Bf109 - Measurement of Air Speed (Fahrt)

[Varrattu]

*** Edited by Varrattu; Nov-13-2023 ***
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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...


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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. Why attempt? 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 warbird:

[[http://kurfurst.org/Performance_test...2_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 pressureAltitude = bf109f.getParameter(part.ParameterTypes.Z_Altitude MSL, -1);
The following conditions will be assumed:
Static Air Pressure to be 1013.25 hPa at MSL;
Air Density to be 1.225 kg/m³ at MSL;

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
Assumption: Static Pressure matches standard atmospheric conditions where p0 = 1013.25 hPa at MSL.
Assumption: Air Density matches standard atmospheric conditions where r0 = 1.225 kg/m³ at MSL.

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
Ambient Air Temperature: ~258 Kelvin (-15°Celsius).
True Airspeed: ~586 km/h,
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 Meter Pressure Altitude [1] and 245 Kelvin ambient air temperature [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

In which q is usually known as the incompressible dynamic pressure,
r is the air density at current flight level,
and V is the Indicated or Equivalent airspeed, defined as the speed at sea level, under ISA conditions, that would produce the same incompressible dynamic pressure that is produced at the true airspeed for a given aircraft altitude. 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.

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 5360 (5000+360) 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 4360 (4000+360) metres.

So, 'Bruhn-Werke GmbH' calibrated the Speed Indicator Fl.22231 to Density Altitude + 360 metres.

The Patch v5.036 autumn map tests with the Bf109F 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 4970 meters ( Density Altitude [2] + 360m ) 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 4970m 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 ~0.7386 kg³ @4970m! 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 'BRUHN' Airspeed Indicator fits to the real world atmosphere...

The latest official 1C:Maddox version of 'Cliffs of Dover' v1.11.20362 meets the relation "q = 0.5 * r * V²".


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

[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...