WX BRIEF

Density altitude

Hot and high factors shorten runways with summer and mountain flying.


Standard density altitude calculation chart. A combination of pressure altitude and air temperature will largely determine density altitude, which is then used to estimate takeoff distances, climb rates and weight limitations.

Propellers are airfoils too, and fuel combustion relies on proper fuel-to-air mixing ratios. In the atmosphere, gravity en­sures that the highest air density is found near Earth’s surface. As we go higher in the atmosphere, we encounter fewer and fewer molecules, meaning that density de­creases.

This is why aircraft have service ceilings. Above those ceilings, there simply aren’t enough molecules to generate sufficient lifting force to keep the aircraft in level flight, and the aircraft doesn’t have the thrust to go faster to compensate. This is where the concept of density altitude comes into play.

Density and altitude

In a standard atmosphere, density altitude is equal to the altitude at which you are flying. Your lift and thrust will react as you would expect them to at that altitude. Near the surface, you would expect and receive ample thrust and lift.

Near your aircraft’s service ceiling, you’ll find climbing and maneuvering difficult, and increasing thrust is unlikely to result in a large change in speed. But, as we well know, the atmosphere is rarely standard—at any given altitude, a pilot is likely to find things colder or warmer, or wetter or drier than standard.

However, another simple physical relationship—the Ideal Gas Law—indicates that those nonstandard conditions will change air density. The Ideal Gas Law states that the volume, pressure and temperature of a gas are all related.

If the air’s temperature increases, the mole­cules will move apart (increasing volume and decreasing pressure), meaning fewer molecules in the original space. Conversely, if the temperature cools, the molecules will contract into a smaller space, meaning that more can fit into the original volume.

To an airfoil, the change in molecular mass per unit of space (such as a cubic meter) brought about by a nonstandard temperature is no different than if the airfoil were operating at a different altitude having the same natural density. Water in the air can also affect air density.

A water molecule weighs much less than the nitrogen or oxygen molecules that make up the majority of the lower atmosphere. So each water molecule that displaces an oxygen or nitrogen molecule in a cubic meter of air decreases the mass of the air in that cubic meter, decreasing the air density.

This is why humid air, even though it feels “heavier,” is actually less dense than dry air. Fortunately, humidity does not alter density altitude as much as air temperature. The end result is that, as the air at a certain altitude becomes warmer or more humid, the aircraft will perform as though it were operating at a higher altitude.

What this means for most pilots is that, on hot and humid summer days, the performance of their aircraft may be significantly degraded. This translates into poor acceleration from adding power, an inability to climb quickly (if at all), a need to decrease weight, add more takeoff and landing distance, and carry more power to maintain level flight.

Figuring density altitude

Upper air maps for Jul 1, 2009. Excessively warm 850-mb temperatures sit under a moderate ridge at 300 mb over the western US. This scenario commonly creates extremely high density altitudes across Rocky Mountain airports.

Each aircraft operations manual should contain a table that allows a pilot to use their pressure altitude and the indicated air temperature to determine a density altitude.

This value, in turn is applied to graphs that will give the pilot runway takeoff lengths, climb rates, power settings and maximum takeoff weight reductions.

In the absence of a density altitude chart, the value can be estimated with some rules of thumb. First, obtain the pressure altitude of the aircraft. This is usually done by setting the altimeter to 29.92 inches of mercury (1013 hPa) and reading the altitude indicated.

If you are not in the aircraft, or you are in the air and don’t want to forget your current altimeter setting, you can estimate the pressure altitude by subtracting 100 ft for each 1/10 inch of mercury (every 3.4 hPa) above 29.92 (1013).

Add 100 ft per 1/10 inch for an altimeter setting (QNH) below 29.92. Once you have the pressure altitude, you can use it to estimate the density altitude. The calculation for density altitude involves pressure and temperature ratios relative to the standard atmosphere, but, as a rule of thumb, first determine how much above or below the ISA temperature your indicated temperature is.

This means starting at 15°C at sea level, and subtracting 2°C for each 1000 ft of altitude. With the ISA temperature in hand, simply add 120 ft for every 1°C (67 ft per 1°F) that the indicated temperature is above the ISA estimate (or subtract if below the ISA temperature).

As an example, consider you are at an airport at 4900 ft MSL. The air temperature is 77°F (25°C) and the altimeter setting is 29.82 inches of mercury.

Since the altimeter is 1/10 inch less than 29.92, the pressure altitude is 5000 ft. At 5000 ft, the ISA temperature should be 5°C, meaning a 20°C difference, or a density altitude of 7400 ft (20°C x 120 ft = 2400 ft added to the 5000 ft pressure altitude).

Unlike absolute pressure (QFE), pressure adjusted to sea level (QNH) is not normally so deviant from ISA sea level pressure that it results in a pressure altitude adjustment of more than a few hundred feet. Using the temperature difference alone should normally give a good ballpark estimate.

 

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