The basics of gas density
But if you're a baseball player or a pilot, the air's density is a key to performance.
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The density of anything is the amount of mass in a particular volume, such as the number of kilograms in each cubic meter of a solid such as wood, a liquid such as water, or a gas such as air. (In American units, density is often described in pounds per cubic foot, which works well enough for ordinary uses. But pounds are a measure of force, not mass. Scientists and engineers use a unit called the slug for mass. Near the Earth's surface, a slug is about 32.2 pounds.)
Unlike solids and liquids, the density of a gas can vary widely. With air, pressure and temperature are the main factors determining density. If the air isn't confined to a container, the density decreases as the temperature rises. Density also decreases as the air's pressure drops.
As anyone who looks at weather maps can tell you, air pressure changes are associated with weather changes. But the air's pressure decreases much more quickly with increasing altitude than anything the weather does. For instance, getting into an airplane and climbing only 2,000 feet on a day with perfect weather takes you into air pressures that are lower than the pressure in the eye of a strong hurricane.
The "standard" air pressure at sea level is 29.92 inches of mercury, while at 2,000 feet above sea level it's 28.82 inches of mercury. This is lower than the pressure measured by a hurricane hunter airplane in the center of Hurricane Charley on August 13, 2004, about an hour before it hit southwest Florida with strongest winds estimated at 140 mph.
A baseball player aiming for fame and fortune by hitting home runs offers a good look at how the decreased air density of high altitude can help. Aerodynamic drag slows a baseball that's hurtling toward the outfield fence. Drag is the force acting opposite to the direction of an object's motion. You can think of it as the force needed to push aside the air's molecules. The force needed to do this -- drag -- decreases as the number of molecules and their weight decrease. That is, drag decreases as air density decreases.
Air density on the WebThe many useful computations of the El Paso National Weather Service office weather calculator include density altitude under "Pressure Conversions".
To learn more on how air density affects baseball, see this archived story on the Golden Gate Weather Services Web site.
For a look at how air density affects auto racing, see this account at USAToday.com. |
An airplane's engine creates the thrust that balances drag. When a pilot increases power, thrust is greater than drag and the airplane goes faster. (To keep things simple, we're looking only at straight-and-level flight.)
The would-be home run hitter doesn't have a throttle. The energy the bat imparts to the ball is the only thrust that it will ever have. From the crack of the bat on, drag is slowing the ball down. The lower the air's density, the lower the drag slowing the ball and the farther it will go before falling to the ground.
Higher temperature also decreases drag, but increasing altitude is the biggest factor for baseball players. Jan Null, a retired National Weather Service meteorologist who runs Golden Gate Weather Services in California, calculated how far balls hit with the same force at different fields would go based on air density. Using the elevation (altitude) of different locations, Null calculated that a homer that would travel 400 feet at sea level would go about 408 feet at Atlanta's Turner Field, which at an elevation of 1,000 feet is the second-highest major league ballpark. The ball would travel 440 feet in Denver's Coors Field, where the elevation is just short of a mile. The seats in the 20th row of the upper deck are purple to indicate they are exactly 5,280 feet above sea level.
Unlike the effect on home-run hitters, low air density decreases the performance of most athletes. As you go higher, the percentage of oxygen in the air remains the same -- around 21 percent. But, since each cubic foot of air contains fewer molecules of all of the gases, each breath brings in fewer of the oxygen molecules that our bodies need to function.
In simple terms, our bodies combine fuel -- the food we eat -- with oxygen to create the energy that powers our bodies, including our brains. An airplane's engine, like your body, combines oxygen with fuel to create power.
As you go higher, the lower drag in low-density air can't make up for the power loss in thin air. Decreased drag also can't make up for an airplane's loss of lift in thin, low-density air.
While the details of exactly how an airplane's wings create lift are complicated, one of the key factors is how many molecules of air's various gases hit the wing each second. Since the air's density affects the amounts of drag, thrust, and lift that an airplane produces, you shouldn't ignore it when you go flying.
Airline pilots, for instance, calculate how much runway will be needed to lift off the ground, and other performance figures, before each flight based on the weather, the airport's elevation, and the airplane's weight.
Such calculations are rarely done for the small airplanes used for flight training, except under unusual circumstances such as a flight to a high-altitude airport on a hot day, or when taking a knowledge test.
This works out well most of the time for most pilots because given the light loads usually carried, the aircraft performance, and the lengths and elevations of runways usually used, the difference between, say, a 60-degree and a 90-degree day at the same airport isn't going to dangerously degrade performance.
During a first flight in hot weather a student might notice that the airplane isn't climbing as briskly as usual, but it still clears the trees at the end of the runway with room to spare. Such routines can lead to dangerous complacency when you fly to an airport at a higher altitude than where you normally fly, on a hot day, and maybe carrying a passenger or two plus luggage.
For this reason, it's a good idea to study the performance charts in the pilot's operating handbook for the airplane you are flying to see how altitude, temperature, and aircraft weight can affect how much runway it will take to lift off, and what distance you'll need to clear a 50-foot obstacle along your takeoff path. Remember that increasing density altitude decreases airplane performance, and decreasing density altitude increases airplane performance.
In most cases, the charts in the handbook enable you to use airport elevation, the temperature, aircraft weight -- and sometimes other factors -- to calculate the distance from the beginning of the takeoff roll to liftoff, and then to clearing that 50-foot obstacle.
Sometimes calculations are done in terms of density altitude, and flight computers normally allow you to calculate this. The concept isn't as difficult as it might seem.
When engineers began designing airplanes early in the twentieth century they needed some firm numbers for air density in order to calculate how their creations would perform at different altitudes. As we've seen, such numbers are moving targets because changes in the weather change the air's density.
The answer was the standard atmosphere, or a listing of figures for temperature, air pressure, density, and other parameters for altitudes from the ground up as high as designers wanted to fly. The standard atmosphere is based on calculations and measurements. Think of it as an "average" atmosphere.
The standard atmosphere table on p. 49 shows only altitudes and air density at those altitudes, using American units.
We can use this table to show what density altitude means. Suppose you were going to take off from a sea-level airport on a warm day. Using the temperature, air pressure, and other factors, you calculate the air's density at that time and place and find that it is 0.002242 slugs per cubic foot.
You'd look at the table and see that this density is found at 2,000 feet in the standard atmosphere. You would say that the density altitude is 2,000 feet. In other words, even though you are at sea level, your airplane would perform as though it were at 2,000 feet on a standard day. This is the density altitude.
You are likely to hear such a figure described as a high density altitude, meaning that the density altitude is higher than the true altitude. But this can be confusing. Most English speakers would think the word high modifies the word density. That is, you might think that the air has a higher density than at low altitudes. But, high really describes the altitude. In other words, the air has a "high-altitude" density.
By the way, the density altitude can be below sea level. For example, if the temperature is 0 degrees Fahrenheit, the density altitude at a sea-level airport could be around minus 4,000 feet.
Unless you take a class in advanced meteorology, you're not likely to ever calculate the air's density. Instead, flight computers or online weather calculators give you the density altitude (see "Air Density on the Web," left).
A baseball player trying to hit home runs doesn't have to do anything different at Coors Field; he just hits the ball as hard as possible.
As a pilot, you can't do things the same as you would at a time and place where the air density is high. Instead, you need to understand how the natural world affects your airplane and use that information to make sound decisions.
Jack Williams is coordinator of public outreach for the American Meteorological Society. An instrument-rated private pilot, he is the author of The USA Today Weather Book and The Complete Idiot's Guide to the Arctic and Antarctic, and co-author with Bob Sheets of Hurricane Watch: Forecasting the Deadliest Storms on Earth.
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