id="ulink_cec1a168-3dad-5b9e-b3b5-f2c9ba6bfae9">(2.12)Values of
Due to the decrease in air density with an increase in altitude, for any given TAS, CAS will decrease as altitude increases. As higher altitudes are attained, the aircraft must fly faster to obtain the same pressure differential. For a given CAS, as an aircraft increases in altitude, the TAS will increase. The higher the aircraft travels in altitude, the greater the difference between CAS and TAS.
Figure 2.13 Altitude and EAS to TAS correction chart.
EXAMPLE
Using our example from the CAS discussion, EAS was determined to be 382.5 kts. If the outside air temperature at a pressure altitude of 20 000 ft is −30 °C, we can utilize Eq. 2.12 to find the TAS. From Table 2.1, the pressure ratio (δ) is 0.4595.
Figure 2.14 depicts the change in TAS between sea level and 15 000 ft when the IAS remains constant. For the respective IAS, the CAS calibration has been applied. As the aircraft climbs, the TAS increases as the air density decreases. The aircraft must travel at 130 kts. TAS to register 100 kts. on the airspeed indicator.
Understanding the relationship between the speeds above, and the calculation of each one, can be facilitated by remembering “ICE‐T.” IAS is read off the airspeed indicator, CAS is IAS corrected for installation/position errors, EAS is CAS corrected for compressibility, and finally TAS is EAS corrected for temperature and pressure.
Figure 2.14 IAS, CAS, and TAS comparison.
Source: U.S. Department of Transportation Federal Aviation Administration (2013).
Mach
The Mach number is found by comparing TAS to the speed of sound for a given set of conditions at a specific altitude. The speed of sound is an important factor in the study of high‐speed flight and is discussed in depth in Chapter 14. Because the aircraft’s speed in relation to the speed of sound is so important in high‐speed flight, airspeeds are usually measured as Mach number (named after the Austrian physicist Ernst Mach). Mach number is the aircraft’s true airspeed divided by the speed of sound (in the same atmospheric conditions):
(2.13)
where
M = Mach number
V = true airspeed (kts.)
a = local speed of sound (kts.)
EXAMPLE
Using the TAS from the previous example (518.6 kts.), when a = 607.3 kts., calculate the Mach number for the aircraft.
Groundspeed
Groundspeed (GS) is the actual speed of the aircraft over the ground, either calculated manually or more commonly nowadays read off the GPS (Global Positioning Satellite) navigational unit. The GS increases with a tailwind and decreases with a headwind, and is TAS adjusted for the wind. Groundspeed equals true airspeed in a no wind situation. Consider an airplane that has departed an airport located at sea level, then lands on a runway located at 5000 ft. Even though the IAS on approach will remain the same as if the airplane was landing at sea level, the TAS (and GS) will be higher at the airport with the higher elevation, thus more runway will be utilized during the landing.
SYMBOLS
| a | Speed of sound (local for a given condition) |
| A | Area (ft2) |
| AGL | Above ground level |
| CAS | Calibrated airspeed (kts.) |
| °C | Celsius temperature (°) |
| DA | Density altitude |
| EAS | Equivalent airspeed |
| °F | Fahrenheit temperature |
| GS | Groundspeed |
| H | Total pressure(head) (psf) |
| IAS | Indicated airspeed |
| °K | Kelvin temperature |
| MSL | Mean sea level |
| M | Mach number (ratio) |
| P | Static pressure |
| PA | Pressure altitude |
| P 0 | Sea level standard pressure |
| q | Dynamic pressure |
| R |
Universal gas constant
|
