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The Front office | What is Density Altitude and How Do We Derive It?

By Chas Hines

The Front Office | June 2019
Saturday, June 1, 2019

Density altitude, to put it blandly, is pressure altitude corrected for non-standard temperature. What that means in English is that the air is the equivalent density (thickness) that you would find at x-thousand feet on an average day. So, if you are at a sea-level DZ with a density altitude of 4,000 feet, it will feel as if you are actually at an elevation of 4,000 feet.

“Well, what exactly is an average day?” you ask. An average day is defined, for aviation purposes, by the international standard atmosphere (ISA)—a metric established by a bunch of standardization agencies (most of which you probably won’t remember past this paragraph, so I’ll spare you) and the U.S. Government.

Anyway, with all that mumbo-jumbo aside, what you get is a model of the atmosphere that has a generally predictable pressure and temperature gradient (we call the change in temperature a lapse rate) that decreases as your altitude increases from sea level well up to the tropopause (the boundary between the troposphere and the stratosphere). Above the tropopause (which varies from as low as 18,000 feet at the poles to 35,000 feet-plus at the equator), the temperature change actually stops for tens of thousands of feet and eventually increases with altitude through the stratosphere.

What you might want to know as a skydiver (and definitely as a pilot) is that this temperature and pressure gradient gives us vital information about aircraft performance, the stability of a given mass of air (i.e., weather information) and an accurate assessment of what the air temperature will be on jump run and even where the lowest dominant cloud layer will be. At sea level, the airplane altimeter (or your barometer at home) on an ISA day will read 29.92 inches of mercury with an air temperature of 15 degrees Celsius. If we were to climb to 5,000 feet above sea level, we would lose about five inches of air pressure and about 10 degrees Celsius, resulting in a readout of 5,000 feet and 5 degrees Celsius. This is because per 1,000 feet in altitude, we lose about one inch of air pressure and two degrees. We call this cooling our dry adiabatic lapse rate.

So, here’s the problem: Not every day is exactly the same. The weather (and the resulting temperature and pressure values) at any given location, altitude and time can vary drastically—just like your emotional state! At sea level, we all know you can have temperatures at the poles significantly different from the 15-degree-Celsius ISA temperature (think -40 degrees in Alaska, or 50 degrees in Death Valley). Air pressure also varies considerably each day, with barometric pressures down to 29.50 inches with moderate-strength weather systems to 30.50 inches on wonderfully clear days. (Yes, low pressure tends to predict bad weather, hint hint).

So, with all that said, let’s do a little bit of math and find out our pressure altitude, then our density altitude.

Calculating the Pressure Altitude and Density Altitude:

Current altimeter setting: 29.50

Field elevation: 5,000 feet

Air temperature: 30 degrees Celsius

First, find your pressure altitude:

pressure altitude = (standard pressure - your current altimeter setting)

                x 1,000 + field elevation

PA = (29.92-29.50) x 1,000 + 5,000

PA = (0.42) x 1,000 + 5,000

PA = 420 + 5,000

PA = 5,420

To find your ISA temperature for your elevation, do the following:

ISA temp = 15°C - [(field elevation/1,000) x 2°C]

ISA temp = 15°C - (5,000/1,000 x 2°C)

ISA temp = 15°C - (5 x 2°C)

ISA temp = 15°C - 10°C

ISA temp = 5°

Finally, find your density altitude:

density altitude = pressure altitude + [120 x (temperature - ISA temperature)]

DA = 5,420’ + [120 x (30°C - 5°)]

DA = 5,420’ + [120 x 25°C]

DA = 5,420’ + 3000’

DA = 8,420’

Are you still awake? If so, congrats! You know how to figure out your density altitude for a given day.

The example above references a nice, warm summer day at a high-elevation DZ (like in Colorado or New Mexico). If you have a density altitude of 8,420 feet, that means your canopy is performing as if it were flying at 8,420 feet even though you are only at 5,000 feet. It will fly significantly more quickly, have a dramatically longer recovery arc and require more space to turn than it would on a cooler spring day. Are you ready to downsize today? Because that is how it will feel.

Of course, if a given day had a higher-than-standard air pressure and/or was considerably colder than ISA, the result would be a density altitude lower than your field elevation. That would be like a free upsize: Your canopy is slower, turns tighter, has a shorter recovery arc and lands in less space. As you can imagine, a high density altitude tends to be a contributing factor in canopy fatalities and aircraft accidents. Remember: If it’s hot, start your final turn higher! You will live longer.

Fortunately, there are thousands of density altitude calculators available on your app store or search engine. You can get these numbers in seconds by just plugging them in and clicking a button. Know what they mean!

Chas Hines | C-41147
FAA Certified Flight Instructor and Airline Transport Pilot

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