What is Density Altitude?

Question

I'm trying to get a deep understanding of the term: Density Altitude.

So I have read the explanations in my instruction book, and online articles. One source explained it differently then the other which confused me.

Wikipedia defines Density Altitude as:

The density altitude is the altitude relative to standard atmospheric conditions at which the air density would be equal to the indicated air density at the place of observation. In other words, the density altitude is the air density given as a height above mean sea level..".

https://en.wikipedia.org/wiki/Density_altitude

So if I would believe Wikipedia then I could look at the ISA table to find the altitude by using the pressure.

Here is an ISA table:

My instruction book (Aerodynamica, prestatieleer en vliegtuigtechniek by Bas Vrijhof on page 112, written in Dutch) claims this:

in de ISA is de dichtheidshoogte altijd gelijk aan de drukhoogte

Translated to English:

in the ISA the density altitude is equal to the pressure altitude.

So, let's say I'm flying in an aircraft, the pressure is "22.22 Hg", and the outside air temperature is -0.9°C. The altitude in the ISA would be 8000 ft. The Density Altitude would also be 8000 ft.

Skybrary defines Density Altitude as:

Density altitude is pressure altitude corrected for temperature.

Link: https://www.skybrary.aero/index.php/Density_Altitude

This explanation contradicts with the Wikipedia explanation:

the air density would be equal to the indicated air density at the place of observation

On another wikipedia article I found this:

De relatie tussen temperatuur, hoogte en luchtdichtheid kan worden uitgedrukt in density altitude.

Translated to English:

The relationship between temperature, altitude and air density can be represented as density altitude.

Link: https://nl.wikipedia.org/wiki/Opstijgen#Benodigde_snelheid

So in short, each source explains Density Altitude in their own manner, some contradict the other which confuse me.

So my question is:

What is Density Altitude?

Answer 1

The concept of 'density altitude' is kind of like the concept of 'wind chill'.

Stick with me here, I'm going somewhere with this.

Cold weather is dangerous for the human body, and wind (because of increased heat loss on human skin) makes it worse. But how much worse? Is it worse to be outside in -10C temperatures with a 20 knot wind, or -15C temperatures with a 12 knot wind? The concept of 'wind chill' resolves those two values into a single easy number.

Density altitude works the same way. It's difficult and tedious to compare and contrast how an airplane will perform on a 25C day with a pressure of 29.80 at an elevation of 600 MSL, versus a 20C day with a pressure of 30.17 at an elevation of 1250 MSL. We need a way to mash all of these variables into one easy-to-use number. That number is density altitude.

So just as I can say "The wind chill is -10C" and it doesn't matter whether it's warm but windy or cold and calm, I can say "The density altitude is 2,000" and everyone will have the same idea of the expected performance of the airplane, no matter what combination of factors led to that result.

Once you start thinking of (and using!) density altitude as a simplification tool, its value becomes a lot more obvious.

Answer 2

Try this article

https://www.aopa.org/training-and-safety/active-pilots/safety-and-technique/weather/density-altitude

As a pilot, we like higher Pressure and Cold Temperatures - it makes the air denser so the engine can create more horsepower. High Pressure systems, where the barometer reads above 29.92, and cold air, where the temperature is below 59F (I'm in the US) mean the aircraft will get off the ground sooner and climb better. So - Winter! Ideal flying time from a performance perspective.

Summer, we may see the same increased barometer reading, but the higher temperature means the air is less dense (heat makes the air expand), so engine performance suffers. Even worse, if there is a Low Pressure system, combined with high temperatures, can make the airplane feel like it is taking off from a higher altitude.

So Density Altitude is the altitude that the airplane thinks it is - the barometer reading with temperature impact added to it.

Answer 3

Suppose you are at a given place, with a given temperature, and the barometer shows –for example– 25.84 inches of air pressure. That's precisely the pressure at 4000 ft of altitude within the 'standard atmosphere'. Hence, you may say that the pressure altitude at that place where you are is exactly 4000 ft.

Suppose now that at the same given place the density of the air (measured or computed from pressure and temperature) is 1.121 Kg/m^3. That's precisely the density at 3000 ft of altitude within the 'standard atmosphere'. Hence, you may say that the density altitude at that same place is instead 3000ft.

Answer 4

Density Altitude, in a nutshell, tells you how the plane is going to perform, in particular the climb performance for takeoffs or go-arounds.

The performance tables in your POH are based on ISA, which for practical purposes no plane ever actually flies in. That means you have to calculate the density altitude for the current conditions and look at that line in the tables to find out what the actual performance will be.

If the density altitude is very high (i.e. approaching your service ceiling), it's possible that your plane won't be able to clear obstacles/terrain or, in extreme cases, even get off the runway. This happens frequently to non-turbo pistons in mountains in the summer, and it is occasionally bad enough that even airliners can't take off from airports like PHX and LAS.

Any time your planned flight will be High, Hot and Heavy (known as the three H's), you need to consider DA and check the performance tables to determine whether it will be safe. High terrain may mean a different route via mountain passes; Heavy load may mean ditching passengers/cargo or fuel, and Hot may mean waiting until night or early morning. If any of these aren't things you encounter regularly, e.g. because you live in a (relatively) cold and flat region, it would be wise to check with a CFI to refresh your knowledge and double-check your plans before you go.

Answer 5

Density Altitude is basically this:

1. Measure the density at a given location (or compute it)
2. Ask yourself: at what elevation do you find that density in the Standard Atmosphere?
3. The answer to question 2 is the density altitude.

More practically, here's how you can compute it:

$$\mathrm{DA_{feet}}=\mathrm{PA_{feet}}+ 120\cdot(T_{\mathrm{OAT}}-T_{\mathrm{ISA}})\tag{1}$$

where:

• $\mathrm{DA_{feet}}$: Density altitude in feet
• $\mathrm{PA_{feet}}$: Pressure altitude in feet
• $T_{\mathrm{OAT}}$: Outside air temperature in Kelvin
• $T_{\mathrm{ISA}}$: Temperature (in Kelvin) found in the standard atmosphere at $\mathrm{PA_{feet}}$ feet

---

If you wonder what the non-approximated equation for density altitude is, here it is:

$$\mathrm{DA}=\frac{T_0}{L}-\frac{T_{\mathrm{OAT}}}{L}\cdot\left(\frac{T_0-L\cdot\mathrm{PA}}{T_{\mathrm{OAT}}}\right)^{\frac{g}{g-R_s\cdot L}}=\frac{T_0}{L}-\frac{T_{\mathrm{OAT}}}{L}\cdot\left(\frac{T_{\mathrm{ISA}}}{T_{\mathrm{OAT}}}\right)^{\frac{g}{g-R_s\cdot L}}\tag{2}$$

where:

• $\mathrm{DA}$: Density altitude in meters
• $\mathrm{PA}$: Pressure altitude in meters
• $T_{\mathrm{ISA}}$: Temperature (in Kelvin) found in the standard atmosphere at $\mathrm{PA}$ meters (i.e. $T_{\mathrm{ISA}}=T_0-L\cdot\mathrm{PA}$)
• $L$: Temperature lapse $=0.0065 \mathrm{~K/m}$
• $T_0$: Standard temperature $=288.15 \mathrm{~K}$
• $g$: Gravitational acceleration $\approx 9.81 \mathrm{~m/s}^2$
• $R_s$: specific gas constant for dry air $\approx 287.058 \mathrm{~J \cdot kg^{−1}K^{−1}}$

A few notes:

• it can be derived directly from the barometric formula in the standard atmosphere and from the definition of density altitude
• it assumes dry air and does not account for humidity
• if $T_{\mathrm{OAT}}=T_{\mathrm{ISA}}=T_0-L\cdot\mathrm{PA}$, then it follows that $\mathrm{DA}=\mathrm{PA}$ (and one can really see that density altitude is basically pressure altitude corrected for temperature)

In order to derive equation 1 from equation 2, we need to compute the Taylor expansion (see this link) of equation 2 around the point $T_{\mathrm{OAT}}=T_0-L\cdot\mathrm{PA}=T_{\mathrm{ISA}}$ and only keep the constant and the linear terms:

$$\mathrm{DA}\approx DA(T_{\mathrm{ISA}})+\frac{DA'(T_{\mathrm{ISA}})}{1!}(T_{\mathrm{OAT}}-T_{\mathrm{ISA}})\tag{3}$$

If you run the math, you get:

$$\mathrm{DA}\approx\mathrm{PA}+(T_{\mathrm{OAT}}-T_{\mathrm{ISA}})\cdot\frac{R_s}{g-R_s\cdot L}\tag{4}$$

which finally looks similar to equation 1. The multiplicative term is:

$$\frac{R_s}{g-R_s\cdot L}= 36.13\mathrm{\frac{m}{K}}=118.55\mathrm{\frac{ft}{K}}$$

And that's the value usually approximated as 120

Answer 6

Try this: Density Altitude

Defined Types of Altitude Pilots sometimes confuse the term “density altitude” with other definitions of altitude. To review, here are some types of altitude:

• Indicated Altitude is the altitude shown on the altimeter.
• True Altitude is height above mean sea level (MSL).
• Absolute Altitude is height above ground level (AGL).
• Pressure Altitude is the indicated altitude when an altimeter is set to 29.92 in Hg (1013 hPa in other parts of the world). It is primarily used in aircraft performance calculations and in high-altitude flight.
• Density Altitude is formally defined as “pressure altitude corrected for nonstandard temperature variations.”

Answer 7

The altimeter, although used primarily to give you altitude, is a pressure gauge. Through mathematical trickery in its innards, it will take the pressure and temperature and QNH and give you an altitude reading.

When you set 29.92 in the window, then the altimeter is truly measuring pressure, albeit in odd units of "pressure altitude". The reading has a one-to-one correspondence with other units of pressure. Just an odd nonlinear conversion to go from one to the other.

Pressure altitude is important, because airfoils fly by pressure. Thinner air but higher speed gives the same pressure, gives the same indicated airspeed. Planes in 1G flight stall at the same IAS, regardless of TAS.

When you make the temperature correction to the altimeter reading, you get density altitude. The altimeter is now measuring density not altitude or pressure. Density altitude is a measure of density. Again, just weird units with a nonlinear conversion to other measures of density.

Density altitude is important, because it tells you how many atoms of oxygen are in each parcel of air, and engines ingest oxygen to generate thrust. The same pressure but higher temperature and therefore less density, and you get less oxygen atoms per gulp.

So to summarize, Density Altitude is actually a measure of density, just an odd one.