Section 3 Density

If no trim change is made, gliders fly faster when the air density is lower. Faster, for example, in Colorado Springs in summer than they do in Minneapolis in winter. Air density is directly related to aerodynamic forces on the aircraft. Maneuverability, (e.g. the number of g’s the aircraft can sustain), and the amount of oxygen available for internal combustion engines are directly proportional to atmospheric density.

When variations in Reynolds number (R_e) are not significant, specific aircraft flight conditions such as wings-level stall, flattest glide, or lowest sink speed occur at a given angle of attack, regardless of the density.

Although the angle of attack for any of these conditions remains the same, the aircraft flight speed for these conditions changes with density. In order to maintain steady or unaccelerated flight, ( approximately defined by lift = weight, constant speed) airspeed at a given angle of attack must go up if density goes down.

Density times airspeed squared must stay constant. For example, If density is 1/4 of the sea level value then airspeed must be 2 times sea level speed to keep the angle of attack and maintain unaccelerated flight. Aircraft airspeed indicators, in fact, indicate the equivalent sea level airspeed, not true airspeed, to eliminate the density effect. We want to know what the density is and how much it varies over possible model flight conditions.

The approximations above have to be modified when density changes rapidly with time as in the case of space shuttle reentry, the SST flying at constant altitude through a pressure gradient, or even the U2 gliding dead-stick from 80,000 feet. For model aircraft in this century, however, they seem to be just fine.

When R_e effects can be ignored the minimum drag in steady level flight does not change with atmospheric conditions. It is the same at all altitudes. This is because the maximum lift-to-drag ratio (L/D) is a constant. When density decreases, however, the speed the airplane has to fly to keep lift equal to weight at the angle of attack for maximum L/D must increase. Because of this the power required to fly at minimum drag increases with decreasing density. If the density is 0.8 times standard density the power required to fly at the same angle of attack will go up by about 12%.

One convenient way to think about density is to compare the density with the density in the standard atmosphere. A density altitudeH_d of 3000 feet, for instance, means that the air density is the same as in the density in the standard atmosphere at 3000 feet.

If the density altitude is known you can look up density in Table 1 below. Density altitude should normally be within three or four thousand feet of your actual altitude (usually higher), which gives you a good check.

Figure 1 shows H_d for sea level pressure as a function of temperature. You can use ATMO99 to compute the density altitude exactly for any set of conditions when you have temperature and pressure. Be careful, however, nation-wide meteorology reports show pressures ’adjusted’ to sea level. Get the local airfield reading (the altimeter setting for an airfield near you will usually be given in terms of the barometric pressure in inches of Mercury). If all you have is the weather map pressure, the procedure is given in the ATMO99 manual

Temperature in Figure 1 is in degrees Fahrenheit - a ’modeler unit’ - instead of Kelvins, the scientific standard. Because atmospheric pressure is still given in “inches of Mercury” (in. Hg) in most sources, I have used this “barometric” unit of pressure measurement here, as opposed to the meteorological standard of millibars. Note that this figure is drawn for a dry atmosphere. When humidity is considered the density altitude will increase slightly.

Atmospheric pressure normally varies from the standard by -2% to + 1% in. Hg at a given location from day to day. Larger variations can occur, for example in the North Pacific Low in winter -4% is not uncommon. Temperature, varies over a larger range. Note that pressures in the rocky mountain west during summer average about 1% below standard.

An example of a large difference, consider two locations:

• Sea level on a fairly cold winter day in a high pressure condition ( e.g. 30 ^oF and 29.92 in. Hg.)
• Colorado Springs (6560 feet altitude) on a warm, low pressure summer day (80 ^oF and 23.01 in. Hg)

The density altitude for these two conditions differs by 12,400 feet. In this example the high altitude density is 69% that of the density of the sea level site and gliding speeds are 20% higher. A 300 second glide in still air would drop to around 250 seconds in this example.

Table 1 shows some standard atmosphere properties. Pressure is shown in barometric units, density is given in English units; slugs per cubic feet. Multiply the sea level, standard atmosphere speed by the “speed ratio” to find speed at altitude. As a crude way of measuring the difficulty of flying at high density a ’power index’ is listed. It assumes engine displacement must be increased enough to make up for the loss in density, then enough more to fly the plane fast enough to maintain lift at the angle of attack chosen.