Weather

A forecast of hot weather wouldn’t stop anyone from taking to the highway in today’s reliable cars. When was the last time you saw a car next to the road on a hot day with the hood up and steam coming from the radiator? That used to be a common sight. Pilots can’t afford to be as blasé as car drivers about hot weather.

NICE DAY OFFERS UNPLEASANT SURPRISE. Imagine you’re taking off from an airport with an elevation of 1,000 feet early in the afternoon on a hot day. The airport’s paved 2,000-foot runway has always been more than long enough for your Cessna 172 to easily clear the trees just past the end of the runway.

As you line up to take off, the automated weather station reports a temperature of 95 degrees and calm winds.

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 say to yourself. And the airplane is far lighter than its maximum takeoff weight.

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 the 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.

You see that the takeoff distance chart in the Cessna’s pilot’s operating handbook (POH) shows that on a comfortable, 50-degree day with no wind you should need 740 feet to lift off a runway with a 1,000-foot elevation, and you need to be 1,320 feet from where you started rolling in order to clear a 50-foot obstacle. For a 90-degree temperature, no wind, and a 1,000-feet elevation, the POH shows that you need at least 885 feet to leave the ground, and you are 50 feet high when the airplane is 1,531 feet from where it began rolling.

The figures confirm your experience. It’s time to review how the weather, especially temperature, affects airplane performance.

AIRCRAFT PERORMANCE DEPENDS ON AIR DENSITY. 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. The mass of the air in a cubic foot (or cubic meter, in the metric system) of the atmosphere is the air’s density.

As the air’s density decreases, an engine produces less power (a turbocharger overcomes this up to a point), the amount of thrust from a propeller or jet decreases, and the amount of lift that wings create also decreases.

Thinner air reduces power because it has fewer oxygen molecules per cubic foot to combine with fuel to produce power. (As you climb, oxygen continues to be roughly 20 percent of the air, but 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 (see “Technique: Density Altitude,” page 50).

High humidity also reduces air density, but the amount of reduction is small and generally is not considered for general aviation performance calculations.

WHAT IS DENSITY ALTITUDE? You learned that density altitude is defined as “the pressure altitude adjusted for nonstandard temperature.” What does this mean?

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

During and after World War I, aeronautical engineers and meteorologists used measurements and mathematical formulas to develop a set of figures called the “standard atmosphere.” You can think of it as a global average atmosphere, with values of air pressure, temperature, and density for each altitude—say, for each 1,000 feet, 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, using a figure called the “density altitude.”

A CLOSER LOOK. The figure above is an abbreviated standard atmosphere table using the common U.S. system of measurements, which will help you understand density altitude. 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. If you’re an engineer or scientist using the U.S. system instead of the metric system for calculations, you have to use slugs. Near the Earth’s surface, a slug produces roughly 32.2 pounds of force pressing down.

The POHs for different airplanes use a variety of charts to aid performance calculations. Often these charts don’t mention density altitude. For example, the takeoff distance chart in the Cessna 172M POH uses the airplane’s takeoff weight, the temperature, and the “pressure altitude” to calculate takeoff distance. The pressure altitude is the figure your altimeter reads when it’s set at 29.92 inches of mercury.

With this setting, it would read zero altitude at a sea-level airport when the weather happens to creates standard atmosphere condition there.

The Cessna 172M chart shows that if you were at sea level with the standard atmosphere pressure in a Cessna 172M weighing 2,300 pounds, you would need 775 feet of runway to lift off if the temperature were 32 degrees Fahrenheit. The chart also shows that if the temperature were 104 degrees at the same air pressure, you’d need 1,030 feet of runway before the wheels leave the pavement.

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. (For this example we won’t worry about how you come to know this.) A glance at the standard atmosphere table shows that this is the standard density for an altitude of 4,000 feet.

In such a case, we’d say that the density altitude at that time and place is 4,000 feet. In other words, the density altitude tells you that an aircraft will perform as though it were at that altitude in the standard atmosphere.

USING PERFORMANCE CHARTS OR APPS. There is no simple way or any instrument you can use to directly measure the air’s density. This isn’t a problem for pilots, because POH performance charts in the use temperature and atmospheric pressure to give pilots performance figures such as takeoff distance and rate of climb.

Today, of course, you can use electronic devices and aircraft performance apps to do the work that pilots without electronic aids do using performance charts and graphs.

With the electronic devices, the density altitude is part of what’s going on “under the hood” when you input the air temperature, altimeter setting, and wind data, and the app tells you how much runway you’ll need to lift off and to clear a 50-foot obstacle.

If you need the density altitude under particular conditions, such as to use in a ground school presentation or because you are curious, go to the Weather Calculator on the El Paso, Texas, National Weather Service office website (www.srh.noaa.gov/epz/?n=wxcalc). Scroll down to “Pressure Conversions,” where you’ll find a link at the bottom of the left-hand column to “Density Altitude.”

If you’re wondering about how it’s calculated, click on “Formulas” at the bottom of the right-hand column. You will be amazed at the complex meteorological physics and mathematics that your iPad uses to calculate your takeoff roll.