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# Differences Between Corrected Airspeeds

This example shows the differences between corrected airspeeds and true airspeed (TAS). The corrected airspeeds are indicated airspeed (IAS), calibrated airspeed (CAS), and equivalent airspeed (EAS). You can use the Aerospace Toolbox `correctairspeed` function to calculate TAS, CAS, and EAS from one of the other two.

### TAS: True Airspeed

True airspeed is the airspeed that we would read ideally (and the airspeed value easily calculated using scripts or functions).

`TASInKTS = 72;`

To determine the speed of sound and pressure at altitude for a standard atmospheric day required to make the airspeed corrections, select an altitude.

```altitudeInFt = 2500; altitude = convlength(altitudeInFt,'ft','m'); [~, speedOfSound, pressure0, ~] = atmoscoesa(altitude);```

### EAS: Correcting for Density Error

An airspeed indicator reads lower than true airspeed (TAS) at higher altitudes. This is due to lower air density at altitude. When the difference or error in air density at altitude from air density on a standard day at sea level is applied to true airspeed, the result is in equivalent airspeed (EAS). Equivalent airspeed is true airspeed modified with the changes in atmospheric density that affect the airspeed indicator.

`EASInKTS = correctairspeed(TASInKTS, speedOfSound, pressure0, 'TAS', 'EAS');`

### CAS: Correcting for Compressibility Error

Air has a limited ability to resist compression. This ability is reduced by an increase in altitude, an increase in speed, or a restricted volume. Within the airspeed indicator, there is a certain amount of trapped air. When flying at high altitudes and higher airspeeds, calibrated airspeed (CAS) is always higher than equivalent airspeed. Calibrated airspeed is equivalent airspeed modified with compressibility effects of air, which affect the airspeed indicator.

`CASInKTS = correctairspeed( TASInKTS, speedOfSound, pressure0, 'TAS', 'CAS');`

### IAS: Correcting for Instrument and Position Error

Indicated airspeed (IAS) is displayed on the airspeed indicator in the cockpit. To calculate IAS, the calibration error of the pitot-static airspeed indicator is applied to the calibrated airspeed.

#### Calibration Error

The airspeed indicator has static vent(s) to maintain a pressure equal to atmospheric pressure inside the instrument. Position and placement of the static vent, angle of attack, and velocity of the aircraft determines the pressure inside the airspeed indicator and the amount of calibration error of the airspeed indicator. The calibration error is specific to a given aircraft design. A calibration table is usually given in the pilot operating handbook (POH) or in other aircraft specifications.

#### Example Calibration Tables

As an example, here is the Cessna 150M airspeed calibration table from "Pilot's Operating Handbook, Cessna 1976 150 Commuter, Cessna Model 150M", Cessna Aircraft Company, Wichita, Kansas, USA, 1976.

Calibration table for 0, 10 and 0 degrees of flap:

```flaps0IAS = 40:10:140; flaps0CAS = [43 51 59 68 77 87 98 108 118 129 140]; flaps10IAS = [40:10:80 85]; flaps10CAS = [42 50 60 69 78 82]; flaps40IAS = [40:10:80 85]; flaps40CAS = [40 50 61 72 83 89]; plot(flaps0CAS,flaps0IAS,flaps10CAS,flaps10IAS,flaps40CAS,flaps40IAS) xlabel('Calibrated Airspeed (CAS) (kts)'); ylabel('Indicated Airspeed (IAS) (kts)'); title('Cessna 150M Airspeed Calibration Table'); legend ('0 degrees','10 degrees','40 degrees','Location','southeast');```

Using this calibration table, the indicated airspeed (IAS) is determined from calibrated airspeed.

```flapSetting = 40; if (flapSetting == 40) tableCAS = flaps40CAS; tableIAS = flaps40IAS; elseif (flapSetting == 0) tableCAS = flaps0CAS; tableIAS = flaps0IAS; else tableCAS = flaps10CAS; tableIAS = flaps10IAS; end IASInKTS = interp1(tableCAS,tableIAS,CASInKTS);```

### Plot Airspeed Comparisons

Using the plot command, you can visualize the impact of correcting for the various sources of error in measuring airspeed compared to true airspeed.

```plot(TASInKTS,EASInKTS,'o',TASInKTS,CASInKTS,'+',TASInKTS,IASInKTS,'*'); xlabel('True Airspeed (TAS) (kts)'); ylabel('Airspeed (kts)'); title('Differences Between Corrected Airspeeds and True Airspeed'); legend ('EAS','CAS','IAS','Location','southeast'); set(gca,"XGrid","off","YGrid","on");```