Library / Aerospace / AER-03
Aerospace
Mach number and speed of sound
Speed as a multiple of the local speed of sound.
- Ref
- AER-03
- Rev
- v1
- Field
- Aerospace
- Result
- M
V true airspeed in m/s, a the local speed of sound, γ the ratio of specific heats (1.4 for air), Rs = 287.05 J/(kg·K) the specific gas constant of air and T the static absolute temperature in kelvin.
The speed of sound depends only on air temperature, not on pressure. Mach number tells you how fast you are going compared to it, and decides whether air behaves as nearly incompressible, transonic or supersonic.
Calculator
- Speed of sound a340.3 m/s
- Speed in knots486 kt
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Sound travels at about 340 m/s at 15 °C and about 295 m/s at −56 °C (the stratosphere), so the same Mach number means very different speeds.
- Compressibility effects start around Mach 0.3; the transonic regime of rapid drag rise is about Mach 0.8 to 1.2.
- The speed of sound changes by only about 0.6 m/s per kelvin, so temperature errors matter little.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| V True airspeed | 50 to 900 m/s | 0.1469 | 2.645 | 2.498 | +10% | +10 % |
| T Static temperature | 200 to 320 K | 0.6971 | 0.8818 | 0.1847 | +10% | −4.65 % |
Sweep of True airspeed
| True airspeed (m/s) | Mach number |
|---|---|
| 50 | 0.1469 |
| 71.76 | 0.2109 |
| 103 | 0.3026 |
| 147.8 | 0.4344 |
| 212.1 | 0.6234 |
| 304.4 | 0.8947 |
| 436.9 | 1.284 |
| 627.1 | 1.843 |
| 900 | 2.645 |
Sweep one variable
Variables and how each one contributes
Mach number
What the equation gives you. Everything else feeds it.
True airspeed
Speed relative to the air. Directly proportional.
Static temperature
Absolute temperature of the air (add 273.15 to °C). Raises the speed of sound with √T, so a hotter day means a lower Mach number at the same speed.
Worked example with the values above
- Speed of sound: a = √(1.4 × 287.05 × 288.1) = 340.3 m/s.
- M = V/a = 250 / 340.3.
- M = 0.7347.
Assumptions and limits
- Ideal gas with constant γ.
- Static, not total, temperature.
- Dry air.
Common mistakes
- Using the total temperature or the temperature in °C.
- Using ground speed.
- Using the sea-level speed of sound at altitude.
Statistics and uncertainty
Because a ∝ √T, a 2% error in temperature gives only a 1% error in a. Airspeed from a pitot tube is usually the dominant source of uncertainty (1–3%).
Where it is used
- Flight envelope and engine intake design.
- Missile aerodynamics.
- Sonic boom and shock wave estimates.
Maths you need
- Absolute temperature: kelvin = °C + 273.15
- Ideal gas: speed of sound from gas properties