The Machmeter has no inputs of TAS or LSS. To do so it would need to be a computer.
The Machmeter is a pressure instrument which is basically an ASI with an altimeter capsule added.
It measures the ratio of dynamic to static pressure.
yes that is true the inputs are Ps-q but q for compressible flow is a comp-lex function the paramters p and q have to be converted to a mach number the function for mach number can be wirtten entirely in terms of those paramterss Ps and q. in the classical Machmeter [stem gusge] the computations are made by the cam gearing form the bellows....
that being said I made an error in the above very cumbersome functions
I'll rewrite it here:
(Ps -q) =CAS
Ps-q= Ps-([dp/dv]) = ...CAS corrected for compressibilty=EAS or
EAS corrected for altitude density ratio 'sigma' =TAS this is what I forgot above
the speed of sound 'a' written as a pressure function =a =
[1/rho^2* [dp/dv]s}^1/2
Ps-([dp/dv])*sigma=TAS or 'V' Mach =V/a
V/a =
Ps-([dp/dv])*sigma/[1/rho^2* [dp/dv]s}^1/2=M=SQR (5 X (Qc/Ps + 1)^((Y-1)/Y) - 1) ...this is from Old Smokey... gamma's come from adiabatic gas laws, but it still has to be solved...but the two will eventually lead to one another
he other major error I made was putting in a0...I don't know why I did that...
so in the above I incorrectly included the ratio a0/a it does not belong...and I forgot to multiply EAS by the altitude density ratio...I put the corrections above...
From Old Smokey
Before I'm accused of over-simplification, take a look at the formulae by which the Airspeed Indicator and the Machmeter are calibrated -
Vc = SQR((Y/(Y-1)) X Po/Qc X ((Qc/Po + 1)^((Y-1)/Y) - 1) X SQR (2 X Qc/Rho0)
M = SQR (5 X (Qc/Ps + 1)^((Y-1)/Y) - 1)
(NOTE - For flight at altitude, substitute Ps for Po in the Vc formula).
Where -
Vc = Calibrated Air Speed, ft/sec
M = Mach Number
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant volume = 1.4
Po = Sea Level Air Pressure
Ps = Static Pressure
Qc = Impact Pressure
Rho0 = Standard Sea level air density
Before I'm accused of over-simplification, take a look at the formulae by which the Airspeed Indicator and the Machmeter are calibrated -
Vc = SQR((Y/(Y-1)) X Po/Qc X ((Qc/Po + 1)^((Y-1)/Y) - 1) X SQR (2 X Qc/Rho0)
M = SQR (5 X (Qc/Ps + 1)^((Y-1)/Y) - 1)
(NOTE - For flight at altitude, substitute Ps for Po in the Vc formula).
Where -
Vc = Calibrated Air Speed, ft/sec
M = Mach Number
Y = A constant, being the ratio of specific heat of air at constant pressure to the specific heat of air at constant volume = 1.4
Po = Sea Level Air Pressure
Ps = Static Pressure
Qc = Impact Pressure
Rho0 = Standard Sea level air density