Bf109 - Measurement of Air Speed (Fahrt)

[Varrattu]

On 4th of May 2023, Team Fusion introduced Update - Patch v5.036.

Along with Patch v5.036, the Team Fusion ambient standard temperatures should have been updated to more realistic atmospheric values. Temperature should vary according to the time of day. For me, this idea is one of the most important steps since the first release of Team Fusion's standard atmosphere. Unfortunately, Team Fusion had to roll back the update to pre-5.036 versions.

Nevertheless, there was enough time for a few tests before the rollback. The tests under v5.036 atmospheric conditions give me reason to urgently request a thorough examination of the Team Fusion atmospheric model and a comparison of airspeed relationships against the former original Team Maddox model. I'm trying to keep my findings, conclusions, suggestions as brief as possible...

I'm going to use the Bf109F as an example because there is a reliable open-source document available about the performance and airspeeds of the real warbird:

http://kurfurst.org/Performance_test...1F2_DB601N.PDF

To compare the authentic values against 'TeamFusion-Bf109F' following values are required:

double indicatedAirspeed = bf109f.getParameter(part.ParameterTypes.I_Velocity IAS, -1);
double trueAirspeed = bf109f.getParameter(part.ParameterTypes.Z_Velocity TAS, -1);
double ambientAirTemperature = bf109f.getParameter(part.ParameterTypes.Z_AmbientA irTemperature, -1);
double geometricAltitude = bf109f.getParameter(part.ParameterTypes.Z_Altitude MSL, -1);

The Patch v5.036 autumn map tests with the Bf109F at approximately 5000m above the Channel revealed the following data.

[1]
Pressure Altitude: 4999.1 metres ~ 5000 metres AMSL
Ambient Air Temperature: 245 Kelvin (-28° Celsius)
True Airspeed: 586.4 km/h ~ 586 km/h
Indicated Airspeed: 459.6 km/h ~ 460 km/h

For comparison, the Pressure Altitude needs to be converted to standard atmospheric conditions [2]. In a sense, it's the altitude at which the Bf109F "feels" it is flying. I'm only going to mention the results here. The methods and formulas are fully described on the internet.

[2]
Density Altitude: ~4610 meters
True Airspeed: ~586 km/h,
Air Temperature at MSL t0 = 288.15°Kelvin = 15°Celsius.
Static Pressure at MSL p0 = 1013.25 hPa at MSL.
Air Density at MSL r0 = 1.225 kg/³ at MSL.

Concerning True Airspeed:
586 km/h max. at 5000 metres ISA Pressure Altitude [1] are possible.

Concerning Indicated Airspeed:
As far as I know, all real German warbirds playable in 'iL2CoD' were equipped with the Bruhn Fl.22231 (60-750kmh) airspeed indicator. The airspeed indicator depends on the Pitot tube Fl.22261 for its operation. The pressure generated by the Fl.22261 for airspeed and altitude is calibrated based on the relationship:

dynamic pressure q = 0.5 * r * V² = 0.5 * r * TAS²

In which q is usually known as the incompressible dynamic pressure,
r is the air density at current flight level,
and V is the True Airspeed at flight level, that would produce the same incompressible dynamic pressure that is produced at ISA sea level conditions

dynamic pressure q = 0,5 * 1,225 * V² = 0,5 * 1,225 * EAS²

Nearly all airspeed indicators that have been used on German warbirds during WWII function this way. It is this definition that makes IAS a useful airspeed measurement without the need to correct for altitude or temperature. Please note: Only under standardized conditions the Indicated Airspeed (IAS) is equal to Equivalent Airspeed (EAS).

So, 460 km/h True Airspeed [1] at Mean Sea Level produces the same incompressible dynamic pressure q(h,TAS) as 586 km/h True Airspeed [1] at 4770 metres. In fact, based on the relationship <q=0.5*r*V²>, the indicated speed depends on a Density Altitude of 4610 metres [2] plus 160 metres = 4770 metres...

From the document 'Flugleistungen, Blatt No.6" (see above mentioned link) we learn that, computed for standard atmospheric conditions the Team Fusion Bf109F should perform as follows.

Pressure Altitude: 5000 Meter above MSL
True Airspeed: ~592 km/h
Indicated Airspeed: ~450km/h

Where 450 km/h Indicated Airspeed at Mean Sea Level produce the same incompressible dynamic pressure q(h,TAS) as ~592 km/h True Airspeed at 5354 (5000+354) metres.

And at
Pressure Altitude: 4000 Meter above MSL
True Airspeed: ~573 km/h
Indicated Airspeed: ~459km/h

Where ~459 km/h Indicated Airspeed at Mean Sea Level produce the same incompressible dynamic pressure q(h,TAS) as ~573 km/h True Airspeed at 4354 (4000+354) metres.

So, 'Bruhn-Werke GmbH' calibrated the Speed Indicator Fl.22231 to Density Altitude +~ 354 metres. I suspect that this indicator had been adjusted for areas of operation in North Africa.Flying through Patch v5.036 autumn map atmosphere with that indicator at approximately 5000m above the Channel should reveal the following data:

[3]
Pressure Altitude: ~5000 metres AMSL
Ambient Air Temperature: ~245 Kelvin (-28° Celsius)
True Airspeed: ~586 km/h
Indicated Airspeed: ~455 km/h

586 km/h True Airspeed at 4964 meters ( Density Altitude [2] + 354m ) altitude produce the same incompressible dynamic pressure q(h,TAS) as 455 km/h True Airspeed at Mean Sea Level. Under standard atmosphere condition, at Mean Sea Level Indicated Airspeed is equal True Airspeed. Please note that the 4964m is not the altitude at which the Bf109F "feels" it is flying.

Conclusion:
When considering the described calibration/correction of the Bf109 air speed indicator accidently as pressure altitude, one might assume that the air density corresponds to ~0,7361 kg³ @5000m or ~0.7390 kg³ @4964m! However, that would be a misinterpretation. The air density actually corresponds to the calculated "density altitude" of ~0.7677 kg/m³ @4610m under standard atmosperic condition where density ~1.225 kg/m³ @0m. The air density is thus actually higher than one would initially assume. It's the atmospheric condition at which the Bf109F "feels" it is flying.

The higher the altitude or speed, the clearer it becomes how ingenious the 'Flugleistungen, Blatt No.6' (see above mentioned link) fits to the real world atmosphere ...
... under North African conditions. For pilots operating above the English Channel, the airspeed indicator correction according to 'Flugleistungen, Blatt No.6' is not suitable.


Kind regards

Varrattu

References:
Kennblatt für das Flugzeugmuster Bf109, Baureihe F1 und F2 mit DB601N, Berlin 1941
Fluglehre, 5.Auflage, Mises (1936)
Fahrtmessung, Prof.Dr.KOPPE (1940)
Normalatmosphäre nach DIN 5450 (1937), Artillerie und Ballistik, Springer Verlag 1939
Beschreibung für FUESS Hoehenmesser 7a,b,c
NACA Report No.110 - The Altitude Effect On Air Speed Indicators, Part I
NACA Report No.156 - The Altitude Effect On Air Speed Indicators, Part II
NACA Report No.420 - Aircraft Speed Instruments
NACA Technical Note No.99 - Notes On The Standard Atmosphere
NACA Technical Note No.616 - Measurement Of Air Speed
NACA Reference Publication 1046 - Measurement Of Speed And Altitude


Edit 2024-09-09:
Fl.22231 pressure q = 0.5 * D(h,m+360) * V²
corrected for
Fl.22231 pressure q = 0.5 * D(h,m+354) * V²

[Varrattu]

In my first post, I made a little oversight there. I mistakenly referred to the return value of the field <Parameter(part.ParameterTypes.Z_AltitudeMSL> as "Pressure Altitude." As a matter of fact, the quantity of geometric altitude (Z) is given to facilitate the computation of, for example, distance between or height of objects.

So, the value (Z)=5000m needs to be translated into the corresponding geopotential altitude (H)=4996m.

The good news: this doesn't significantly alter the result of my calculation example...

[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 geometric altitude (Z,m) as a function of metric length 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, all German WWII airspeed indicators were corrected for certain air pressure conditions in the battle area they were used. Consequently, airspeed indicators show readings that are safer for piloting. The performance table [ref.5], for example, shows airspeeds corrected for density altitudes DA+354 metres.

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 correction 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 calibration space was 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) correspond approximately to the atmosphere being designed by Team Fusion.

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

[Varrattu]

Intentionally left blank.