## Measuring and Calculating Air Speed

# Measuring Air Speeds

## By Dave Esser

### Caveat: Every effort is made to assure the accuracy of this information but errors sometime occur in typing or translation to html for the internet. The information provided here is for general education and understanding only and not for the purpose of actual use in any aviation activity or other calculation of air speed.

Knowing how fast an aircraft is traveling is just as important, if not more so, than knowing how fast a car is moving. However, the measurement of an aircraft’s speed is a bit more complex than the speedometer on an automobile. In this article we will discuss the various types of air speed and how they are measured.

Pilots speak of several types of air speed. When read directly off the air speed indicator, the value is called indicated air speed (IAS). Indicated air speed has several factors that must be corrected in order to determine the actual speed of an aircraft over the ground. To determine the aircraft’s indicated air speed, two pressures are measured. A pitot tube is positioned on the exterior of the aircraft so that the air molecules of the atmosphere “ram” into it. The faster the aircraft is traveling, the greater the ram pressure. As an aircraft climbs, the atmospheric air pressure decreases, as does the ram pressure. To account for this, the aircraft has a static air pressure port that is also connected to the air speed indicator. The greater the difference between the ram and static pressures, the greater the indicated air speed.

As an aircraft changes its air speed and configuration, such as occurs when slowing down and lowering flaps and landing gear, the airflow pattern over the fuselage changes. This change of airflow affects the pressure in the pitot tube and static port. To account for this, the pilot refers to an air speed calibration chart to read the calibrated air speed (CAS). Each type of aircraft has its own calibration chart because the airflow pattern depends on the aircraft itself.

With some aircraft, such as the TB-9 Tampico, the IAS is approximately equal to CAS at all air speeds. This is true for relatively slow-moving aircraft because they have an air speed envelope (the difference between the maximum and minimum speeds) of less than 50 knots. This small envelope means that the airflow pattern does not significantly change from slow to fast air speeds. A jet transport aircraft has a speed envelope of more than several hundred knots.

The airflow pattern over a Boeing 737 cruising at 400 knots with flaps and gear up is significantly different than when the aircraft is landing at 150 knots with gear and flaps down.

When flying faster than 200 knots, the air ahead of the aircraft becomes compressed. This air compression increases the air density and the pressure in the pitot tube. To account for compressibility, the pilot refers to an air speed compressibility chart. The greater the CAS and the higher the altitude, the more the pilot must subtract to attain the equivalent air speed (EAS).

As an illustration, imagine being in a speedboat and sticking your hand out into the wind. The wind pushes your hand back with a particular dynamic force. Now imagine sticking your hand into the rushing water. The dynamic pressure exerted on your hand by the water is greater than that of the air because of the higher density of water. As air is compressed into a pitot tube, the increased density of compression increases the dynamic pressure and therefore the air speed that is read on the air speed indicator. The more the air is compressed, the greater the error.

The air will be more compressed the faster the aircraft is traveling and the higher the pressure altitude. Think of the air at lower pressure altitudes as being pre-compressed by the force of the air pressure. Think of this air as pre-compressed concrete block. Think of the air at higher pressure altitudes as not being compressed, and therefore like a sponge. When the same force is applied to a concrete block and a sponge, the sponge will be more compressed, as is the case with air. So for the same CAS as the pressure altitude increases, so does the amount that must be subtracted from the CAS to determine the EAS. Equivalency charts are used to make this correction. The pilot enters the CAS and pressure altitude into the chart and determines how much to subtract. Equivalency charts are not airplane-specific.

It is the EAS that the aircraft feels. EAS is a measure of the dynamic pressure exerted on the aircraft. This dynamic pressure plays a key role in the lift and drag created by the aircraft. For a given EAS the aircraft feels the same dynamic pressure, and therefore lift and drag, regardless of altitude. The higher the density altitude, the thinner the air, and the faster an aircraft must travel through the air mass to obtain the same EAS. The actual speed of the aircraft through the air mass is called the true air speed (TAS).

A pilot flying at high altitudes must account for reduced air density. Imagine the space shuttle in orbit – even though the orbital speed is more than 17,000 knots, there is virtually no atmosphere to ram into a pitot tube. The EAS would be nearly zero. By knowing the air density, the pilot can calculate the actual speed through the air mass, or true air speed. The only time that EAS is equal to true air speed is when an aircraft is flying at standard sea level (SSL) conditions. It is to the TAS that the velocity of the wind is applied, to determine the speed over the ground. The presence of a tailwind or headwind will increase or decrease the ground speed.

Dynamic pressure represents the kinetic energy of the relative wind. We recall that the formula for kinetic energy is one-half the mass multiplied by the square of the velocity or KE = ½ m v^{2}.

Because air is a fluid, its mass is represented by its density or r (rho). The symbol r_{0 }represents the air density at standard sea level. Here are the equations for dynamic pressure (q): ½ r V_{TAS}^{2} = q = ½ r_{0} V_{EAS}^{2}.

This means that the dynamic pressure can be determined by taking one-half the air density multiplied by the squared velocity in TAS (V_{TAS}^{2}). The same value will be obtained by taking one-half the SSL air density multiplied by the squared velocity in EAS (V_{EAS}^{2}).

Rearranging the previous equation, the following equation is obtained: V_{TAS}^{2 }(r_{ }/r_{0}) = V_{EAS}^{2}.

The term r_{ }/r_{0 }represents the ratio of the air density at some altitude to that of SSL. This density ratio is referred to as sigma or s. Making this substitution, the equation becomes V_{TAS}^{2 }s^{ }= V_{EAS}^{2}.

Taking the square root of all terms yields V_{TAS}^{ }= V_{EAS.}^{ }

Solving for V_{TAS, }the equation becomes: V_{TAS}^{ }= V_{EAS}^{ }(1/ ).

The term 1/ is referred to as the standard means of evaluation, or SMOE. This means that in order to determine the TAS, the EAS is multiplied by SMOE: V_{TAS}^{ }= V_{EAS}^{ }x (SMOE).

At approximately 40,000 feet the SMOE value is 2. This means that if the EAS, what the aircraft feels, is 200 knots, then the TAS, or actual speed through the air mass, would be 200 knots x 2, or 400 KTAS.

Mach refers to the ratio of an aircraft’s speed to that of the local speed of sound (a). The phrase “local speed of sound” is used because the speed of sound’s propagation through the air is a function of the velocity of the air molecules themselves. Recall that the temperature of the air reflects the average molecular velocity, so the speed of sound is a function of air temperature. At the SSL temperature of 15°C the speed of sound is approximately 662 knots (a_{0 }= 661.74 knots). As the temperature decreases with altitude, the local speed of sound (a) also decreases.

The formula for determining the local speed of sound is a = a_{0 }x_{ }, where a_{0} represents the speed of sound at SSL. The term T_{0} represents the SSL temperature of 15°C in Kelvin (288 K). Kelvin is an absolute temperature scale. For example, zero degrees Celsius is equal to 273 K. The ratio of the local temperature to that of SSL is called theta or q.

Making this substitution, the equation becomes a = a_{0 }x or a = 661.74 knots x .

So the determination of an aircraft’s Mach number would be Mach = TAS / (661.74 knots x ).

Pilots of high-altitude fast-moving aircraft are more concerned with exceeding their maximum safe Mach number than they are with dynamic pressure limitations such as never-exceed red lines. As an aircraft approaches the speed of sound, the accelerated airflow over the top of the wings will exceed the speed of sound before the aircraft’s speed through the air exceeds the speed of sound. The speed range in which both subsonic and supersonic airflows exist over an aircraft is called transonic. This is the speed range in which commercial jetliners cruise. If a jetliner were to exceed a safe Mach number, the excessive area of sonic airflow could result in a dangerous buffeting similar to that of a stall. If this high-speed buffet increases, it can result in aircraft-control prob-lems. Most commercial airliners cruise at around Mach 0.85.

Because of the importance of maintaining a cruise speed below a maximum operating Mach number (Mmo), high-speed aircraft must have a Mach-indicating device. This is typically represented by a red-and-white striped hand on the air speed indicator that moves as the speed of sound changes. This “barber pole” indicates the fastest speed at which the aircraft should cruise. It is interesting that a Mach meter does not require a temperature input to determine the highest speed that can be attained without exceeding the Mmo. It seems contradictory that the speed of sound is a function of temperature and that the Mach meter does not need to know what the temperature is. Here is why:

Remember that the formula for Mach is the ratio of TAS to the local speed of sound, or Mach = TAS / a.

Because TAS is EAS multiplied by SMOE, and the local speed of sound is the SSL speed of sound multiplied by the temperature ratio, the previous equation can be rewritten as Mach = {EAS x (SMOE)}/ (a_{0 }x ) or Mach = {EAS x (1/ )}/( a_{0} x ).

Moving the SMOE term to the denominator yields Mach = EAS / (a_{0 }).

Combining the temperature ratio and density ratio under a common radical becomes Mach = EAS / (a_{0 }).

Now the magic. Certain gasses behave in such a way that they can be said to be ideal gasses. These gasses obey the ideal gas equation, which states that the temperature ratio (theta or q) when multiplied by the density ratio (sigma or s) equals the pressure ratio (delta or d), or d = q x s. The pressure ratio represents the ratio of the ambient pressure divided by the SSL pressure of 29.921 inches of mercury, or d = P_{ }/P_{0}.

Substituting d for q s under the square root radical becomes Mach = EAS / (a_{0} x ) or Mach = EAS / (661.74 x ) or Mach = EAS / (661.74 x ).

So, the moral of the story is that a Mach meter needs only pitot static inputs to determine the Mach number of an aircraft. That’s because the gasses that make up our atmosphere behave in a manner consistent with the ideal gas equation.

Keeping track of all the different types of air speed is a bit complicated, but pilots do have one thing going their way – there aren’t nearly as many speed limits in the air. So, the next time a police officer asks if you know how fast you were going, you might respond by asking, “Do you mean indicated, calibrated, equivalent, true, ground speed, or Mach?” That will just about guarantee that you’ll get a ticket. L

*Dave Esser is a professor of aeronautical science at Embry-Riddle Aeronautical University. He may be contacted at *esserd@cts.db.erau.edu*.*

WOMAN PILOT **•** January/February 2000