Engineering
Mach Number, Speed of Sound in Air & Aerodynamic Dynamic Pressure (q) formulas
Calculate local speed of sound a = SQRT(1.4 * 287.05 * (T_C + 273.15)), flight Mach Number V / a, compressible regime, and dynamic pressure 0.5 * rho * V^2.
Local Mach number in a constant-property ideal-air model
For dry ideal air with fixed gamma1.4 and specific gas constant287.05J/(kg·K), sound speed follows absolute temperature. Temperature must exceed absolute zero. These constant properties are an approximation; humidity, composition and high-temperature effects can require another model.
V is speed relative to the local air, not ground speed. Mach1 is sonic; below1 is subsonic and above1 is supersonic by speed. Transonic describes a flow regime near sonic conditions whose extent depends on geometry, so it is not a universal exclusive numeric bin.
Dynamic pressure q=0.5*rho*V² is not a complete structural load or, for compressible flow, generally the stagnation-minus-static pressure. Aerodynamic forces also require area and suitable coefficients. The temperature and density inputs are independent illustrative values, not a standard-atmosphere altitude calculation.
| Aerodynamic Input | Cell | Flight Condition | Computed Output |
|---|---|---|---|
| Ambient Air Temp (T_C) | B2 = 20 C | 293.15 K (no altitude inferred) | Speed of Sound a = 343.23 m/s |
| True Airspeed (V_ms) | B3 = 250 m/s | 900 km/h jet cruise | Mach M = 250 / 343.23 = 0.7284 |
| Air Density (rho) | B4 = 1.225 kg/m^3 | q = 0.5 * 1.225 * 250^2 | Dynamic Pressure q = 38,281.25 Pa |
| Speed400m/s | V set to 400 m/s | 400 / 343.23 = 1.1654 | Mach1.1654; slightly above sonic speed |
Local Speed of Sound a (m/s) & Flight Mach Number M = V / a
Converts Celsius B2 to Kelvin (+273.15) inside SQRT(1.4 * 287.05 * T_K).
=IF(OR(COUNT(B2:B4)<>3,B2<=-273.15,B3<0,B4<=0),"Invalid inputs",ROUND(B3 / SQRT(1.4 * 287.05 * (B2 + 273.15)), 4))Aerodynamic Dynamic Pressure q = 0.5 * rho * V^2 (Pascals)
Lift and drag forces equal q * S * C_L and q * S * C_D.
=IF(OR(COUNT(B2:B4)<>3,B2<=-273.15,B3<0,B4<=0),"Invalid inputs",ROUND(0.5 * B4 * (B3 ^ 2), 2))Try the example
Use the original values or change them to test your understanding.