Spitfire Mk IIa performance tests - Patch 1.07.18301

[klem]

Originally Posted by bongodriver

Why dont you guys set altimeter to 1013? this is what will give you standard pressure altitude which is what most charted data is based on, theres not much need to actualy test at sea level, simply start the testing at 1000ft and the data can be projected for the last 1000ft to sea level.

Manstons surveyed elevation was 150ft during wartime and tides are never factored, an elevation is based on mean sea level i.e. the average of all tide heights.

are you guys using the density altitude conversion for the tests?

Because the CoD environment doesn't seem to be set to 1013. In any case the True Airspeeds are calculated in the script using IAS, Altitude and the CoD environment data (apparent pressures and temperatures) including Density Altitude:

//calculate TrueAirspeeds and MACH
//Pressure Altitude P_alt=Ind_Alt+145442.2*(1- (alt_set/1013.25)^0.190261)
Pressure_Alt = I_Altitude+145442.2*(1- Math.Pow((C_AltimeterPinion/1013.25),0.190261));
//Density altitude (D_Alt) = P_Alt +(StdTemp0/.0019812)*(1-(StdTemp0/OAT)^0.2349690) ; = P_Alt +(273.15/.0019812)*(1-(273.15/OAT)^0.2349690)
Density_Alt = Pressure_Alt + 137870.9872804361 * (1 - Math.Pow((273.15 / Z_AmbientAirTemperature),0.2349690));
//TrueAirspeed_mph = CS/(1-6.8755856*10^-6 * ''DA'')^2.12794 (NB assume IAS = CS)
TrueAirspeed_mph = I_VelocityIAS / Math.Pow((1 - 6.8755856 * Math.Pow(10, -6) * Density_Alt), 2.12794);
TrueAirspeed_kph = TrueAirspeed_mph / 0.621371192;
TrueAirspeed_kt = TrueAirspeed_mph / 0.868976242;
//Mach Number (M) = TAS/CS; CS = sound speed= 38.967854*sqrt(T+273.15) where T is the OAT in celsius; TAS is true airspeed in knots.
MACH = TrueAirspeed_kt / (38.967854 * Math.Sqrt(Z_AmbientAirTemperature + 273.15));

There is no CoD C# parameter for Pressure to set the Altimeter by so I have to measure it and/or set it by reference to True Height. I am assuming 'True Height' is from Mean Sea Level. Can't think what else it would be. I set the Altimeter to read as near as possible to True Height when on the runway so I won't hit the sea on low level tests and I'll have near-correct Altitude reading on he Altimeter. Having said that, at a setting of 992mb its about 4 feet out at sea level but its about 2,000 feet out at 20,000 ft. something wrong somewhere. I don't thionk it matters at the moment as he performance is so far off but I'll include some mB vs Altitude error checks after the next patch.

EDIT: Did some tests.
Max Alt setting available is 1045mB. At True Height 20,000 ft, Alt reading ~19,900. Closest I could get.
Alt setting 1045mB at TH 15,000ft, Alt reading ~15,500. Alt setting for correct TH reading 1027mB
Alt setting 1027mB at TH 10,000ft, Alt reading ~10,500. Alt setting for correct TH reading 1007mB
Alt setting 1007mB at TH 5,000ft, Alt reading ~5,800. Alt setting for correct TH reading 998mB

Am I missing something?

[Crumpp]

At 992mb at 19C, the density altitude at sea level is 1194 feet.

If the atmosphere is correct, then standing at sea level is the same as being at 1200 feet altitude on a standard day to the airplane.

Your altimeter is just a barometer and measures pressure. It will only show some 554 feet!!!

All the altimeter sees is pressure while the aircraft sees density. Test flying is done at pressure altitude and performance calculated according to density altitude.

Set the ALTIMETER to 29.92inHg or 1013Mb. That is your altitude for starting your performance calculations.

[klem]

Originally Posted by Crumpp

At 992mb at 19C, the density altitude at sea level is 1194 feet.

If the atmosphere is correct, then standing at sea level is the same as being at 1200 feet altitude on a standard day to the airplane.

Your altimeter is just a barometer and measures pressure. It will only show some 554 feet!!!

All the altimeter sees is pressure while the aircraft sees density. Test flying is done at pressure altitude and performance calculated according to density altitude.

Set the ALTIMETER to 29.92inHg or 1013Mb. That is your altitude for starting your performance calculations.

Well that would skip the first calculation of Pressure Altitude from indicated altitude and altimeter setting and I might try that but I don't see how that would change the resulting TAS.

I'm not a test pilot, I'm just doing the Maths and it took me a while to get my head around how to do these tests. I did it that way so I could fly at/very near sea level on the altimeter although as bongodriver says I could just project the 0ft value.

I'm not sure what your trying to say other than to collect the readings in a different way that skips one calculation step.

Do you think my results will be incorrect for some reason? See above fornulae drawn from
http://williams.best.vwh.net/avform.htm#Mach
and my Hurricane results
http://forum.1cpublishing.eu/showthread.php?t=33135

[ACE-OF-ACES]

Originally Posted by klem

Am I missing something?

I think so.. In that I found and error in your Density Altitude calculation

See the following REVIEW of your Java code.

Before we do that, I took the liberty of re-wording the formulas you used from Williams site, i.e.

http://williams.best.vwh.net/avform.htm#Altimetry

I also added more detailed definitions all in all with the goal of making them easier to read and follow

ISA Standard Temperature Lapse Rate

TLR = 0.0065°C/m = 0.0019812°C/ft

Relationship between pressure and indicated altitude

Alt_corr = (T_o/TLR) × [1 - (Altimeter_set/P_o)^0.190261]
Alt_corr = 145442.16 × [1 - (Altimeter_set/P_o)^0.190261] <-- in feet
Alt_corr =  44330.77 × [1 - (Altimeter_set/P_o)^0.190261] <-- in meters

Alt_pressure = Alt_ind + Alt_corr

Where:

Alt_ind       = Altimeter Indicated Altitude with corresponding Altimeter Setting
Altimeter_set = Altimeter Setting
P_o           = ISA Standard Pressure @ SL
T_o           = ISA Standard Temperature @ SL
TLR           = ISA Standard Temperature Lapse Rate

Relationship between pressure and density altitude

Alt_density = Alt_pressure + (T_std/TLR) × [1 - (T_std/OAT)^0.2349690]

Where:

T_std = T_o - Alt_ind × TLR = Standard Temperature in Kelvin
T_o   = ISA Standard Temperature @ SL
TLR   = ISA Standard Temperature Lapse Rate
OAT   = Outside Temperature in Kelvin

Now lets review your Java implementation of Williams formulas

Pressure Altitude

//Pressure Alt = P_alt = Ind_Alt + 145442.2*(1 - (alt_set/1013.25)^0.190261)
Pressure_Alt = I_Altitude + 145442.2 * (1 - Math.Pow((C_AltimeterPinion/1013.25),0.190261));

Everything looks fine here, but keep in mind this is only valid when I_Altitude is in feet, which will be the case when testing RAF planes, but it will switch to meters when testing LW planes.

Density Altitude

//Density Alt = P_Alt +(StdTemp0/.0019812)*(1-(StdTemp0/OAT)^0.2349690);
//Density Alt = P_Alt +( 273.15 /.0019812)*(1-( 273.15 /OAT)^0.2349690);
Density_Alt = Pressure_Alt + 137870.9872804361 * (1 - Math.Pow((273.15 / Z_AmbientAirTemperature),0.2349690));

Here you made a Standard Temperature calculation error..

It is not a constant!

It varries with Alt_ind (see above)

Which causes several problems..

1) You created a constant (137870.9872804361) when it should not be a constant!
2) You subtracted the wrong value from 1

Here is the Java code you want to use

Density_Alt = Pressure_Alt + (T_std/TLR) * (1 - Math.Pow((T_std / Z_AmbientAirTemperature),0.2349690));

Where:

T_std = 288.15 - Alt_ind × TLR
TLR   = 0.0065

If you plan on doing any testing above 36Kft than you will want to adjust T_std as follows

if ( height < tropopause ) then
   T_std = T_o - Alt_ind × TLR
else
   T_std = T_tropopause

Where:

tropopause starts at 11.0km (36089.24ft) and ends at 20km (65,616.78ft)
TLR = 6.49(°C/1,000m) = 1.98(°C/1,000ft) = 3.56(°F)/1,000ft
T_Topopause = -56.5(°C) = 216.65(°K)

Thus no need to check for height above 65kft in that I don't think the X-15 is in the game.. Yet! Or if the sequal includes the Bf-109K-4 with the uber FM you might have to add that check!

SUMMARY
I don't know if I would use Williams formulas.. I have some concerns with how he handles some of the units, but since you were using his formulas I thought it best to review those formulas. Also not sure if you can use Z_AmbientAirTemperature directly in that it is not realitve to I_Altitude.. And as you know small temp differences can have a big effect on Density Altitude calculations, so hopefully these are small differences. Might be better of using the ISA Standard Temp formulas adjusted for temp.

Hope this helps! S!

PS see attached where I did a quick ROC test and ploted the different altitudes

[klem]

Originally Posted by ACE-OF-ACES

I think so.. In that I found and error in your Density Altitude calculation

See the following REVIEW of your Java code.
...............................................
Where:
T_std = T_o - Alt_ind × TLR = Standard Temperature in Kelvin
T_o = ISA Standard Temperature @ SL
TLR = ISA Standard Temperature Lapse Rate
OAT = Outside Temperature in Kelvin[/code]

Now lets review your Java implementation of Williams formulas

Here is the Java code you want to use

Density_Alt = Pressure_Alt + (T_std/TLR) * (1 - Math.Pow((T_std / Z_AmbientAirTemperature),0.2349690));

OK I get the Constant versus T_std/TLR error, I made the mistake of taking it directly from his example

Where:
T_std = 288.15 - Alt_ind × TLR
TLR = 0.0065

OK

If you plan on doing any testing above 36Kft than you will want to adjust TLR as follows

if ( height < tropopause ) then
   TLR = 6.49(°C/1,000m) = 1.98(°C/1,000ft) = 3.56(°F)/1,000ft
else
   TLR = -56.5(°C) = 216.65(°K)

Where:
tropopause starts at 11.0km (36089.24ft) and ends at 20km (65,616.78ft)

I don't but I might build that into the code in case anyone else wants to use it.

Also not sure if you can use Z_AmbientAirTemperature directly in that it is not realitve to I_Altitude.. And as you know small temp differences can have a big effect on Density Altitude calculations, so hopefully these are small differences. Might be better of using the ISA Standard Temp formulas adjusted for temp.

The Z_AmbeintAirTemperature appears to be the OAT at the altitude, it decreases with alt at around 0.0021C/ft

Hope this helps! S!

It does, thanks. Also learning from Robo that the BCO doesn't work unless I wiggle the throttle.

[ACE-OF-ACES]

Originally Posted by klem

The Z_AmbeintAirTemperature appears to be the OAT at the altitude, it decreases with alt at around 0.0021C/ft

Roger that..

But my point is it is NOT realitive to 'I_Altitude'..

As far as I can tell it is realitive to 'Z_AltitudeAGL' and/or 'Z_AltitudeMSL'.

In short, the Z_AmbeintAirTemperature value your using may be the OAT realitive to another 'altitude' and not the one the plane is currently at..

For an example of which I speak, look at the TIME TO CLIMB picture I posted

Note at the higher altitudes (around 17.5Kft) the "Z" altitudes are quite different (higher) from the indicated, pressure and density.. Thus in and around that area when you use Z_AmbeintAirTemperature (OAT) your getting the temperature 'realitive' to the "Z" altitudes and not the OAT realitive to indicated, pressure, and density. How big of an error that will introduce.. Not sure have not calcualed it yet, but knowing how a little temperature difference can have a big effect on the calcuation of density altitude one should take pause.

Again, not 100% sure yet, need to test that to prove it to myself! I just wanted to bring it up should you come across it while testing

[klem]

Originally Posted by ACE-OF-ACES

Roger that..

But my point is it is NOT realitive to 'I_Altitude'..

As far as I can tell it is realitive to 'Z_AltitudeAGL' and/or 'Z_AltitudeMSL'.

In short, the Z_AmbeintAirTemperature value your using may be the OAT realitive to another 'altitude' and not the one the plane is currently at..

For an example of which I speak, look at the TIME TO CLIMB picture I posted

Note at the higher altitudes (around 17.5Kft) the "Z" altitudes are quite different (higher) from the indicated, pressure and density.. Thus in and around that area when you use Z_AmbeintAirTemperature (OAT) your getting the temperature 'realitive' to the "Z" altitudes and not the OAT realitive to indicated, pressure, and density. How big of an error that will introduce.. Not sure have not calcualed it yet, but knowing how a little temperature difference can have a big effect on the calcuation of density altitude one should take pause.

Again, not 100% sure yet, need to test that to prove it to myself! I just wanted to bring it up should you come across it while testing

OK, well there is the parameter I_AmbientTemp. William's example calls it Actual Temperature. It looks as though that is what he means, actual emperature as measured in the aircraft environment, "the outside air temperature (OAT) or static air temperature (SAT) refers to the temperature of the air around an aircraft".

Now, regarding:
Density_Alt = Pressure_Alt + (T_std/TLR) * (1 - Math.Pow((T_std / I_AmbientAirTemperature),0.2349690));
(now with I_AmbientAirTemperature)

Where:
T_std = 288.15 - Alt_ind × TLR
TLR = 0.0065

and

if ( height < tropopause ) then
TLR = 6.49(°C/1,000m) = 1.98(°C/1,000ft) = 3.56(°F)/1,000ft
else
TLR = -56.5(°C) = 216.65(°K)

I have two questions.

1. TLR is a rate so presumably below the Tropopause the Temperature Lapse is - Alt_Ind x TLR but above the Tropopause the Temperature Lapse is simply 56.5C ?
and similarly......
2. Within the DA calc, T_Std/TLR would appear to calculate an altitude. Does it hold good above the Tropopause where the lapse rate is zero or should I be capping T_Std at 288.15 - 56.5 = 231.65K once T_Std/TLR hits 56.5?

EDIT: Sorry, ref Q.2, I meant should I replace T_Std/TLR with some other expression above the Tropopause??

EDIT2: Think I've got it

if ( 15 - Pressure_Alt_ft*0.0019812 < -56.5)
{
TropAlt = PressureAlt - 56.5/0.0019812
TempStd = 288.15 - 56.5;
Density_Alt_ft = Pressure_Alt_ft + (TempStd/0.0019812 + TropAlt) * (1 - Math.Pow((TempStd / I_AmbientAirTemperature),0.2349690));
else
TempLapse= Pressure_Alt_ft*0.0019812;
TempStd = 288.15 - Templapse;
Density_Alt_ft = Pressure_Alt_ft + (TempStd/0.0019812) * (1 - Math.Pow((TempStd / I_AmbientAirTemperature),0.2349690));
}
TempStd = 288.15 - TempLapse;
Density_Alt_ft = Pressure_Alt_ft + (TempStd/0.0019812) * (1 - Math.Pow((TempStd / I_AmbientAirTemperature),0.2349690));

[ACE-OF-ACES]

Originally Posted by klem

OK, well there is the parameter I_AmbientTemp.

Ah yes, I forgot about that one!

I just don't recall if every plane had one? I noticed that when a plane does not have a guage for a said "I" value that said value is not aval to read/log.

But we can use that value and log it along with the "Z" value (which is allways active) you were using to see if they are the same, or if they diverage at some point (alt). If they don't than I was worring for nuttin and we can continue to use the "Z" value.

Originally Posted by klem

I have two questions.

Ok lets see if I have two answers!

Originally Posted by klem

1. TLR is a rate so presumably below the Tropopause the Temperature Lapse is - Alt_Ind x TLR but above the Tropopause the Temperature Lapse is simply 56.5C ?

Exactally!

Take a look at any standard atmosphere table/graph and you will see that is indeed the case

Originally Posted by klem

and similarly......
2. Within the DA calc, T_Std/TLR would appear to calculate an altitude. Does it hold good above the Tropopause where the lapse rate is zero or should I be capping T_Std at 288.15 - 56.5 = 231.65K once T_Std/TLR hits 56.5?

EDIT: Sorry, ref Q.2, I meant should I replace T_Std/TLR with some other expression above the Tropopause??

EDIT2: Think I've got it

if ( 15 - Pressure_Alt_ft*0.0019812 < -56.5)
{
TropAlt = PressureAlt - 56.5/0.0019812
TempStd = 288.15 - 56.5;
Density_Alt_ft = Pressure_Alt_ft + (TempStd/0.0019812 + TropAlt) * (1 - Math.Pow((TempStd / I_AmbientAirTemperature),0.2349690));
else
TempLapse= Pressure_Alt_ft*0.0019812;
TempStd = 288.15 - Templapse;
Density_Alt_ft = Pressure_Alt_ft + (TempStd/0.0019812) * (1 - Math.Pow((TempStd / I_AmbientAirTemperature),0.2349690));
}
TempStd = 288.15 - TempLapse;
Density_Alt_ft = Pressure_Alt_ft + (TempStd/0.0019812) * (1 - Math.Pow((TempStd / I_AmbientAirTemperature),0.2349690));

Let me look at your code a bit.. and ill get back to ya!

So, one answer, one pending!

[ACE-OF-ACES]

My bad..

When checking for the tropopause, i.e.

if ( height < tropopause ) then
else
end

We have to adjust the whole T_std equation, not the the TLR!

Note I had this

if ( height < tropopause ) then
   TLR = 6.49(°C/1,000m) = 1.98(°C/1,000ft) = 3.56(°F)/1,000ft
else
   TLR = -56.5(°C) = 216.65(°K)

Which is wrong!

What we want to do is this

if ( height < tropopause ) then
   T_std = T_o - Alt_ind × TLR
else
   T_std = T_tropopause

Where

T_Topopause = -56.5(°C) = 216.65(°K)