KayPam,
And, if you compute EAS/CAS, you will find 0.94.
There is a similar question reported
here and, as noted by numerous responses immediately above, the factor is completely irrelevant to the question, and the answer marked correct above is clearly wrong. Nevertheless, the figure is equivalent to the quotient of two compressibility factors
f/
f_0 using equations 11, 16, and 20, in
NACA Report 837 (Aiken, W., 1946). The ratio depends only on pressure altitude and Mach number and is therefore independent of temperature deviation.
Mach number is measured from (Pt-Ps)/Ps.
So, say you don't have any device to correct your machmeter for compressibility (which is a problem in itself.. but let's assume that).
The machmeter will overread, due to compressibility.
There is no Mach number in an incompressible flow because the speed of sound is infinite. Neither Mach meters nor airspeed indicators need to be "corrected for compressibility" so it does not necessarily follow that determining Mach number by a quantity such as `
(Pt - Ps) / Ps` will result in an error. The Mach number can be related to the normalised pressure rise `
(Pt - Ps) / Ps` using a simple algebraic expression without needing to adopt an incompressible flow assumption. The applicable technical standard for Mach meters (
SAE AS8018 citing
NASA Technical Note D-822) assumes an isentropic flow in relating pressure rise to Mach number. The same is true for airspeed indicators, although in their case the impact pressure
q_c–the pressure rise–is normalised by standard sea-level pressure. Impact pressure (for M ≤ 1) is related to Mach number by:
M^2 = 5*(-1+(1+q_c/p)^(2/7)),
and to true airspeed v by:
v^2 = 7*(p/rho)*(-1+(1+q_c/p)^(2/7)), rho is ambient air density.
Because these equations are based on an isentropic model they account for variation in density as air is brought to rest in a pitot probe. The latter was first given in this form by Saint-Venant and Wantzel in
Journal de l'École polytechnique, vol 16, 1839 (according to Stanton [
link]).
In an incompressible flow the relationship for true airspeed squared is simply,
v^2 = 2*q/rho,
and
q is dynamic pressure which is the difference between total and static pressures in an incompressible flow. This incompressible flow model is not used by Mach meters or airspeed indicators. Dynamic pressure may be thought of as a first order approximation of impact pressure - see for example the paragraph following eqn 2, and particularly figure 2, in
NACA Report 247 (Zahm, A., 1926). The inverse relationships for impact and dynamic pressures are,
Isentropic flow: q_c = p*(-1+(1+(1/7)*(rho/p)*v^2)^(7/2)), and,
Incompressible flow: q = (1/2)*rho*v^2.
The Maclaurin expansion of p*(-1+(1+(1/7)*(rho/p)*v^2)^(7/2)) about v^2 = 0 is (1/2)*rho*v^2 which is the Euler-Bernoulli solution to Euler's equation for an incompressible flow.
The first use of a compressibility factor, of which I'm aware, in a circular slide rule for obtaining TAS from CAS, as in eqn 9 in NASA Technical Note D-822 or eqn 20 in NACA Report 837, is described in Ezra Kotcher's (of Bell X-1 fame) US patent
2342674 of 29th Feb 1944 for an Air Speed Computer. For on the influence of errors see
NACA Technical Note 1605 (Huston, W., 1948),
Accuracy of Airspeed Measurements and Flight Calibration Procedures.