ATSC 113 Weather for Sailing, Flying & Snow Sports

Air Density and Density Altitude

Learning Goal 2c. Determine "density altitude" and explain why pilots use it

Overview

When the air is thinner (less dense), then aircraft have reduced ability to take-off and to climb (gain altitude).   In general, thinner air is found at higher altitudes, so we anticipate that aircraft climb-performance would be reduced at high altitudes.  

But if low-altitude air is hot enough, then the air density decreases, causing poor aircraft performance similar to what the aircraft would normally find at higher altitudes.   Namely, hot low-altitude air can seem like a higher altitude for aircraft flying through it.  This "seems like" altitude is called the "density altitude". 

If the air is hot enough, the air might be so thin that aircraft cannot take off.  Or even if you can take off, you might not be able to climb to a high enough altitude to get over tree-tops or mountain ridgetops. This is what caused the plane crash shown in this video: https://www.youtube.com/watch?v=RNcXFm0EQqU .

Thus, pilots aways consider density altitude before they plan their flights in high-altitude hot conditions.

Density

Air density is the mass (kg) of air molecules within a volume (cubic meter). Think of the air in an empty cardboard box.

Density = mass / volume. 

We often use the Greek symbol "rho" (ρ) for air density.  Air density ( ρ) also depends on air pressure ( P ) and air temperature ( T ). As aircraft climb to higher altitudes where the pressure is lower, the density is also lower.  Also, for any fixed pressure, if you make the air warmer, then the air molecules are bouncing into each other faster and are pushing each other futher apart. Namely, the kilogram of air spreads out into a larger volume causing its density to decrease.  Hence, hotter air has lower density, and acts like higher-altitude air where the air is thinner.

This relationship (density decreases when pressure decreases or temperature increases) is described by the ideal gas law. 

Extra info for experts; not needed for this course.

  • The Ideal Gas Law is: ρ = P / (R T) where R = 0.287 (kPa/K)·(m3/kg) is called the gas constant for dry air.

  • We can look at the ideal gas law to anticipate which factors will decrease the air density.

    Since pressure ( P ) is in the numerator (top of the fraction) in the ideal gas law, then decreasing pressure will decrease density. But recall from Learning Goal 10a that pressure decreases with increasing altitude in the atmosphere. Thus, we expect lower densities at higher altitudes, as plotted in Learning Goal 10a. Namely, aircraft performance decreases as altitude increases.

    With temperature T in the denominator (bottom of the fraction) in the ideal gas law, increasing temperature causes decreasing air density. Thus, hotter air temperatures will also decrease aircraft climb-performance.

Aircraft Performance

Airplanes need a certain air density in order to fly. Lower air density means fewer air molecules that the aircraft encounters. At lower density there is less air flowing over the wings, so the wings get less lift. There are fewer oxygen molecules getting into the engine to burn with the fuel, so the engine makes less power. The airfoils of the propellor can "bite" on fewer air molecules, so it also generates less thrust if the air density is less.

So you can see there is a problem. If wings get less lift, then the airplane needs to fly faster to get the lift back to the desired value. However, both the engine is running slower and the propellors are less effective, so there is less ability to make the airplane fly faster. If the air density is too low, then the aircraft cannot maintain its altitude or cannot climb any higher.

As a result, decreasing air density will decrease the climb-performance of the aircraft.  Namely, if the density is lower, then the aircraft will need a longer runway to take-off, and once it takes-off, it will climb (gain altitude) more slowly.  This is sketched in the figure below.


density-altitude sketch

The top figure is for high pressure and cold temperatures, such as in winter (i.e., low density altitude). The red arrow represents how much runway length would be needed to take off, and the dashed black line (with grey shading below it) shows the climb angle of the aircraft.

The bottom figure represents the same location on a hot summer day (i.e., higher density altitude). The longer red arrow shows that the aircraft needs a longer runway, and the dashed line shows a shallower climb angle than for winter.  Thus, the air in the bottom figure has lower density, and thus the aircraft performance is worse; namely, it acts like it would at a higher altitude.  The bottom figure represents higher "density altitude" than the top figure.  (Figure courtesy of US FAA Aviation Weather AC 00-6B, 2016.)


We can anticipate the problem with low density, based on the ideal gas law.  Lower pressure and higher temperature cause lower density; namely, they cause more difficulty in taking off and climbing.

Pilots need to consider both pressure-altitude and temperature when calculating the climb-performance of their aircraft. Namely, is the aircraft performance good enough to allow the aircraft to be able to take off?  If so, how much runway length is needed?  Does the aircraft have good enough performance to climb over a high mountain range? Can the aircraft fly fast enough to arrive at the destination on time? How much payload weight and fuel can the aircraft carry for air of a certain density?

But most pilots are not scientists or engineers.  So they need an easy way to estimate the effect of higher altitudes and warmer air on aircraft performance.  To make it easier for the pilot to estimate these performance changes, a concept called "density altitude" was invented.

Density Altitude

First, a bit of background information. We know that for a standard atmosphere (Learning Goal 2a) there is a known pressure, temperature, and density for any given altitude, such as was listed in Table 1-5 in Learning Goal 2a. The aircraft performance for any altitude in a standard atmosphere is well documented in the flight manual (or pilot operating handbook) for each aircraft. Pilots use their flight manual to determine aircraft takeoff distance, climb rate, etc.

If a low pressure weather system moves into your area, then the pressure is lower than standard. As a result, the aircraft performance is less than you would expect for any altitude you fly. Namely, the aircraft performs worse - - as if it were at a higher altitude.

Simlarly, if you are flying on a very hot day at any altitude, the ideal gas law tells us that the density is less than it would have been compared to a standard atmosphere temperature. Namely, the aircraft performs worse, as if it were at a higher altitude where the air is thinner. For any given actual temperature and pressure altitude (the altitude estimated from atmospheric pressure alone), if these weather conditions are non-standard, then the aircraft behaves as if it were flying at a different altitude in a standard atmosphere. This altitude that the aircraft "feels" is called the density altitude.

While the explanation above was a bit complicated, the result is very easy for pilots to use. First, pilots set the aircraft altimeter to use a pressure of 29.92 inches of mercury, and then they note the altitude that the altimeter indicates.  This gives them the "pressure altitude".   Second, the pilots read the outside air emperature from the thermometer attached to the aircraft. Finally, they use a chart or lookup table to find the corresponding density altitude. Knowing the density altitude, they can use their flight manuals to determing the aircraft performance. Here is the lookup table for density altitude, courtesy of the FAA Aviation Weather Services Manual.

Solved Example:

For example, suppose you wanted to take off from Jackson Hole airport in Wyoming, where the actual airport elevation is 6451 ft (≈ 2 km) above sea level. Suppose it is a hot summer day with an outside air temperature of 95°F (≈ 35°C). Also suppose that a low pressure is in the area, so the altimeter reads 7000 ft pressure altitude. From the horizontal (almost bottom) axis of this chart, find where 35°C would be, then follow those tick marks vertically upward. From the left axis, find the tick mark corresponding to 7,000 ft pressure altitude, and follow those tic marks horizontally to the right. Where your temperature and pressure-altitude tick marks meet, read the density altitude from the red diagonal lines.

When I do it, I find roughly 11,000 ft density altitude from this chart!  Namely, although the actual elevation of the airport is 6,451 feet above sea level, the hot air makes the airport seem like it is at an altitude of 11,000 feet.  At that high density altitude where the air is so thin, I am sure that flight manuals for many small aircraft would indicate very poor aircraft performance.


My Scary flight experience at Jackson Hole airport.

The scenario was not contrived. On one of my cross country flying trips with my wife, I stopped at Jackson Hole airport along the way. It is a very beautiful location, but on that day it was very very hot. When I arrived, I saw many aircraft parked on the ramp, with their pilots standing nearby cursing at the weather. It was so hot that their aircraft were not able to take off, according to their flight manuals.

So I got out my density altitude chart and looked at the flight manual for the aircraft that I had rented. I calculated that I could take off, but only if I did not take on a full load of fuel (to save weight). So after refueling (partially) and getting my takeoff clearance, I started down the runway on my takeoff.

Apparently the runway was hotter than I expected because I used up almost all of that long runway before the plane could finally lift off. My climb rate was VERY poor - I was not gaining altitude fast enough. I was just barely keeping above ground level. So I decided to stay in the airport traffic pattern circuit for a few laps as I tried to gain more altitude. It was embarassing. There were a couple places where we were so low that we just barely cleared some telephone poles. Finally, after a few trips around the traffic pattern circuit, I was high enough that the air was cool enough that the aircraft starting gaining altitude faster. That scary experience made me better appreciate density altitude.

Summary

Lower pressure, higher altitude, and warmer temperatures cause a higher "density altitude".  Higher density altitudes indicate poorer aircraft performance.  Poorer performance means you need longer runway to take off, your aircraft will climb more slowly, you can carry less weight such as fuel or payload, you cannot climb to as high an altitude (called the service ceiling), and you need a longer runway to land.  If density altitude is too high, then you might not be able to take off safely.

If you have an exam question requiring computation of the density altitude, we would also provide the graphical tool with the exam.


Key words: density, ideal gas law, pressure altitude, density altitude, flight manual

Extra info for experts; not needed for this course.

Image credits. All the photos were taken by Roland Stull, and the drawings were made by Roland Stull, and all are copyright by him and used with his permission, except where indicated near the photo.