4. Imeson, Sparky, Mountain Flying Bible, Aurora Publications, Jackson, Wyoming, 2001, pg. 2-11

5. www.hqjmtc.army.mil/weather/densalt.html 

6. Imeson, Sparky, Mountain Flying Bible, Aurora Publications, Jackson, Wyoming, 2001, pg. 2-12