Flight Training Magazine
Why airplanes like cool days betterBy Jack Williams (From AOPA Flight Training, July 2003.)
Imagine you've flown your Cessna 172 out to a nice resort airport for the weekend. The runway is only 2,000 feet long, but it's paved and has always been more than adequate.
You had planned to fly back Sunday evening, but reports that clouds and rain could move in late in the day prompt you to leave around noon on Sunday.
It's hot, and you recall learning about the danger of flying in a hot day's thin air, but-as you recollect-this is a problem for high-altitude airports; you are taking off from an elevation of 1,000 feet, almost sea level, you tell yourself.
Besides, you have only one friend with you and just a little luggage; the airplane isn't loaded to anywhere near its maximum weight.
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.
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 on the hill past the end of the runway, but not by as much as you would like-when you looked down you saw leaves, not a green blur as you usually do.
After returning home, you decide to try to figure out what might have happened before taking your airplane in for an engine check. Maybe the weather, not an engine problem, gave you a few anxious moments.
First, you turn to the "Takeoff distance" chart in the Cessna's pilot's operating handbook (POH) and see 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 that's flown by a factory test pilot. Still, you are normally off the ground well before the half-way point and 50 feet in the air before the end of the runway.
But for a 95-degree day, the book shows you need 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, 1,531 feet-for a test pilot in a new plane-on a hot day.
You could stop here, saying, "I know heat makes the air thinner, which is why the airplane doesn't fly as well as when it's cool." But, like many pilots, you're curious and want to know the "why" as well as the "what" of the flying game. You are a pilot who's motivated to learn more about density altitude. You want to learn why an airplane doesn't perform as well on a hot day as on a cool day, which falls under the heading of density altitude.
First, let's take a brief look at air density and airplane performance. You can think of density as the number of molecules of the gases that make up the air (mostly nitrogen and oxygen) per cubic foot of air; that is, 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. As a memory aid, keep in mind "hot, high, and humid" as the conditions that lower air density.
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, but humidity is also important. We'll come back to it after looking at heat and height.
In the case of the Cessna 172 that didn't want to take off on a 95-degree day, we can go to a "weather calculator" on the Web, plug in some numbers, and find out that even though the runway elevation was 1,000 feet, on a 95-degree day with low humidity and low barometric pressure-remember, some bad weather was moving in-the density altitude would be something like 3,690 feet. (This number and the density altitude figures below are rounded off.)
In basic terms, this means that the airplane was performing as though it were taking off from an airport at an elevation of 3,690 feet, not 1,000 feet. To see where this number comes from, take a look at the table on page 54, which is a very abbreviated version of a standard atmosphere chart.
You can think of the standard atmosphere as a global average atmosphere, with values of air pressure, temperature, and density for each altitude. This one is in the system that uses altitude in feet, air pressure in inches of mercury, temperature in degrees Fahrenheit, and density in slugs per cubic meter (you can't use pounds because that's a unit of force, not mass). At the Earth's surface, a slug is about 32.2 pounds.
Aeronautical engineers invented the standard atmosphere early in the twentieth century because they needed some firm numbers-well, really a number for air density-to calculate how the aircraft they were developing would perform at different altitudes. The chart shows us that on a "normal" day, the air pressure at 1,000 feet is 28.86 inches of mercury, the temperature 55.4 degrees, and the density is 0.002309 slugs.
When we say that the density altitude on the day we took off was 3,690 feet, we mean that the actual air density was a little more than halfway between the 0.002176 slugs for 3,000 feet and the 0.002112 for 4,000 feet.
The POHs for different kinds of aircraft deal with density altitude in different ways. The handbook for the 1976 Cessna 172M, for instance, has a chart that uses only runway elevation and temperature, and you calculate takeoff distances from it without considering air pressure or humidity.
Other handbooks have charts that enable you to use air pressure and temperature to find a density altitude. You can also use mechanical (E6B) or electronic computers to find it. You then use another handbook chart that gives performance data for a range of density altitudes.
A handy way to find a more precise density altitude is to go to the weather calculator on the El Paso National Weather Service official Web site.
To calculate the density altitude, you put in the temperature, the station pressure, and the dew point. The station pressure is the actual reading from a barometer at the station, which is not reported. But, you could estimate it closely by using the altimeter setting, which is reported.
The standard atmosphere chart shows us that the standard pressure at sea level is 29.92 inches, and at 1,000 feet, 28.86. To estimate station pressure, find the difference between 29.92 and the altimeter setting. If the altimeter setting is 29.82 inches, or 0.1 inch less than 29.92, you could subtract that amount from the standard pressure for 1,000 feet, coming up with a station pressure of 28.76.
These were the readings used to come up with the 3,690-foot figure above. Lowering the air pressure by 0.5 inch of mercury sends the density altitude to 4,470 feet.
The dew point used was 30 degrees (weather stations report dew point). This would be very dry. If you increased the dew point to 75 degrees, which would be the kind of humidity found on the coast of the Gulf of Mexico in summer, the density altitude soars to 4,000 feet.
To understand why humid air is less dense than dry air, you have to get rid of the idea that humid air has had water added to it. It has a higher percentage of water vapor-a gas-than dry air.
You might recall Amadeo Avogadro's law from a long-ago chemistry class. Without getting too complicated, in the early 1800s Avogadro discovered that a particular volume of a gas, say a cubic foot, at the same temperature and pressure always has the same number of molecules no matter what gas is in the container. This means that if you add some water vapor molecules to a cubic foot of air, an equal number of nitrogen or oxygen molecules leave. Water vapor molecules are lighter than either oxygen or nitrogen. This is why adding water vapor makes air less dense.
Performance charts for general aviation aircraft generally don't include humidity in their density altitude or other performance tables because it's not as important as air pressure and temperature. Still, you shouldn't forget it.
Since performance charts are based on figures obtained by test pilots flying airplanes in the very best condition, you should always add a fudge factor to your calculations to account for the fact that you probably aren't a test pilot and your airplane, even if very well maintained, likely has lost a little pep with age. If it's humid, you should increase your personal fudge factor more than usual.
One advantage of a Web density altitude calculator is it gives you a chance to play with different figures to see how density altitude is affected by temperature, air pressure, and humidity. You could then use the figures obtained with performance charts from the airplane that you fly to see what they mean with regard to performance.
A little bit of this could save you from having a more exciting flight than you really wanted the next time you take off in hot and humid air.
Jack Williams is the weather editor of USAToday.com. An instrument-rated private pilot, he is the author of The USA Today Weather Book and co-author with Dr. Bob Sheets of Hurricane Watch: Forecasting the Deadliest Storms on Earth.