This page has been updated 22 December 2001 in response to comments. Thanks.
More definitions: Absolute altitude is the altitude above the surface and is abbreviated AGL. True altitude is the actual distance above mean sea level and is abbreviated MSL. Neither absolute altitude nor true altitude are affected by variations in atmospheric conditions such as barometric pressure, temperature, or humidity. If everybody measured altitude with a GPS, we could end this discussion. But not all airplanes have GPS, so to keep airplanes from running into each other or the ground, we all must use the altimeter for controlling our airplanes' altitudes. Our altimeters are simply adjustable pressure gauges which makes everything a little more interesting.
Indicated altitude is the altitude reading from the altimeter. The altimeter has an adjustment knob to compensate for changes in barometric pressure; this adjustment knob is where the pilot dials in the "altimeter setting". Pressure altitude is the indicated altitude when the altimeter setting is the standard pressure of 29.92.
Most texts define Density Altitude as Pressure Altitude corrected for non-standard temperature. This definition for Density Altitude fits the charts and whiz wheel calculators that are commonly used. I provided the discussion on this web page to help you understand how the values in the charts can be derived.
Oh yeah. Elevation is the height of the ground level above mean sea level. So, MSL = AGL + Elevation.
Density Altitude is defined as "Pressure Altitude adjusted for temperature." Pressure altitude is defined as the altimeter reading when the Kolmsman window (barometer setting) is set to 29.92. To adjust for temperature, I prefer the method published in Sparky Immeson's "Mountain Flying Bible": take the difference between the current temperature and the "standard temperature" for the altitude; then multiply this difference by 60 ft/deg.F. I've found that this easy method gives results that are anywhere from right on to 5 percent high.
The "standard temperature" for altitudes up to 12,000 feet can be found in the Standard Air Column table below. Just copy the Altitude and Temperature columns onto a 3x5 card, get it laminated at the nearest office supply store, and put it in the kit you use to lug your maps, paper and pencil, and checklists, etc. to the plane.
Why bother with density altitude? After you calculate density altitude, you're supposed to look up your airplane's performance in the POH (usually). Then you can determine runway length's for takeoff. Of course, those calculations are for new planes. I double those figures to be absolutely certain. My manly pucker factor (that tendency to pull a donut hole out of my seat) increases when I only have enough runway to multiply the POH value by 1.5. I never go below that, which means I always check this before I go to a new runway.
To understand why air is thinner at some times and in some places than others, read on. Some would say, "prepare to suffer" but I hope you think it is interesting.
The Ideal Gas Law can be expressed as:
PV=nRT
Where P is pressure ("Hg), V is volume (ft^3); n (moles, lbs/lbmole); M (molecular weight, lbs/lbmol); R (gas law constant = 21.85 ("Hg*ft^3/lbmol/deg R); T (deg R).
Remember to add 459 to T (deg F) to obtain T (deg R).
Hopefully, you'll figure out fairly soon that the altimeter setting is not the same as the actual pressure except at sea level (MSL = 0). For example, at an airport at elevation of 5000', an actual pressure of 24.92 "Hg requires no adjustment from the Standard Air Column; therefore, the altimeter setting will be given by the weather folks as 29.92 "Hg even though the actual (absolute) pressure is much less. Because you have a pressure gauge (your altimeter) as part of your standard airplane instruments, you have a quick way of determining actual air pressure. P = (Altimeter Setting) - (Indicated Altitude/1000).
The molecular weight of dry air is approximately 29. This value decreases with humidity because you're mixing in a gas component with a molecular weight of 18 - even though humid air feels heavy. Actually, this heavy feeling is a lung thing - it is just a little harder to breathe.
How much does air weigh? First, let us use "D" for density (because I can't find an html character for rho - which looks like a slightly warped lower-case p).
D = nM/V (lbs/ft^3)
Plugging in the Ideal Gas Law to replace n/V with P/RT,
D=PM/RT
For dry air at sea level at 59 F and 29.92"Hg ("standard conditions") D=(29.92)*(29)/(21.85)/(59+459) = 0.0765 (lbs/ft^3)
The higher the altitude, the lower the pressure, usually the lower the temperature, and the lower the air density. When you stack miles of air on top of you, its weight (density in lbs/ft^3 times volume in ft^3) results in a force applied to you (in lbs or pounds). This weight divided by area is the calculation of force per unit area, or pressure (in lbs/ft^2; or lbs/in^2 = psi; or "Hg). As you climb, there is less air above you, so the weight of the air (measured as air pressure) drops.
As the pressure of air decreases, its density also decreases. Stated another way, the air expands. Now, most people have experienced the cooling effect of a high pressure gas being suddenly released to the atmosphere. A similar effect is generally seen in air. Air at higher altitudes is generally cooler than the air below it. This phenomenon is due to the same cooling effect associated with expanding a gas. Exceptions are often seen with temperature inversions, storms, and other unstable conditions.
The effect of humidity on air density can be determined as follows: The molecular weight of water is 18. The average molecular weight of dry air is 29. As more moisture enters the air, the average molecular weight drops. Looking back at the density equation, we can see that a reduced value of "M" will reduce the air density. This fact surprises many people at first because the higher humidity causes a heavy feeling. The heavy feeling is probably due to increased difficulty our bodies have losing heat and breathing oxygen when it is hot and humid.
The design of the airplane altimeter is based a criterion called the "Standard Air Column." This refers to dry air that starts at sea level (MSL = 0) with a barometric pressure of 29.92 "Hg and a temperature of 59 deg F. As you climb within the Standard Air Column, the temperature drops 3.5 deg F per 1000 feet and the pressure drops 1 "Hg per 1000 feet.
The following table shows the changes in temperature and pressure for the Standard Air Column, where "h" is height above mean sea level in ft. Also provided is the calculated density for the Standard Air Column.
| h | P | T | D |
| 0 | 29.92 | 59.0 | 0.07651 |
| 1,000 | 28.92 | 55.5 | 0.07446 |
| 2,000 | 27.92 | 52.0 | 0.07238 |
| 3,000 | 26.92 | 48.5 | 0.07026 |
| 4,000 | 25.92 | 45.0 | 0.06812 |
| 5,000 | 24.92 | 41.5 | 0.06608 |
| 6,000 | 23.92 | 38.0 | 0.06388 |
| 7,000 | 22.92 | 34.5 | 0.06164 |
| 8,000 | 21.92 | 31.0 | 0.05937 |
| 9,000 | 20.92 | 27.5 | 0.05707 |
| 10,000 | 19.92 | 24.0 | 0.05474 |
| 11,000 | 18.92 | 20.5 | 0.05237 |
| 12,000 | 17.92 | 17.0 | 0.04997 |
A couple more basic questions: Why does the pressure drop as you climb? The answer to this is pretty basic - Because the static pressure at any altitude or elevation is primarily determined by the cumulative weight of the air above. The higher you climb, the less air remaining above you.
Why does the temperture in the Standard Air Column drop as you climb? The answer to this is a little more complicated because it is counter-intuitive when one remembers that cold air is more dense than warm air at the same pressure. What is involved is the energy of air: if you insulate some air (prevent energy or heat transfer between neighboring chunks of air) and then expand that air (or move it upward), the temperature of the air will drop in the same way that spray out of a pressurized hairspray or deodorant can or fire extinguisher is colder that the room temperature of the pressurized can or fire extinguisher. Because air is actually moving around (including up and down) a lot during the daytime, it cools and warms as it climbs and descends faster than it can exchange heat with surrounding air. Therefore, the air temperature during the day tends to be reasonably approximated by the Standard Air Column.
Humidity readings are given in a number of ways. The most common data form is Relative Humidity, given in %. (This is the form we will use on this page. Other forms can be converted.) What relative humidity means is that the air is holding x% of the moisture is could possibly hold at this temperature. Because the air can hold more moisture at a higher temperature, the amount of moisture in the air at 50% RH and 80 F is much more than the amount of moisture in the air at 50% RH and 30 F.
To find out how much moisture (and the resulting effects on air density and our beloved density altitude), we must look at the equation for water vapor pressure, which is:
P (water vapor) = exp[-3.032 + 0.0442T - 0.00007T^2].
This equation is simply a curve-fit based on the data provided in the table below, which was obtained from the ASME steam tables. In this equation and the table below, P is in "Hg and T is in degrees F. This calculation is no big deal if you have a nice calculator. If you don't have a nice calculator, the following table will get you close. If the temperature is less than 40 F, then don't worry even at 100% RH. If the temperature is greater than 120 F and you have significant humidity, then you have other problems (like death or the inability to golf, for example).
| T | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| P, H2O | 0.25 | 0.36 | 0.52 | 0.74 | 1.03 | 1.42 | 1.93 | 2.60 | 3.45 |
The density of air calculated at your location (your temperature, pressure, and humidy) will correspond to the density of air at a certain altitude in the Standard Air Column. That Standard Air Column altitude with the same air density as the air density calculated for your location is your density altitude. You can make a table like the one above showing density altitude (equal to Standard Air Column altitude) and air density, or we can fit the Standard Air Column data to provide an equation for finding the Standard Air Column altitude for any density between sea level and 12,000 MSL.
h = (11,346 - 148,300D)/(0.37921 - D)
For example, you might be preparing to take off and you determine the Pressure is 25.77"Hg and the Temperature is 76 F. Assuming dry air (we'll figure humidity effects later), the Density is (25.77)(29)/(21.85)(76+459) = 0.06381 lbs.ft^3 = D. Plugging the actual density into the above equation, we find that the actual air density corresponds to a Standard Air Column altitude of 5970'. What we have just calculated is the Density Altitude. Density altitude is not to be used as a height reference, but can be used to determine the performance capabilities of your aircraft. Your aircraft will behave as though it was at a higher altitude if the density is lower; and the density will be lower if the temperature is higher, the pressure is lower, or the humidity is higher. You can use estimates of density altitude for leaning the mixture or for estimating true airspeed from indicated airspeed (remember, add 2% for each 1000 ft. to your indicated airspeed to estimate actual airspeed).
An example calculation, your data indicates 50% RH, 70 F, and 27.84"Hg. What is your density altitude? First, lets get the D.A. without considering humidity.
D = (27.84)(29)/(21.85)(70 + 459) = 0.06985
h(D.A.) = [11,346 - (148,300)(0.06985)]/(0.37921 - 0.06985) = 3190'
Now, lets see the effect of humidity in this example. First, at 70 F, we see from the table (or by plugging the equation into our nice calculators, if we are so lucky!), we see that the maximum (or "saturated") water vapor pressure is 0.74 "Hg at 70 F. 50% RH means the actual water vapor pressure is 50% (or one-half) of the saturated value, or 0.37"Hg. Given that the total air pressure in this example is 27.84 "Hg, we find that the dry air pressure is (27.84 - 0.37 =) 27.47 "Hg.
The actual air molecular weight in this example is [(0.37)(18) + (27.47)(29)]/27.84 = 28.85. Not much of a reduction.
D = (27.84)(28.85)/(21.85)(70+459) = 0.06949
h(D.A.) = [11,346 - (148,300)(0.06949)]/(0.37921 - 0.06949) = 3360'
From this example, we can see our airplanes' performance curves only need to consider another 160' altitude. (You need higher temperatures and humdities for this effect to be significant.) To summarize, the calculation procedure is (1) find the "saturated water pressure for the given temperature; (2) find the actual water pressure by multiplying saturated water pressure times %RH/100; (3) find the dry air pressure by subtracting the actual water pressure from the total air pressure; and (4) find the new average value of M to use in the density equation by calculating:
M = [(P dry air)(29) + (P water)(18)]/(P total)
One more example showing a higher altitude. 60 %RH, 60 F, and 23.59 "Hg. Without considering the effects of humidity,
D = (23.59)(29)/(21.85)(60 + 459) = 0.06033
h(D.A.) = [11,346 - (148,300)(0.06033)]/(0.37921 - 0.06033) = 7520'
P(saturated) = 0.52
P(H2O, actual) = 0.52(60/100) = 0.312
P(dry air) = 23.59 - 0.31 = 23.28
M = [(23.28)(29) + (0.31)(18)]/23.59 = 28.85
D = (23.59)(28.38)/(21.85)(60 + 459) = 0.05904
h(D.A.) = [11,346 - (148,300)(0.05904)]/(0.37921 - 0.05904) = 8090'
In this case, the effects of humidity were more significant (a 570' density altitude increase).
The computation of %RH from dew point is outlined below without examples. First, the definition of dew point is the temperature at which the actual humidity begins to condense (in other words, becomes saturated). Therefore, the steps for obtaining %RH from dew point are: (1) find the saturated water pressure at the dew point (or P, sat, dew pt); (2) find the saturated water pressure at the actual temperature (or P, sat, actual); (3) dividing (P, sat, dew pt) by (P, sat, actual) and multiplying by 100% gives RH%.
An example from Alaska pilot at 1200' MSL: 29.40 "Hg and -60 F,
D = (29.40)(29)/(21.85)(-60 + 459) = 0.09780
h(D.A.) = [11,346 - (148,300)(0.09780)]/(0.37921 - 0.09780) = -11,220'
To keep from running the engine way too lean, Carb Heat must be fully applied and the Mixture kept at full rich even at cruise altitudes!
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