novicef
4th Jan 2013, 01:57
Could somebody please explain why when cruising at a constant Mach No.
you get a change in Mach No. when there is a change in temperature or wind speed. How does the FMC resolve this?
There is nothing in the FMC manuals to explain this.
Thanks
novicef
737Jock
4th Jan 2013, 08:06
Temperature:
M = TAS / a (local speed of sound)
The local speed of sound varies only with temperature. Warmer temperature is higher speed of sound, lower temperature is lower speed of sound.
Thus when the temperature changes, your true airspeed will be divided by a different local speed of sound. Thus the mach number change with constant TAS.
If TAS is constant an increase in a, indicating an increase in temperature, will lead to a decrease in M (dividing by a bigger number) and vice versa.
Wind:
As seen only temperature changes the Mach number at constant mach. So if the temperature is constant what you are looking at is most likely a change in TAS.
The following is general fmgs behaviour, when flying cost index:
Basicly when you encounter tailwind the FMGS will want to profit as long as possible from this tailwind to reduce fuel burn, thus TAS/CAS is lower then in no wind conditions.
With headwind the FMGS will want to get out of this wind asap in order not to have to spent long amounts of time in the headwind, thus TAS/CAS is higher then in no wind condition.
If we look again at the Mach formula M = TAS/a, we see that a is constant. So if TAS increases and we divide by an equal local speed of sound a, the natural consequence is that M increases. And of course vice versa.
Personally I don't see Mach increase when I select a fixed mach number, what I see is a change in TAS.
Just look at the formula and keep Mach constant:
If M is constant and TAS becomes greater then, a must become greater as well. Divide a bigger number by a bigger number to get the same outcome.
If M is comstant and a becomes greater then, Tas mist become greater as well.
The important thing to remember is that Mach only changes with local speed of sound which is completely dependent on temperature!