Help: Calculating Mach number

[MightyBoo]

Hi all,

- Using the LSS formula a = 39 √ T and..
- Mach number (M) = Speed of aircraft (TAS) ÷ Local speed of sound (a)

What is the Mach number of an aircraft doing 453 knots groundspeed, with a 58 knot headwind component, cruising at FL380, at ISA plus 5 degrees Celsius?

Appreciate if the workings can be illustrated. Thank you all.

[FlyingStone]

TAS = GS + headwind = 453 + 58 = 511 kts

LSS = 39 x sqrt(T) = 39 x sqrt (273.15 - 56.5 + 5) = 580,63

M = TAS/LSS = 511 / 580,63 = 0,88

[S7EVIN]

Temperature drops 1.98°C every 1000ft up to FL360 where it remains constant at -56,5°C.

FL380 at ISA + 5° means -56,5+5=-51,5°C

Headwind means that groundspeed will be lower than TAS, so TAS will be 453+58=511kts.

You have what you need. Remember to convert °C in K before using the temperature in the LSS formula.

[MightyBoo]

Thank you guys.