Ta 152 vs P47N: level speed

[moot]

This is a continuation of a tangent off the P47M thread:  How the Ta152H manages to compete (historically at least) with the P47M despite it's huge power deficit.


Gonna work on translating this one in a bit.


I don't remember where I found this one, but I think it's HoHun that made it.  It should be reliable.
edit - Or not.  The 213E with GM1 boost is supposed to put out 1740 HP at 40k... more info on that one when I find it.

[dtango]

Moot:

Well for starters, just as your Jumo 213E shows engine power output is not a constant.  Just because the P&W R2800-57C (P-47M engine) could run at 2800 HP WEP at 32,000 feet doesn't mean that it puts that power out at a different altitude.  I don't have R2800-57C power output curves be we can conjecture from a few different ways:

1) From wwiiaircraftperformance we have some data on the P-47M:

http://www.wwiiaircraftperformance.org/p-47/p-47.html#p47-m

Notice 2 interesting lines:

Guaranteed Performance:
(a) High Speed at 38,750 ft. (Critical Altitude) with 2100 BHP
(d) High Speed at 42,000 ft. (Critical Altitude) with 1700 BHP

Notice the significant drop off in engine power output from 38,750 to 42,000 ft.

Secondarily, the critical altitude for the engine on WEP is the following from that report:

Additional Performance:
(a) High Speed at 32,000 ft. (Critical Altitude) with 2800 BHP (W.E.P.)


2) We can compare against the P-47N since it was fitted with the same R2800-57C with late models having the R2800-77
Since HTC has this the P-47N modeled they have an power output curve they are modeling for possibly the R2800-57C or similar engine with a max power output of 2800 HP.  Here's a comparison of speeds based on WEP:



Notice the power drop off at about 30,000 feet for the P-47N.

So variation in engine power output with altitude is probably a big factor in answering your question.  Let me also just caution that as in anything having to do with aerodynamics it's wise not to over generalize - in this case only evaluating differences in power for instance.

Tango
412th FS Braunco Mustangs

[Karnak]

Remember, the P-47 has a turbo charger so it puts out a constant power until it exceeds its critical altitude.  I seem to recall the P-47N's turbo charger has a critical altitude between 30,000 and 33,000ft.

[dtango]

Remember, the P-47 has a turbo charger so it puts out a constant power until it exceeds its critical altitude.  I seem to recall the P-47N's turbo charger has a critical altitude between 30,000 and 33,000ft.

Yes, and the P-47M's critical alt is listed at 32,800 for 2800 HP WEP max as pointed out above.

Tango
412th FS Braunco Mustangs

[Widewing]

Moot:

Well for starters, just as your Jumo 213E shows engine power output is not a constant.  Just because the P&W R2800-57C (P-47M engine) could run at 2800 HP WEP at 32,000 feet doesn't mean that it puts that power out at a different altitude.  I don't have R2800-57C power output curves be we can conjecture from a few different ways:

1) From wwiiaircraftperformance we have some data on the P-47M:

http://www.wwiiaircraftperformance.org/p-47/p-47.html#p47-m

Notice 2 interesting lines:

Guaranteed Performance:
(a) High Speed at 38,750 ft. (Critical Altitude) with 2100 BHP
(d) High Speed at 42,000 ft. (Critical Altitude) with 1700 BHP

Notice the significant drop off in engine power output from 38,750 to 42,000 ft.

Secondarily, the critical altitude for the engine on WEP is the following from that report:

Additional Performance:
(a) High Speed at 32,000 ft. (Critical Altitude) with 2800 BHP (W.E.P.)


2) We can compare against the P-47N since it was fitted with the same R2800-57C with late models having the R2800-77
Since HTC has this the P-47N modeled they have an power output curve they are modeling for possibly the R2800-57C or similar engine with a max power output of 2800 HP.  Here's a comparison of speeds based on WEP:

(Image removed from quote.)

Notice the power drop off at about 30,000 feet for the P-47N.

So variation in engine power output with altitude is probably a big factor in answering your question.  Let me also just caution that as in anything having to do with aerodynamics it's wise not to over generalize - in this case only evaluating differences in power for instance.

Tango
412th FS Braunco Mustangs

The best way to determine in-game performance is to test it.... I added the AH2 P-47N speed curve to the graph you put together. Note that the P-47N can buzz along at 40k doing 460 mph.

Speeds are as follows, TAS per E6B.

Sea Level: 366 mph
10,000 ft: 402 mph
15,000 ft: 419 mph
20,000 ft: 438 mph
25,000 ft: 455 mph
30,000 ft: 476 mph
35,000 ft: 474 mph
40,000 ft: 460 mph
45,000 ft: 419 mph




My regards,

Widewing

[moot]

Dtango - By avoiding generalizations, you mean not to freely mix P47N and M, and two entirely different planes' (47N and 152H) speeds at two different altitudes?  That would be what I'm curious about. How the 152 with something like 1740 HP @ 41k can compete with the P47N powered by 2800 HP @ 32k.  It seems like relatively huge difference in power and small difference in altitude that, everything else considered, still amounts to only slightly different level speed.  I'm going to test the AH 152 so that we've got the real figures (even the 47N's posted speed chart is off, yikes), but whether in-game or historically, the relative proportions are the same.  The 152 is running at ~60% horsepower and manages to keep up with the 47N.  Stoney pointed out that it's probably due in majority to aerodynamics.

So I'll try and find the figures (we already have speed, just need to translate that aerodynamics chart) for at least the critical alts (~41k for the 152, since it's probably more sensible to go by historical numbers than by simulated ones - AH's 152's 32k critical alt) and maybe we can figure out why this almost 1000 HP deficit only costs the 152H about 5 MPH.

[dtango]

Widewing- thanks for the tests.  Just to clarify my chart comes from HTC themselves using their compare tool and of course I have no idea what weights those numbers are based off of.

Moot- by over-generalizing I mean focusing in on a single variable like power output.  Aero is a tricky animal and there are many factors.  For instance as per Stoney one logical conclusion we can also make is that the P-47M's drag curve is steeper than that of the 152.  Also contrary to what Stoney said you can't discount exhaust thrust either.  For example a long time ago there was a graph that showed the BMW801-D and the amount of exhaust thrust, between 100-200 HP depending on altitude makes a difference especially at the altitudes we are talking about.

The P-47N and P-47M comparison for engine power output proxy is close because the -57, -73, -77 R2800's were essentially the same according to Graham White.  Stoney also mentioned drag as well.  In the realm of the flight envelope we're dealing with drag rise is exponential. 

Tango
412th FS Braunco Mustangs

[moot]

That's fine, I'll find the right numbers.  I just want to see how you guys crunch them to arrive at that incongruity between power and bottom line speed.  Is this feasible for a comparison between a P47N or M (you guys pick, I don't know which one is best) at 32k and a 152H at 32 or 41k, both running at max power?

We've got power: the two jugs both made 2800 HP at 32k.  The 152 made 1740 HP at either or both 32 and 41k (need a bit more research to figure this one out).
I assume drag is available easily enough for either of the jugs, and that the german table I posted has enough info (gonna translate that in a bit).
That would leave only exhaust thrust as unknown, and since we know the other side of the equation (top speeds), I presume we could figure this one out.. ?

[uptown]

wow, way too many whiskey sours last nite to get into this right now. But interesting thread

[Wmaker]

Some contributing factors that come to mind, largely already mentioned...

- Prop eff (Probably not a big factor, but might play a small role)

- Drag coeff; while I'm not saying that the difference have to be huge, I'd wager that Ta-152 has smaller drag coeff.

- P-47N has 6.6 square meters more wet area, M has 4.57m^3 more. And like Stoney mentioned, Ta-152's wing is probably more efficient at high alts.

- Exhaust thrust can be quite a big factor as it increases at any given HP output as the altitude increases, because of less air resistance for the gases to expand. This of course helps P-47s turbosupercharger aswell but it is already factored into the given output at alt.

- Also, just small increase in speed needs huge increase in power at those speeds, even with the relatively small air density...

Moot, when I have time I'll do some quick & dirty calcs and give you the .xls to play with.

[Wmaker]

By factoring in only the differences in power and wet area the speed difference at 32kft was only roughly 11mph. I used constant 0.025Cd and 0.8 prop eff for both powers and added generous 300hp exhaust thrust for Ta-152's power figure. While being in no way accurate representation of the speeds of these two planes it goes to show that even a small variation in Cd or Propeff makes a huge difference at those speeds EDIT/(and the wing area, of course)/EDIT, where you would need to add huge amounts of power to get any speed increase that way.

[Wmaker]

"Reverse engineered" the figures a bit to get the speed equation to match with the speeds in Widewing's chart. They both now have the same prop efficiency which of course isn't the case in real life but it does give an idea how it is entirely possible for Ta-152 to hit the numbers it does. In the table below I gave Ta-152 200hp of exhaust thrust.

[moot]

While being in no way accurate representation of the speeds of these two planes it goes to show that even a small variation in Cd or Propeff makes a huge difference at those speeds EDIT/(and the wing area, of course)/EDIT, where you would need to add huge amounts of power to get any speed increase that way.

That's what I was looking for, thanks!  Can I see the math?

I have another aerodynamics riddle to make sense of in the other Ta152 thread.  Will post enough details to make it solvable, later today.. It's more or less as interesting, would be grateful if you gave it a look.

[Widewing]

Measured speeds of the Ta 152H-1 using E6B. 25% fuel.

Sea Level: 364 mph
5,000 ft: 384 mph
10,000 ft: 388 mph
15,000 ft: 409 mph
20,000 ft: 418 mph
25,000 ft: 435 mph
30,000 ft: 457 mph
35,000 ft: 459 mph
40,000 ft: 457 mph
45,000 ft: 426 mph*

*Estimated


My regards,

Widewing

[Wmaker]

Can I see the math?

The basic equation for aircraft speed: V=((2*eta*P)/(rho*S*Cd))^(1/3)

Where:

eta = prop efficiency
P = power
rho = air density at given alt
S = wing wet area
Cd = Drag Coefficient