CAS to EAS
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The compression of the air caused by rapid passage though it causes a rise in local density. The density is raised by a factor which is a function of the Mach No. The formula is a series expansion which takes the following form:
Compressibility = ( 1 + M squared/4 + M to the fourth/40...)
That's usually enough terms. M is Mach No in the above formula.
Thus at M 0.5 the density increase is approximately 6% and when M = 1.0,the increase is about 28%. Above Mach 1, the formula breaks down.
This does not lend itself to any kind of easy mathematical breakdown, so the correction is usually applied by tables or by the use of a compressibility correction window on a pilots' nav computer such as the CRP-5.
Compressibility = ( 1 + M squared/4 + M to the fourth/40...)
That's usually enough terms. M is Mach No in the above formula.
Thus at M 0.5 the density increase is approximately 6% and when M = 1.0,the increase is about 28%. Above Mach 1, the formula breaks down.
This does not lend itself to any kind of easy mathematical breakdown, so the correction is usually applied by tables or by the use of a compressibility correction window on a pilots' nav computer such as the CRP-5.
I'm bigoted @rsehole. Ignore me.
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In conclusion of my findings I should first like to thank oxford blue for his post.
I should like to quote from The Standard Handbook for Aeronautical and Astronautical Engineers (McGraw-Hill 2002, ISBN 0071362290, Mark Davies [editor]) which I have found most resourceful.
"The EAS is the equivalent airspeed which the airplane would have at sea level (air density rho0) if it developed the same 'dynamic pressure' as it does at its TAS at the altitude concerned (air density rho.)
Thus, q = 1/2 rho0 V^2 = 1/2 rho V^2
Thus, Ve = rt[(rho/rho0)V] = rt(sigma V)
Eas is a very useful parameter for engineer analysis. However for flight operations reference is made to CAS.
CAS (Vc)
The Calibrated Airspeed - rarely referred to as Rectified Airspeed - is the airspeed reading on a Calibrated Airspeed indicator corrected to a Pitot Static system, that is assumed to be entirely free of error. It is common practice in aircraft operations to write KCAS (knots CAS.) A better representation of the reading of an airspeed indicator than that given above is provided by:
(pt/p) <compressible> = (1+ (y-1/2)M^2)^y/(y-1)
reference 10.68
which applies to compressible flow.
As the Pitot Static system provides a measurement of (Pt - P) this term will be isolated on the left-hand side of the equation, and noting that y = 1.4 and M = V/a the equation becomes:
(Pt - P) = p{[1+ 0.2(V/a)^2]^3.5 -1}
reference 10.69
The compressibility correction factor is negligibly small for operations below about 10,000 ft and 200 kts Vc.
A useful equation for converting Vc to Mach number, accouinting for compressibility correction is:
M = rt( 5 { [ 1/d { [ 1 + 0.2 (Vc/a0)^2]^3.5 -1 } +1 ]^1/3.5 -1 }
reference 10.72 (page.. 10.122)
Vc = Ve + DVc
| DVc | given by:
DVc = a0{ rt( 5 { [ d { [ 1+ 0.2M^2 ]^3.5 -1 } +1 ]^1/3.5 -1}) -M rt(d)}
end quote.
Further information can be obtained from AFFTC-TIH-99-01, Aircraft Performance Flight Testing, Edwards AFB. Available from http://www.jeminas.com/aviation/pdf/...ht_Testing.pdf
I hope this may serve to answer any future queries regarding this flavour of airspeed.
I should like to quote from The Standard Handbook for Aeronautical and Astronautical Engineers (McGraw-Hill 2002, ISBN 0071362290, Mark Davies [editor]) which I have found most resourceful.
"The EAS is the equivalent airspeed which the airplane would have at sea level (air density rho0) if it developed the same 'dynamic pressure' as it does at its TAS at the altitude concerned (air density rho.)
Thus, q = 1/2 rho0 V^2 = 1/2 rho V^2
Thus, Ve = rt[(rho/rho0)V] = rt(sigma V)
Eas is a very useful parameter for engineer analysis. However for flight operations reference is made to CAS.
CAS (Vc)
The Calibrated Airspeed - rarely referred to as Rectified Airspeed - is the airspeed reading on a Calibrated Airspeed indicator corrected to a Pitot Static system, that is assumed to be entirely free of error. It is common practice in aircraft operations to write KCAS (knots CAS.) A better representation of the reading of an airspeed indicator than that given above is provided by:
(pt/p) <compressible> = (1+ (y-1/2)M^2)^y/(y-1)
reference 10.68
which applies to compressible flow.
As the Pitot Static system provides a measurement of (Pt - P) this term will be isolated on the left-hand side of the equation, and noting that y = 1.4 and M = V/a the equation becomes:
(Pt - P) = p{[1+ 0.2(V/a)^2]^3.5 -1}
reference 10.69
The compressibility correction factor is negligibly small for operations below about 10,000 ft and 200 kts Vc.
A useful equation for converting Vc to Mach number, accouinting for compressibility correction is:
M = rt( 5 { [ 1/d { [ 1 + 0.2 (Vc/a0)^2]^3.5 -1 } +1 ]^1/3.5 -1 }
reference 10.72 (page.. 10.122)
Vc = Ve + DVc
| DVc | given by:
DVc = a0{ rt( 5 { [ d { [ 1+ 0.2M^2 ]^3.5 -1 } +1 ]^1/3.5 -1}) -M rt(d)}
end quote.
Further information can be obtained from AFFTC-TIH-99-01, Aircraft Performance Flight Testing, Edwards AFB. Available from http://www.jeminas.com/aviation/pdf/...ht_Testing.pdf
I hope this may serve to answer any future queries regarding this flavour of airspeed.
