8th Jul 2012, 16:26   #13 (permalink)
Pugilistic Animus

Join Date: Dec 2006
Location: The No Trangression Zone
Posts: 1,741
Quote:
 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...

Quote:
 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

Last edited by Pugilistic Animus; 8th Jul 2012 at 16:43.