Weather

Many of the things you learn in ground school classes or self-study can seem abstract and theoretical until one day, in an airplane, you wish you had payed closer attention. Density altitude is a good example. You know what density is; it’s how much the stuff in a particular volume weighs. The density of aviation gasoline is 6 pounds per gallon, for example. Altitude, of course, is how high you are above sea level. But, how can density have an altitude?

Let’s consider an imaginary scenario showing why you need to understand density altitude.

A summer flight. Imagine you’ve flown your Cessna 172 from your sea-level home airport to an eastern mountain getaway airport for the weekend. The runway is only 2,000 feet long, but it’s paved and has always been more than adequate.

After seeing a forecast for thunderstorms later in the day, you push up your departure to noon instead of 5 p.m. as originally planned. It’s hot, and you recall learning about the danger of flying in a hot day’s thin air. But you tell yourself that this is a problem at high-elevation airports. You’re taking off from an elevation of 1,000 feet—almost sea level, you tell yourself. Besides, you have only one passenger and just a little luggage; the airplane isn’t near its maximum weight even with full fuel tanks. “You can never have too much fuel,” an older pilot had once told you.

The automatic weather station is reporting that it’s 95 degrees—unusually hot for your part of the country—with not a breath of wind stirring.

White-knuckle takeoff. On the takeoff roll, the airplane feels a little sluggish, and instead of lifting off a third of the way down the runway as usual, you’re halfway to the end when your wheels leave the ground. You clear the trees past the end of the runway, but not by nearly as much as you would like.

After landing safely at home, you decide to try to figure out what might have happened before taking your airplane in for an engine check. Maybe the hot weather, not an engine problem, gave you a few anxious moments.

The “Takeoff distance” chart in the Cessna’s pilot’s operating handbook (POH) shows that on a comfortable, 50-degree day you should need 740 feet to lift off, and 1,320 feet from where you started rolling to clear a 50-foot obstacle. You know these figures come from a new airplane flown by a factory test pilot.

For a 90-degree temperature and 1,000-foot elevation, the POH shows that you need at least 885 feet to leave the ground: almost 20 percent farther than on a cool day. Climbing 50 feet requires 1,320 feet on a cool day, but 1,531 feet when you took off.

In simple terms, you can look at air density as the number of molecules of the gases that make up the air (mostly nitrogen and oxygen) per cubic foot of air. In common terms, it refers to how much a cubic foot of air weighs.

As the air’s density decreases, it reduces the power that an engine produces (a turbocharger overcomes this up to a point), the amount of thrust from a propeller or jet, and the amount of lift that a wing creates. That is, “hot and high” conditions lower air density. We say the air is “thinner.”

Thinner air reduces power because it has fewer oxygen molecules per cubic foot to combine with fuel to produce power. (Oxygen continues to be roughly 20 percent of the air; there are fewer molecules of all kinds.) Lift and thrust are reduced because fewer air molecules per second are flowing around the wings to lift them or around the propeller to push it forward.

Air, like anything else, expands as it heats up, which means that a cubic foot of hot air has fewer molecules, or is less dense, than a cubic foot of cooler air. As we go higher in the atmosphere, the air becomes less dense because there is less air above us squeezing down on the air where we’re flying. Heat and height, or altitude, are the two factors that aviators commonly use when calculating air density.

High humidity also reduces air density, but generally it is not considered for general aviation performance calculations.

We learn that density altitude is defined as: “the pressure altitude adjusted for nonstandard temperature.” But what does that mean?

In practical terms, the pressure altitude is the altitude your altimeter indicates when it’s set for 29.92 inches of mercury. The temperature piece is a reference to a set of figures known as the standard atmosphere. These figures give standard numbers for air temperature, density, and atmospheric pressure for each altitude.

During aviation’s early days, aeronautical engineers and meteorologists developed the standard atmosphere as a way to design and characterize aircraft performance in the atmosphere’s ever-changing density with altitude and weather changes. You can think of the standard atmosphere as a global average atmosphere, with values of air pressure, temperature, and density for each altitude, say each 1,000 feet up as high as engineers need.

Engineers designing aircraft give performance figures in terms of the standard atmosphere. Pilots use the actual atmospheric conditions at the time of a flight to calculate expected performance.

The table on this page is an abbreviated standard atmosphere table using the common U.S. system of measurements. Note that the air’s density is given in slugs per cubic foot, not pounds. Pounds are commonly used in the United States for density, but strictly speaking we shouldn’t do this because pounds are a measure of force, not density. Near the Earth’s surface, a slug is roughly 32.2 pounds of force pressing down.

To see how density altitude works in performance calculation, assume that the actual density of the air right above the runway you plan to use turns out to be 0.002112 slugs per cubic foot. This is the standard density for an altitude of 4,000 feet.

We say that the density altitude at that time and place is 4,000 feet. In simple terms, the density altitude tells you that an aircraft will perform as though it were at that altitude in the standard atmosphere.

There is neither a simple way nor an instrument you can use to measure the air’s density. This isn’t a problem for pilots, however. In fact, performance charts such those as in the Cessna 172 POH use temperature and atmospheric pressure to give performance figures, such as takeoff distance and rate of climb. Some, but not all, will give you the density altitude to use with other charts or performance calculators.

If you need the density altitude, such as to use in a ground school presentation, go to the Weather Calculator on the El Paso, Texas, National Weather Service website. Scroll down to “Pressure Conversions,” where you’ll find a link at the bottom of the left-hand column to “Density Altitude.” Click on “Formulas” at the bottom of the right-hand column. This will help you appreciate all of the work performance charts or calculators do for you.