Marcel_MPH,
DYNAMIC PRESSURE
I’m not sure of the approach that you’re taking here, but my first thought is that you’re relating the dynamic pressure associated with a given Calibrated Airspeed (CAS). CAS is, of course, the pilot’s practical source of Dynamic Pressure information, as the vital performance characteristics of the aircraft, such as Lift and Drag, depend upon Dynamic Pressure. Pressure may be measured in any number of terms, Pounds per Square Inch, Hectopascals, you name it. The CAS appropriate to a particular dynamic pressure is valid at Sea Level ISA conditions, and the Airspeed Indicator is calibrated for this. The problem is that Dynamic Pressure alone cannot be measured from a Pitot tube, as Impact Pressure is measured instead, the difference being the compression of the air due to Mach Number as Air is compressible.
The simplistic approach for low and slow flight is that air is incompressible. The older airspeed indicators were calibrated for incompressible flow, and used the formula –
V = SQR (2 Q / Rho)
Where Q = Dynamic Pressure, Rho = Air Density, and V = True Airspeed.
Unfortunately for this simplistic formula, compressibility plays an increasingly greater error as speed and altitude are increased, and as Impact Pressure, not Dynamic Pressure is sensed by the Airspeed Indicator, correction for compressibility must be made to yield Dynamic Pressure – the ‘f’ factor.
The calibration formula is as follows –
Vc = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1]) * SQR (2 Qc / Rho0)
Where –
Vc = Calibrated Airspeed in ft/sec,
Qc = Impact Pressure in Lb/ft^2,
Rho0 = Sea Level Air Density = .0023769 slugs/ft^3,
Po = Sea Level Air Pressure = 2116.2 Lb/ft^2,
Y = A constant for air = 1.4, being the ratio of the Specific Heat of Air at constant pressure to that at constant volume (Y = Gamma, I don’t have a Greek key-board)
The Left-most portion of the equation is the ‘f’ factor –
F = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1])
At altitude, the Static Pressure,
P, is substituted for
Po in the equation.
I’ll leave it to you to convert the various units of measurement to your own requirements.
PS : I don’t care if the U.S. Navy thinks that Sea Level Air Density = .002378 slugs/ft^3, if Douglas thought that it was 0.0023769 slugs/ft^3, that’s good enough for me.
Regards,
Old Smokey