The Complexity of Speed Concepts in Aviation: TAS and Mach
While sitting in the seat of a passenger plane, you might look at the flight information on the screen in front of you and rejoice, saying, "We are going at 900 kilometers per hour!" However, when the pilots flying that plane look at the speed indicators in the cockpit, the values they see are very different from what is on your screen. In aviation, speed is too complex to be expressed with a single simple number and is classified according to various references.
Two of the most important of these references are True Airspeed (TAS) and Mach Number. To determine an aircraft's performance, fuel consumption, and aerodynamic limits, it is vital to understand the relationship between these two concepts and to convert them into each other. You can use our Mach Number Calculator tool for quick conversions.
Different Speed Terms: IAS, TAS, and Ground Speed
Before getting into the subject, it is necessary to summarize how speed is measured in aircraft:
- IAS (Indicated Airspeed): It is the raw speed measured by the air pressure entering from the aircraft's pitot tubes. Since the air thins (its density decreases) as the plane climbs, IAS always appears much lower than it actually is at high altitudes.
- TAS (True Airspeed): It is the corrected version of IAS, stripped of air density and temperature errors at that altitude. It gives the actual physical distance the aircraft travels per second relative to the air mass it is in.
- Ground Speed: It is TAS with the effect of wind added (or subtracted). This is the value you get via GPS showing the aircraft's speed relative to the ground.
Why Do We Convert Between TAS and Mach?
Since air density decreases when climbing to high altitudes, the aircraft needs to fly with a higher TAS to keep the plane in the air (to create lift). However, as altitude increases, the air cools. As the air cools, the speed of sound drops.
This means: While our aircraft needs a higher TAS to provide lift at high altitudes, it also approaches aerodynamic limits (shock waves, Mach limits) faster due to the decreasing speed of sound. Therefore, while flying at low altitudes, pilots usually fly the plane based on IAS (Indicated Airspeed), but at high altitudes (usually above 26,000 feet), they switch their speed reference to the Mach number. Because what determines the aircraft's structural limits at high altitude is the Mach number.
Conversion Logic from TAS to Mach Number
If you know the TAS value of an object, you also need to find the speed of sound in the environment it is currently flying in to find its Mach number. The formula for conversion is fixed:
Mach Number = TAS / Speed of Sound
So how do we find the speed of sound? As we mentioned in our previous articles, the only thing that determines the speed of sound is the absolute temperature. Under ideal conditions (sea level, 15°C standard atmosphere), the speed of sound is considered to be approximately 340.29 m/s (1225 km/h or 661 knots).
Step-by-Step Conversion Example:
- Determine the TAS Value: Let our aircraft's TAS speed be 450 knots.
- Find the Ambient Temperature (OAT): Let's assume the outside air temperature (OAT) at 30,000 feet altitude is -44°C. Converting this temperature to Kelvin: 273.15 + (-44) = 229.15 Kelvin.
- Calculate the Speed of Sound at That Altitude: If we do an approximate calculation with the Speed of Sound formula (a = 38.94 * √T, in knots), the speed of sound at this temperature comes out to be about 589 knots.
- Find the Mach Number: Mach = TAS (450) / Speed of Sound (589) = 0.76 Mach
Conversion from Mach Number to TAS
In a reverse scenario, you might be a dispatcher or a simulation pilot doing flight planning. You want the aircraft's cruising speed to be Mach 0.82, but what will be the true airspeed (TAS) of this aircraft in kilometers per hour in a windless environment?
This time we reverse the formula:
TAS = Mach Number * Speed of Sound
If the air temperature is -54°C (219.15 Kelvin) at an altitude of 35,000 feet, the speed of sound at this altitude is approximately 1062 km/h.
TAS = 0.82 * 1062 = 870.8 km/h
Practical Way for Instant Conversion
Even though pilot candidates learn these calculations during their aviation training, nobody deals with these mathematical formulas on paper in real life or during flight planning. The flight computers (FMC) of modern aircraft perform these calculations in milliseconds.
If you also want to simulate this delicate balance between TAS, Mach, and air temperature, and convert the values into each other, you can use our Mach Number Calculator tool as the most reliable and fastest way. By simply entering two known values, you can get rid of the conversion mess in seconds.
