Hot air can create challenges for aircraft performance.
By Karsten Shein
Comm-Inst Climate Scientist
One of the primary factors in creating lift is the density of the air through which the aircraft is moving. Air density also factors into the amount of thrust an engine produces, either in terms of power produced by the combustion of fuel and air in the engine, or the efficiency of propellers.
Air density is simply a measure of the mass of air molecules in a given volume of space. Normally, air density at sea level is 1.225 kg per cubic meter, and it’s half that at 21,860 ft, because the force of gravity tends to concentrate the molecules near the surface.
The reason they all don’t pancake into a thin layer of air just at the surface is something called hydrostatic equilibrium. At any given level, the air exerts a pressure in all directions, including upward. That pressure is produced by the air density and temperature at that level.
Because fluids like to flow from areas of higher pressure (like at the surface) to lower (outer space), the pressure gradient creates a net upward force. If the force exceeds the downward pull of gravity, the molecules at that level will rise. If gravity exceeds the upward pressure gradient force, the molecules will descend.
That adjustment will continue until, for every level of the atmosphere, the air density is just right to balance the 2 forces in hydrostatic equilibrium. This density versus altitude relationship is part of the International Standard Atmosphere (ISA) – a set of average conditions of temperature, pressure, and density relative to altitude on which we base aircraft performance numbers.
As air density decreases, so does aircraft thrust at a set power level, and at a set speed, lift, and drag. Because lift is dependent on true airspeed, as density decreases, the loss of lift must be compensated by an increase in thrust. Above an aircraft’s service ceiling, the air density is too low for the aircraft to generate enough lift or thrust to maintain the altitude.
Of course, the density of the air at any level will be affected by temperature and humidity. When energy is absorbed by air molecules, they become more active. This increased activity translates into the molecules releasing more sensible (heat) energy, meaning warmer air. It also means that the molecules will spread further apart as they move around more rapidly. Fewer molecules in a given area means less density.
Understanding density altitude
If the amount of energy received by the molecules is less than the amount they are releasing, they will slow, become more tightly packed (denser), and release less and less sensible energy (colder). This inverse relationship between density and temperature helps us understand density altitude.
Pressure is also related to density and temperature. Recall that each volume of air is exerting a pressure force in all directions on the air around it. That pressure depends on the number of molecules in the volume and their motion.
In the atmosphere where air is not constrained, adding energy will increase temperature and thus decrease density as the heated molecules spread apart, which means that the air pressure will decrease.
An increase in air temperature above the ISA temperature at a given altitude means that the air density at that altitude will be less than what it would be under ISA conditions. Since the aircraft only responds to density, it will behave as if it were at a higher ISA altitude.
Conversely, if the outside air temperature (OAT) is less than what ISA would suggest for that altitude, the aircraft will operate as though it were at the altitude where that temperature would normally be found in the ISA. This reference altitude is the density altitude. Humidity also plays a role in adjusting air density.
Water molecules weigh less than the oxygen and nitrogen molecules they displace as more water vapor is added to the atmosphere. This decrease in overall molecular mass decreases the air pressure exerted at that altitude, destabilizing the hydrostatic equilibrium and allowing some molecules to move out of that altitude.
In net, the decrease in density with increasing humidity is tiny relative to any change brought about by temperature, which is why the humidity component of the density altitude equation is usually left out. While understanding your density altitude is arguably most critical when you are planning your takeoff, it is also important to know for estimating your aircraft’s ability to clear approaching obstacles.
For most pilots, density altitude only becomes a critical factor during the summer months at higher-altitude airports. At airports well above sea level, aircraft performance is already reduced, necessitating longer takeoff and landing rolls and more sluggish climb-outs.
If a runway is sufficiently short, pilots may need to sharpen their pencils and reduce takeoff or landing weight to compensate for not having the additional runway they need. When a heat wave or even a clear and sunny afternoon are thrown into the mix, it can add several hundred to several thousand feet to the airport’s altitude.
There are several ways to determine the density altitude at which your aircraft “thinks” it’s operating. There is a formula that can be Googled but it’s not applied easily.
Instead, if we know the pressure altitude and the air temperature, we can use a density altitude calculator available through several websites or mobile phone applications, or you can use the density altitude chart provided in most aircraft pilot operating handbooks.
Pressure altitude, or QNE, is the ISA altitude at which the measured station pressure would be expected. It is an adjustment of actual altitude to correct for non-standard pressure – either higher pressure than normal, or lower.
A low pressure moving over the area would mean a pressure altitude higher than the absolute altitude above sea level, while a high would put the QNE below the absolute altitude. For example, the ISA atmospheric pressure for an airport at 5000 ft MSL is roughly 24.90 in Hg.
If a low came through and dropped that pressure to 24.70, the corresponding QNE would be 5200 ft MSL, meaning your actual altitude is 200 ft below what your pressure altimeter would be reading. This is the science behind the saying “when flying from high to low, look out below.”
If you are on the ground, you can determine the pressure altitude by dialing 29.92 in Hg or 1013.25 hPa into your altimeter and reading the altitude.
If you don’t have a pressure altimeter available, the rule of thumb for finding pressure altitude is to subtract the altimeter setting from 29.92 and multiply the result by 1000.
This provides the difference between the field elevation and the pressure altitude. For example, at an altimeter setting of 30.25, the pressure altitude is (29.92 – 30.25) x 1000 = –330 ft, meaning that, under that high pressure, the pressure altitude at a 5000-ft airfield is 4670 ft. In order to go from pressure altitude to density altitude, you also need to know the OAT.
Enter the temperature and pressure altitude into the calculator and it will crunch through a fairly complex equation to deliver density altitude.
Using the density altitude chart is just as simple. Find the pressure altitude on the vertical axis and the temperature along the horizontal axis.
Trace across and up, respectively, until the 2 grid lines intersect. The sloping lines that run across the graph are the density altitude lines. Read the nearest lines on either side of the intersection between your pressure altitude and temperature, and interpolate the density altitude.
For example, given a pressure altitude of 10,000 ft and a temperature of 20° C, the intersection falls just short of the 13,000 ft density altitude line, or roughly 12,800 ft. Pressure altitude and OAT are also needed to calculate aircraft performance factors such as takeoff or landing distance and climb rates.
For a given weight, aircraft require a specific true air speed on takeoff for the lifting surfaces to produce enough lift to counter that weight. A typical takeoff distance calculation will start with OAT and pressure altitude to account for density altitude, factor in aircraft weight, and finally take account of headwinds or tailwinds.
Changes in any of these variables can have a big impact on the amount of runway needed. For example, a Raytheon King Air B300 taking off at maximum weight in 15° C temperature and 4000-ft pressure altitude might need 4452 ft of runway. At 25° C you’d need an additional 600 ft.
Add 1000 ft of pressure altitude and those lengths become 4850 ft and 5507 ft, respectively. This mix of variables also means that above a given combination of OAT, pressure altitude, and weight, an aircraft might have a 15,000-ft runway, but still not be able to lift off.
To use the King Air example again, at 6000-ft pressure altitude and 35° C, no amount of runway would help it take off with max weight. The only option is to reduce weight by at least 1000 lb (454 kg) and have 6000 ft of runway with no obstruction.
High altitude airports While most of us don’t normally load our aircraft to the limits, we can see the effects of decisions such as these in larger commercial passenger and cargo aircraft that routinely operate out of high-altitude tropical airports, such as NBO (Nairobi, Kenya) at 5328 ft MSL, or UIO (Quito, Ecuador) at 7874 ft MSL.
Although these airports have runways that exceed 13,000 ft (4000 m) in length, many operators schedule landings and departures at night, when the temperatures drop and the aircraft can take off and land safely carrying heavier loads.
Because of the limitations that aircraft weight places on the equation, this is an important consideration for operators as air temperatures continue to rise globally. Where once there may have only been a day or 2 each summer at PHX (Sky Harbor, Phoenix AZ) or DEN (Denver CO) when density altitude rose too high for a fully-loaded Boeing 767 to take off, now there may be a dozen of those hot days, and a decade from now there may be 20 or 30.
This translates into more flights needed to carry the loads, at more cost to aircraft operators, and more congestion at major airports. Anticipating high density altitudes At least on a short lead time, high density altitudes can be anticipated.
A look at surface weather maps will identify areas of high pressure. During the summer, those often mean elevated temperatures and heat waves. The record-setting heatwave in the Pacific NW this summer, for example, was well forecast several days in advance.
Metars from your airports will also show you the temperature and altimeter setting so you can calculate density altitude. Since the greatest impacts of density altitude are felt at higher-altitude airports, it is also worth taking a look at upper air charts, such as the 500- and 300-mb charts.
These will show more reliably what the pressure is like above those surface highs. A heat dome at the surface coupled with a low pressure aloft can produce much higher density altitudes than a heat wave alone. You should also look at wind flow.
If winds are blowing warm air into the area and there is a low nearby, you can expect increased density altitudes. You can also use the forecast high temperature for the day or two ahead to make a reasonable estimate of the highest density altitude you may encounter at an airport.
Whether using a forecast high or the currently reported temperature, it’s a good idea to factor in an extra few degrees as a margin of safety. Temperatures reported by an airport or nearby town may be taken over grass or a light surface, but with the sun baking a dark concrete or asphalt runway, the temperature along the takeoff or landing path – especially in the 50 ft closest to the surface – may be as much as 5°–10° warmer than what is being reported. If you do notice such a temperature difference as you position on the runway, let the tower know so your fellow pilots can be more accurate in their density altitude and performance calculations.
Karsten Shein is cofounder of 2DegreesC.org. He was director of the Midwestern Regional Climate Center at the University of Illinois, and a NOAA and NASA climatologist. Shein holds a Comm-Inst pilot license.