My introduction to density altitude was early in my private pilot training in an Ercoupe. On the first takeoff of the day my instructor wanted to simulate a high-altitude takeoff, so he set the throttle at about two-thirds power and said, “Go, and don’t hit the fence at the end of the runway.” He also said this is what it might feel like if the density altitude was high. Density altitude? I had no clue. After the flight he gave me a fairly cursory explanation of the concept. That was more than 62 years ago. Hopefully, instructors do a much better job now of explaining the theory and practice for the concept.
What is Density Altitude?
Our atmosphere is mainly nitrogen (78 percent) and oxygen (21 percent) molecules (N2, O2), with atomic masses of 28 and 32 respectively, so the average mass of these air molecules (ma) is 29 protons. When air moves with velocity (v), the kinetic energy of one cubic centimeter of air is half the density times velocity squared. Multiplying that by the lift coefficient and wing surface area gives the lift of the aircraft, so if the density drops so does lift. Propeller thrust suffers in a similar way.
So how does the density drop? The pressure of air is p = nkT, where k is the Boltzmann constant and T is the temperature of the air. If a parcel of air at your airport is heated at constant pressure, the particle density (n) must drop, and therefore the mass density drops. You can ask, at what altitude would I find air with this lower density on a standard atmosphere day? It would be higher up, at the density altitude of the airport.
Figure 1. Air density for the ISA model temperature profile. It drops roughly exponentially with altitude (by half at 22,000 feet).
If this density altitude is not reported on the ATIS or automated weather how do you find it? In my last article in Flight Levels I explained how the atmospheric pressure changes with elevation, as determined by the solution to the barometric equation when the atmospheric temperature profile is given by the ISA model (International Standard Atmosphere). You can also find the density of the atmosphere as elevation increases using the barometric equation, solving for n instead of p as a function of height, again using the ISA model for temperature. Details of that solution are found in my web article, Barometric and Density Altitudes. This solution for air density on a standard day neglects the partial pressure of water vapor in the atmosphere, typically around 1 percent at sea level.
Just as the pressure drops (roughly) exponentially with altitude on a standard day, so too does the air density. A plot of air density versus altitude on a standard day is shown in Figure 1. It is halved at 22,000 feet. As with pressure calculations, the density altitude computation requires knowing the temperature profile of the atmosphere, and the ISA model is just that; a model. In the actual atmosphere there are errors in both pressure and density because the profile is unknown.
Lift will drop proportionally with density if you keep the airspeed and angle of attack constant (same coefficient of lift). Also, horsepower on piston engines drops about 3 percent for every thousand feet of altitude, so that factors into performance as well.
Figure 2. Density altitude vs airport elevation for 80 degrees F and 100 degrees F, when the pressure at the airport is standard (29.92 at sea level, reduced by the ISA model for the airport elevation).
Calculations for density altitude are done by first calculating the drop in density at your airport compared to a standard day. Calculate the ratio of the actual temperature to the ISA temperature for your airport, and then we use that ratio and the density equation to determine the altitude at which this lower density is found on a standard day. That density altitude is shown in Figure 2 for two different temperatures, but with standard pressure (29.92 at sea level). If the altimeter setting is above 29.92”, the air density is a little higher that normal so the density altitude will be slightly less (see my web article on how to calculate that as well). Increasing temperature will likely raise the density altitude much more than increased pressure will lower it.
Using density altitude and information from your pilot operating manual, you will be able to determine the degradation of performance (runway required, climb rates) with altitude. But, a general rule of thumb for normally aspirated engines is to add 10 percent to required runway length per 1,000 feet of density altitude to 8,000 feet, and 15 percent per 1,000 feet over that.
For landing add 2 percent to the IAS for each 1,000 feet to determine true airspeed (but land at the same IAS at all altitudes). The increased TAS increases landing distance according to the square of the speeds. For example, landing at 110 percent true airspeed increases distance by 21 percent (1.102 = 1.21). The above rules of thumb are from Sparky Imeson of Mountain Flying, LLC.
How to find your Density Altitude
Figure 3. Density altitude from the DALT page in Utilities on the Garmin 650/750.
If you don’t get the density altitude from ATIS you can use the Koch chart to find the increase in runway and decrease in climb rate. Or you may get density altitude from your GPS. On the Garmin 650/750 you can determine density altitude, TAS, and winds from this choice on the Utilities page. If you touch Use Sensor Data, much of this data will be filled out automatically. You cannot determine density altitude from the GNS 430/530 or G1000. Wouldn’t it be nice if these touchscreens offered DA as one of the data fields you can put on the map!
In summary, the topic of density altitude involves several things; understanding what it means, why temperature largely determines that altitude, how it degrades aircraft performance, and how to find that altitude each time you plan to take off or land in a high-density altitude situation.
Dr. Thomassen has a PhD from Stanford and had a career in teaching (MIT, Stanford, UC Berkeley) and research in fusion energy (National Labs at Los Alamos and Livermore). He has been flying for nearly 60 years, has the Wright Brothers Master Pilot Award, and is a current CFII.
