Airspeed Measurement
There are several reasons to measure airspeed. It is necessary to know whether we have sufficient dynamic pressure to create lift, but not enough to cause damage, and velocity is necessary for navigation. If dynamic pressure can be measured, velocity can be calculated. Dynamic pressure cannot be measured directly, but can be derived using Bernoulli’s equation as the difference between the total pressure and the static pressure acting on the airplane:
q=PT-PS
The system that accomplishes this is the pitot static system. It consists of a pitot tube that senses total pressure (PT), a static port that senses ambient static pressure (PS), and a mechanism to compute and display dynamic pressure. We will not concern ourselves with the workings of that mechanism, but simply consider it as a “black box”.
At the entrance to the pitot tube, the airstream has both an ambient static pressure (PS) and a dynamic pressure (q). Inside the pitot tube, the velocity of the air mass is reduced to zero. As velocity reaches zero, dynamic pressure is converted entirely to static pressure. This converted static pressure is added to the ambient static pressure (PS) to form a total static pressure equal to the free airstream total pressure (PT). This total static pressure is connected to one side of a diaphragm inside the black box.
The static pressure port is a hole or series of small holes on the surface of the airplane’s fuselage that are flush with the surface. Only ambient static pressure (PS) affects the static port; no dynamic pressure is sensed. The static port is connected to the other side of the diaphragm in the black box.
The ambient static pressure (PS) is subtracted from the total pressure (PT), giving dynamic pressure (q), which is displayed on a pressure gauge inside the cockpit. This gauge is calibrated in knots of indicated airspeed (KIAS). Indicated airspeed (IAS) is the instrument indication of the dynamic pressure the airplane is exposed to during flight. To determine true airspeed, certain corrections must be made to IAS.
Instrument error is caused by the static pressure port accumulating erroneous static pressure; slipstream flow causes disturbances at the static pressure port, preventing actual atmospheric pressure measurement. When indicated airspeed is corrected for instrument error, it is called calibrated airspeed (CAS). Often, installation and position error are combined with instrument error. Even the combination of all three errors is usually only a few knots, and is often ignored.
Compressibility error is caused by the ram effect of air in the pitot tube resulting in higher than normal airspeed indications at airspeeds approaching the speed of sound. Equivalent airspeed (EAS) is the true airspeed at sea level on a standard day that produces the same dynamic pressure as the actual flight condition. It is found by correcting calibrated airspeed for compressibility error.
True airspeed (TAS) is the actual velocity at which an airplane moves though an air mass. It is found by correcting EAS for density. TAS is EAS corrected for the difference between the local air density (ρ) and the density of the air at sea level on a standard day (ρ0):
As instrument error is typically small, and compressibility error is minor at subsonic velocities, we will ignore them and develop TAS directly from IAS:
The pitot static system is calibrated for standard sea level density, so TAS will equal IAS only under standard day, sea level conditions. Since air density decreases with an increase in temperature or altitude, if IAS remains constant while climbing from sea level to some higher altitude, TAS must increase. A rule of thumb is that TAS will be approximately three knots faster than IAS for every thousand feet of altitude.
Ground speed is the airplane’s actual speed over the ground. Since TAS is the actual speed of the airplane through the air mass, if we correct TAS for the movement of the air mass (wind), we will have ground speed.
GS = TAS − HEADWIND
GS = TAS + TAILWIND
“ICE-TG” is a helpful mnemonic device for the order of the airspeeds.
MACH NUMBER
As an airplane flies, velocity and pressure changes create sound waves in the airflow around the airplane. Since these sound waves travel at the speed of sound, an airplane flying at subsonic airspeeds will travel slower than the sound waves and allow them to dissipate. However, as the airplane nears the speed of sound, these pressure waves “pile up” forming a wall of pressure called a shock wave, which also travels at the speed of sound. As long as the airflow velocity on an airplane remains below the local speed of sound (LSOS), it will not suffer the effects of compressibility. Therefore, it is appropriate to compare the two velocities. Mach Number (M) is the ratio of the airplane’s true airspeed to the local speed of sound:
Since airplanes accelerate airflow to create lift, there will be local airflow that has a velocity greater than the TAS. Thus an airplane can experience compressibility effects at flight speeds below the speed of sound. Critical Mach number (MCRIT) is the free airstream Mach number that produces the first evidence of local sonic flow. Simply put, an airplane exceeding MCRIT will have supersonic airflow somewhere on the airplane. Consider a positively cambered airfoil at Mach 0.5. The maximum local airflow velocity on the surface is greater than the true airspeed speed but less than the speed of sound. If an increase to Mach 0.82 boosts the surface airflow velocity up to the local speed of sound, this would be the highest speed possible without supersonic airflow and would determine MCRIT.
