Ta-152H-1 climb rate

[Timppa]

I have been trying to calculate the climb rate of the Ta-152H-1.

First the climb rates in AH2, that are supposedly generated by the game engine:



The calculation used the following datasheets:

Manufacturer drag data. Cd0 (climb) and the Oswald efficiency factor ( e ) were obtained here:
http://img.photobucket.com/albums/v424/timppa/FW190_Ta152_drag.jpg

Jumo 213E engine chart:
http://img.photobucket.com/albums/v424/timppa/Jumo213E-performance_chart.png

Exhaust thrust chart:
http://img.photobucket.com/albums/v424/timppa/abgasschub_Jumo213E.gif

My calculation was somewhat simplified, it did not take into account:
- Ram effect
- Climb speed is calculated with constant EAS, not optimum at each altitude
- Possible propeller efficiency drop due to Mach-induced tip losses.
- Kinetic energy correction, as the TAS is slowly increasing with altitude.

The calculation was done using the same weight ( 11,501 lb = 5,217 kg) so that the AH2 curves and the calculation can be compared directly:

My results from the calculation:

Weight,W: 5216.6 kg
   11501   lb
Wing Area, S: 23.3 m2
Wing Span, b: 14.44 m
Prop Diameter, D: 3.6 m
Parasitic drag coefficient, Cdp: 0.029   
Aspect ratio, AR: 8.949   
Oswald efficiency factor, e: 0.727   
Prop. efficiency correction, Pcorr: 0.8587   
Altitude: 0 m
   0 ft
Temperature,T: 288.2 K
Density, rho: 1.225 kg/m3
Power at altitude, Pmilitary: 1580 PS
      1558 hp
      1162 kW
Exhaust thrust; TEmil: 960 N
Climb speed:   69.5 m/s
      250 km/h
      155 mph
Propeller efficiency a:   7.198901785   
   eta: 0.899053658   
Propeller efficiency: 0.77   
Total thrust: 13872 N
Parasitic drag, Dp: 2012 N
Induced drag, Di: 1860 N
Climb rate: 13.6 m/s
   2673 fpm

This procedure was repeated at each altitude, with both Climb and Special Emergency -power. The graphical result is as follows:


As a comparison, our old forum member Hohun calculated it also with his own spreadsheet , taking account of the ram effect, tip losses, and with optimal climb speed (compared also with AH2 curves):



Note that the blue line represents Start/Not -leistung, which ( according to the pilot handbook ) was cleared for 30min duration. IMO it would be more representative to use it as MIL -power in AH2. Btw. the same applies to the Fw190D-9 as well:



Conclusions:
AH climb curves are quite a lot different from the calculated ones . Not only by magnitude, but by shape as well. For example there seems to be emergency power enabled in the third supercharger gear also, which does not correlate with the posted engine chart. I can only think that HTC have used different engine data.
The climb rate, especially at military power is significantly lower than it should be (by calculation).

[JunkyII]

You seem to have spent some time on this........I never really looked at the 152s climb chart but yours I would agree with more after flying it most of this tour....it gets to 15K quite fast.


Didn't Moot have a thread which changed the TA152 awhile back though? At the the time I could have cared less but I know something changed maybe they just havn't changed the charts to go with it.

 

[RTHolmes]

1. do you have any test charts? AH figures are usually based on real world tests, and these can be way off the design's predicted numbers.

2. AH only models one time-limited power setting (WEP). most of the engine types Ive looked at had several settings, so the WEP modelling in AH is a best-fit compromise for the 1-stage WEP we have modelled (apart from the Lanc which still hasnt been given its WEP ).

3. you might get more people looking into this if you can translate the german terms and do it in mph/fpm - this stuff is hard enough to get your head around without having to do metric conversions as well

[Badboy]

Hi Timppa

The climb rate, especially at military power is significantly lower than it should be (by calculation).

The prop efficiency values mentioned appear to be too high.

Hope that helps.

Badboy

[dtango]

I concur with Badboy.  Prop efficiency based on momentum theory is about .70 at 155 mph.  Taking 7% out of your total thrust available I get a rate of climb based on your data at 12.3 m/s and 2411 ft/m at sea level instead which is pretty darn close to what the AH chart says.

[Krusty]

I recall reading several places references to the US testing of the Ta-152H-1 after the war, and despite the lack of MW50 and similar additives, the plane STILL had about the same climb rate as ours does on WEP. That means it was running on something closer to AH's milpower but getting numbers much higher than we get.

I would not be surprised one iota if the climb rate was less than it should be. It's the worst climb rate in the game without WEP (2300fpm) . Doesn't seem right that such a heavy plane gains almost double the RoC with WEP engaged. I expect that the calculated numbers might somehow reflect that US flight test better, but have only read references to the US test, never saw it myself.

[Stoney]

I recall reading several places references to the US testing of the Ta-152H-1 after the war, and despite the lack of MW50 and similar additives, the plane STILL had about the same climb rate as ours does on WEP. That means it was running on something closer to AH's milpower but getting numbers much higher than we get.

I would not be surprised one iota if the climb rate was less than it should be. It's the worst climb rate in the game without WEP (2300fpm) . Doesn't seem right that such a heavy plane gains almost double the RoC with WEP engaged. I expect that the calculated numbers might somehow reflect that US flight test better, but have only read references to the US test, never saw it myself.

Well, the P-47N climbs like a pig on mil power, but rockets up on WEP.  So, given the large increase in power available on WEP, its easy to see how a big, heavy plane can get a drastic increase in climb with the extra boost.  Climb is all about excess power, so the more available, the higher its going to be.

[Krusty]

To paraphrase the multiple references to the same report, the Ta-152 exceeded 3000 fpm while "dry" (because they had no additives or boosts to use in the test), so like I said I wouldn't be surprised if the HTC modeling was too low.


Then again, I repeat I have not read the US report. That might explain the higher climb rate in some way I don't know.

[Timppa]

Hi Timppa

The prop efficiency values mentioned appear to be too high.

Hi Badboy,
I used used the formulas you posted in the "Prop efficiency" thread a while back.

I concur with Badboy.  Prop efficiency based on momentum theory is about .70 at 155 mph.

Can you show your math. My math below, calculated in another way, from:
http://electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/stallSpeedMath.html

Speed   155   mph
Power   1560   BHP
Power fraction   0.77   
Prop. Diameter   3.6   m
   11.81   ft
Gear ratio   2.4   
Engine rpm   3000   rpm
Prop rpm   1250   
J   0.924   
C_P   0.140   
J/C_P^1/3   1.78
   

[dtango]

Hi Timppa:

The ~.7 at 155 mph is just an estimate by looking at a similar propeller curve I've done.  The math comes from a cubic solve of equation #5 here (which is derived from propeller momentum theory of thrust):
http://www.mh-aerotools.de/airfoils/propuls4.htm

No matter, I checked your values using the standard J and Cp equations and I think I found where your calculations went awry.  It appears your Cp is too low.  I get the following values for Cp and J/Cp^(1/3):

Cp= .1795
J/Cp^(1/3) = 1.637

You can see these values map to a lower prop efficiency on the curve from Perkins & Hage you posted.  For some reason you're throwing in a .77 factor into the power which results in making the propeller more efficient than it is.

The standard Cp equation is:

Cp = (550*BHP) / (rho*n^3*D^5)  for english units where:

BHP = hp
n = prop revolutions per second
D = prop diameter in feet

Hope that points you in the right direction.

[Timppa]

Cp= .1795
J/Cp^(1/3) = 1.637

You can see these values map to a lower prop efficiency on the curve from Perkins & Hage you posted.

Hmm, how can we look the same curve so differently.

Using the formula I get actually Cp= 0.1737 and J/Cp^(1/3) = 1.656. But both lead to practical efficiency of 0.76-0.78.

To get the efficiency of 0.7 would require J/Cp^(1/3) of around 1.20-1.25.

For some reason you're throwing in a .77 factor

into the power which results in making the propeller more efficient than it is.

It appears that you did not look the link I provided. I should not have done that, as it seems to cause only confusion (and i did not even use the Brooke's formula in my OP). I quote the relevant part:

C_P = 52.5 * gamma* BHP / [(N / 1000)^3 * D^5 * rho / rho_0],

where gamma is fraction of full power being applied, BHP is engine brake horsepower, N is prop RPM, D is prop diameter in ft, rho is the air density, and rho_0 is the air density at standard sea level.

I used gamma as 1580PS (MIL)/2050PS (WEP)=0.77, leading to efficiency of 0.78-0.80.
I admit that I am not sure of the validity of the concept of  power fraction. Also the formula of C_P leads to values about 5% too high even with gamma=1.

[drgondog]

Hmm, how can we look the same curve so differently.

Using the formula I get actually Cp= 0.1737 and J/Cp^(1/3) = 1.656. But both lead to practical efficiency of 0.76-0.78.

To get the efficiency of 0.7 would require J/Cp^(1/3) of around 1.20-1.25.


It appears that you did not look the link I provided. I should not have done that, as it seems to cause only confusion (and i did not even use the Brooke's formula in my OP). I quote the relevant part:

I used gamma as 1580PS (MIL)/2050PS (WEP)=0.77, leading to efficiency of 0.78-0.80.
I admit that I am not sure of the validity of the concept of  power fraction. Also the formula of C_P leads to values about 5% too high even with gamma=1.

Timppa - I don't believe that propeller efficiency varies with with any ratio of Power applied versus Power potentially available..... Therefore "gamma' is not appropriate other than a value of "1"when Bhp is known.

[Badboy]

Hi Badboy,
I used used the formulas you posted in the "Prop efficiency" thread a while back.

Hi Timppa,

Yep, and as you pointed out, there are a number of issues with that method. It is a good way to estimate the maximum theoretical efficiency of a propeller, but if you really want to estimate a realistic value there are a number of factors that should be taken into account. For example, the calculation makes a number of very unrealistic assumptions. At the very beginning there was the assumption that the air flowing through the prop disk did two things, firstly that the flow moved directly aft and secondly that it formed a cylinder with the same diameter as the prop. The calculations that followed were based on those assumptions and neither of them are correct. The prop stream does not flow directly aft, there is significant rotation in the prop stream which spirals around the fuselage as it goes, with a corresponding loss of energy that is no longer available to produce thrust. Also, the air in front and behind the prop does not correspond to a cylinder in shape. Those two factors alone result in a significant difference between theoretical values and those seen in practice, particularly at the low aircraft forward speeds during climbs. In addition, there is parasite drag between the the air and the prop blades, and interference effects between the blades, and all of that has been ignored. You also mentioned other factors, including Mach losses, that occur at higher forward speeds where the rotation of the prop and aircraft speed combine to create very high tip speeds. Since there are a number of factors that produce significant energy losses that occur both at low and high speeds, the calculations I presented previously have to be accepted for what they are, ideal values, not practical ones.

When I carry out calculations that allow for the losses discussed above at full power, the efficiency curve looks like this. 



It isn't entirely smooth, because I only used 14 points to generate it, but you will notice that at 155mph the efficiency is around 71.5%.

Despite the fact that I refined that analysis over a period of time to include a variety of losses, I have since abandoned that approach in preference for the use of real prop curves and methods that make it possible to generate specific prop curves from wind tunnel data and to produce general prop curves. However, since it is essentially a data based approach it depends on the use of look up tables and interpolation. Even so it is still very appropriate for use in software for modelling purposes, and I believe it yields more accurate results for the practical prediction of aircraft performance.

If you would like to find a way to use the tools you have (which are already fairly sophisticated) to make predictions that are a better fit for what you see in the game there is an approach you can use and I'll explain it when I have more time. 

Hope that helps.

Badboy

[Krusty]

This is all above my head, but from what I'm reading here I'd like to point out one thing and ask one thing.


Badboy, how does this match up to real life? Say you plug in the values for a P-51D. Do they match up to historically accurate values? (or if not P-51D some other plane with plenty of documentation/testing, not the scarce/rare Ta-152H-1)

And, I'd like to point out:

It isn't entirely smooth, because I only used 14 points to generate it, but you will notice that at 155mph the efficiency is around 71.5%.

Doesn't the Ta152 climb at around 165-170mph? That would put the efficiency (on that chart) about 74% to 75% Not too much higher but it's definitely higher. Just a thought.

[Timppa]

If you would like to find a way to use the tools you have (which are already fairly sophisticated) to make predictions that are a better fit for what you see in the game there is an approach you can use..

I would definitely like to see that.

I have not seen tested climb curves of this plane but there is a few calculated datapoints in the document "Einmotorige Jäger: Leistungsdaten" from Focke-Wulf.
http://img.photobucket.com/albums/v424/timppa/leistungsdaten-1-10-44.jpg

I tested AH2 climb performance against these data points:

Weight in FW calculation: 4760 kg =10,494 lb.
AH2 Ta-152H-1 with half internal fuel: 10,711 lb, fuel burn =0 ).

Climb rate at full throttle altitude of 9900m ( 32,500 ft ), MIL power:
FW:  9.7 m/s ( 1910 fpm )
AH2: 1265 fpm ( =34% less )

Climb rate at full throttle altitude of 8800m ( 28,900 ft ), WEP:
FW:  14.5 m/s ( 2850 fpm )
AH2: 1985 fpm ( =30% less )

Climb to 10000 m ( 32,800 ft ):
MIL:
AH2: 17.5 min
FW:  13.8 min (=21% less )

WEP:
AH2: 12.3 min
FW:  10.1 min (=18% less )


Testing a little bit further:
Comparing the FW calculation with AH2, it seems that the Fw190A-8 climb figures match exactly.
For the Fw190D-9, the FW values are about 10% better.
It is only with the Ta-152H-1 where the numbers differ significantly ( by 20-30%).