The Density Formula | Flying Magazine

Density Formula for Calculating Density Altitude

How to determine density altitude the old-fashioned way

Density Altitude

Density Altitude

Finding pressure altitude when you're not sitting in the airplane is a bit more complicated, but here’s a nifty formula.

Flying

We all know that as density altitude increases, there is a corresponding decrease in the power delivered by our airplane’s engine and the effectiveness of our propeller. For a typical non-turbocharged light single-engine airplane, this can result in a takeoff roll that’s 25 percent longer for every 1,000 feet of elevation above sea level. The most dangerous combination of conditions are a heavy load, unfavorable wind, high temperature, high airport elevation and high humidity.

With so many variables to consider, how are we supposed to know when our density altitude is too great for the conditions? The density formula provides one way to figure this information out. After we calculate our density altitude, we can then compare it against the performance information in our aircraft manual.

We could use an E6B computer or an iPad app to calculate density altitude, but what if we accidentally left the flight computer and iPad at home? Is there an easy way to calculate approximate density altitude without the aid of these gadgets?

There sure is, and it’s a formula we as pilots should probably commit to memory.

First off, what is density altitude? From our private pilot exam prep, we know it is “pressure altitude corrected for non-standard temperature.” That’s just a fancy way of saying it’s where the airplane “feels” like it is. For example, if the density altitude is 5,000 feet at sea level, your airplane is going to take off as though it’s already flying at 5,000 feet.

How do we calculate density altitude using the density formula? There are just two pieces of information you’ll need for a rough approximation: pressure altitude and temperature. Where do you find this information? Easy: for temperature, you look at the thermometer in your airplane. For pressure altitude, set the window in your altimeter to 29.92. Whatever value it reads is pressure altitude.

Finding pressure altitude when you're not sitting in the airplane is a bit more complicated, but here’s a nifty formula:

pressure altitude = (standard pressure - your current pressure setting) x 1,000 + field elevation

That’s a pretty simple formula since two of the variables will always be the same and the other two are easy enough to find. Let’s say our current altimeter setting is 29.45 and the field elevation is 5,000 feet. That means (29.92 - 29.45) x 1,000 + 5,000 = 5,470 feet.

Easy! Now let’s move on to step two, finding density altitude. Here’s the formula:

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

Now, before your eyes glaze over, here’s how simple this density formula is: We already have the value for pressure altitude from our last calculation; OAT is degrees Celsius read off our thermometer (let’s say it’s a balmy 35 °C today) and ISA Temp is always 15 °C at sea level. To find ISA standard temperature for a given altitude, here’s a rule of thumb: double the altitude, subtract 15 and place a - sign in front of it. (For example, to find ISA Temp at 10,000 feet, we multiply the altitude by 2 to get 20; we then subtract 15 to get 5; finally, we add a - sign to get -5.)

So, in the example above:

density altitude = 5,470 + [120 x (35 - 5)]

Working out the math, our density altitude is 9,070 feet.

This is a rough estimate, but it will be pretty close to the actual value. Try this formula the next few times you go flying (or, just for fun, run some scenarios using Microsoft Flight Simulator) and before you know it you’ll be able find your ballpark density altitude without digging in your flight bag for that E6B. It also provides a back-up option for any time your app malfunctions or you forget your equipment at home.

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