Bf109 - Measurement of Air Speed (Fahrt)

[Varrattu]

2023-Dec-17, meanwhile 1C Entertainment and Team Fusion have published 'Cliffs Of Dover - Blitz' v5.040 and we are flying in a 24-7-365 virtual atmosphere that, at first glance comes very close to the German 'Normalatmosphäre nach DIN 5450' of 1937 [ref.1]. And what we have known as the International Standard Atmosphere for nearly 50 years [ref.2]. All in all, that's quite good for carrying out a few more airspeed tests ...

The 'Cliffs Of Dover - Blitz' v5.040 atmosphere
If something that I'm writing is not clear, please leave a comment, and I'll do my best to make it clearer.

The sea-level quantities of pressure, temperature, density, and the acceleration of gravity for Team Fusion -Blitz- atmosphere v5.040 are assumed as follows:

Air temperature for dry air................ Tsl = 273,15+15 = 288,15° Kelvin exact
Acceleration of gravity........................ g = 9,80665 m/s exact

Air pressure for dry air..................... Psl = { 287.053 * 1.2250 * 288.15 } = 101325 [ Pa ] exact
Air density for dry air....................... Dsl = { 101325 : ( 287.053 * 288.15) } = 1.2250 [ kg/m³ ]. exact

In case of air, using the perfect gas law and the above sea-level conditions, we have that the specific gas constant for dry air is
.................... Rair = { 101325 : (1,225*288,15) } = 287.053 [JkgK].

Temperature gradient or lapse rate, assumed to be -0,0065 [ °K] = -0,0065 [ °C] per geopotential meter from sea level up to at least 8500 geopotential meters.

For mission builders, the v5.040 atmosphere temperature profile, given as a quantity in degrees Kelvin, can be used to establish a relationship between pressure, temperature, density, and the acceleration of gravity via the hydrostatic equation and the ideal gas law. Assuming the air is modeled as a dry, perfect gas that obeys the laws of Charles and Boyle:

air density Dh = { Ph : (Rair * Th) } = Dsl * { (Tsl * Ph) : (Psl * Th) }

This equation formes the basis for numerous flight simulations, also for 1C-Maddox 'Cliffs Of Dover' v11.20362 …

The altitude is given as a function of geometric altitude (Z,m) by

getParameter(part.ParameterTypes.Z_Altitude MSL, int subtype)

where subtype <-1> returns the geometric altitude (Z,m) above sea level in meters.

Here, we must make a distinction between the FMB geometric altitude (Z, m), which represents the actual 'tape measure metric' altitude above sea level, and the geopotential altitude (H, m), which is a pressure altitude consistent with the assumption of a constant value of gravity (g=9.80665) [ref.2], [ref.3], [ref.4].

Relation between geometric altitude Z,m and geopotential altitude H,m is

H,m = ( Z,m * 6356766 ) : ( Z,m + 6356766 ),

where 6356766 is the nominal radius of the earth.

The 'Cliffs Of Dover - Blitz' v5.040 flight test
If something that I'm writing is not clear, please leave a comment, and I'll do my best to make it clearer.

I will continue to use the Bf109F-1 because there are reliable documents available regarding the performance and airspeeds of the warbird [ref.5] [ref.6]. To compare the 'TeamFusion-Bf109F' against authentic values [ref.5] following FMB script values are required:

double geometricAlt = bf109f.getParameter(part.ParameterTypes.Z_Altitude MSL, -1);
where <geometricAlt> reveales the geometric altitude as quantity in meters above sea level.

double indicatedAirspeed = bf109f.getParameter(part.ParameterTypes.I_Velocity IAS, -1),
where <indicatedAirspeed> reveales IAS as quantity in kilometers per hour (km/h),

double trueAirspeed = bf109f.getParameter(part.ParameterTypes.Z_Velocity TAS, -1),
where <trueAirspeed> reveales TAS as quantity in meters per second (m/s).

double outerAirTemp = bf109f.getParameter(part.ParameterTypes.Z_AmbientA irTemperature, -1),
where <outerAirTemp> reveales OAT as quantity in degrees Kelvin.

The Patch v5.040 summer map tests with the Bf109F at 5004m geometric altitude above the Channel revealed the following quantities.

Geometric Altitude...................... Z,m = 5004.14 [m]
Ambient Air Temperature........ T @ Z,m = 255,544 [°K]
Indicated Airspeed............. IAS @ Z,m = 441,1 [km/h]
True Airspeed..................... TAS @ Z,m = 570,0 [km/h]

Before doing any more calculations, it's absolutely crucial to convert geometric altitude into geopotential altitude. The corresponding value of geopotential altitude, Hm, is 5000.2 km, less than 0.1 percent difference. What is important, however, is that when we use any equation assuming a constant value of gravity (g)=9.80665), we must use the geopotential altitude [ref.2], [ref.3], [ref.4]:

H,m = ( Z,m * 6356766 ) : ( Z,m + 6356766 ),
H,m = ( 5004.14 * 6356766 ) : ( 5004.14 + 6356766 ),
H,m = 5000.2 [m]

Consequently, for the current test we are calculating the properties for the pressure altitude of 5000.2 m.
Once pressure altitude has been determined, the density altitude is calculated using outside air temperature. Density altitude is formally defined as the “pressure altitude corrected for nonstandard temperature variations.”

Ambient Air Temperature.......T = 255.544 [°K]
Static pressure....................P = 54018 [Pa]
Air density..........................D = 0.7364 [ kg/m³ ] = { 54018 : ( 255.544 * 287.053 ) }
Density altitude.............. ...DA = 4996 meters

4996 meters density altitude is the altitude at which the Bf109F "feels" it is flying with 570 km/h true airspeed.

Well, in a WWII single seat fighter the dynamic or impact pressure is the only directly measurable quantity that relates to the aircraft's speed with respect to the air. The Bf109F was equipped with the Bruhn Fl.22231 (60-750kmh) airspeed indicator [ref.6]. The airspeed indicator depends on the Fl.22261 Pitot-Static tube for its operation. The pressure generated by the Pitot tube for airspeed at current altitude is calibrated based on the relationship: dynamic pressure q = 0.5 * D * V².

Doubtful that any WWII pilot has ever flown under so-called standard conditions. So, German WWII airspeed tables were corrected for certain air pressure conditions in the battle area they were used. Consequently, airspeed tables show readings that are safe for piloting. The performance table [ref.5], for example, shows airspeeds corrected for density altitudes DA+354 metres. Where density altitude (DA) is equall to pressure altitude.

Fl.22231 pressure q = 0.5 * D(4996+354) * V²

Different reference frames can lead to different observations of the same event. So, if I apply a 'calibration range' (German: Eichraum) as per [ref.5] for the airspeed test at approximately 5000 metres pressure altitude above the Strait of Dover (TF v5.040), the following relations would result.

Geometric Altitude....................... Z,m = 5004 [m]
Geoptential Altitude..................... H,m = 5000 [m]
Ambient Air Temperature........ T @ H,m = 255,544 [°K]
Density Altitude........................... DA = 4996 [m]
Indicated Airspeed............. IAS @ H,m = 433,5 [km/h]
True Airspeed................... TAS @ H,m = 570,0 [km/h]

It is obvious that the altitude relation of the airspeed indicator 433:570 km/h (IAS:TAS) according to [ref.5] is not suitable for the operating area around the English Channel. I suspect that the airspeed indicator has been adjusted for areas of operation in North Africa. Commonly used values applied to 'calibration ranges' (German: Eichraum) for 25°, and 30° degrees Celsius at sea level.

On the other hand, 441:570 km/h (IAS:TAS) calculated by Team Fusion correspond approximately to Standard Atmosphere Conditions.

To be continued.

References:
[1] Normalatmosphäre nach DIN 5450 (1937)
[2] 1976 International Standard Atmosphere (PDF)
[3] 1962 Manual of the US Standard Atmosphere (PDF)
[4] 1940 Terrestrische Navigation (Ringbuch der Luftfahrttechnik (p.361-p371)
[5] Kennblatt für das Flugzeugmuster Bf109, Baureihe F1 und F2 mit DB601N, Berlin 1941
[6] Fl.22231 - Bf109F ErsatzteilListe 04.1941 (JPG)
[7] NACA Reference Publication 1046 - Measurement Of Speed And Altitude, Chapter III (p.25)
[8] Standard Atmosphere Calculator
[9] Airspeed Conversions (CAS/EAS/TAS/Mach)

Edit 2024-05-30:
Fl.22231 pressure q = 0.5 * D(h,m+360) * V²
corrected for
Fl.22231 pressure q = 0.5 * D(h,m+354) * V²