P-47M whine whine whine

[Widewing]

The 47M's powerloading is only a little better than the 51D's, compared to the K4.  The D11's is slightly better than the M's.. This is as far as acceleration to respective top speeds goes.
(Image removed from quote.)
That's in dogfighting trim (ammo for 10 kills, ~12-15min fuel @ wep). They're less competitive when loaded.  

This is based upon sea level HP, correct? Power loading is completely dependent upon altitude. For example: The P-51D made 960 hp at 30k, whereas the P-47M made 2,800 hp. Indeed, the P-47M made 2,800 hp from sea level all the way up to critical altitude (approx 32.6k).

At 30k, the M was the fastest accelerating fighter ever tested by the Army up until the time it was tested. The P-38L ranked 2nd. In game, if you do acceleration testing at just 20k, you find that many of the super-uber low level birds are generally not very impressive. As one example; the P-38G and the Tempest have identical times accelerating from 200 mph TAS to 300 mph TAS at 22k. In comparison, the P-38L accelerates from 200 mph TAS to 300 mph TAS in 1/3 less time than the Tempest or P-38G at that same height.

Power loading is totally dependent on altitude, or the ability of an engine to produce power at altitudes from sea level to critical altitude (FTH).


My regards,

Widewing

[moot]

Wingnutt - Yeah but I was curious if you had any numbers to quantify that.  Anyway, it's not worth trying with this many gaps of info, and when the AH acceleration is a bit unpredictable:  Historical docs like the ballpark acceleration comparisons at wwiiaircraftperformance.org show that e.g. the Tempest is supposed to be a pretty sluggish accelerator.  Not like in AH. With just powerloading figures (no aerodynamics figures), you get this:

Not the full picture, not conclusive.

Thanks Widewing, SL loading, yes, and that changes everything yep.

[Stoney]

2200/2800 mil/WEP for the C series R-2800 in the N and M models.  The paddle blade props were pretty much standard on later D models.  Our D-25 has a paddle blade prop.  Our D-11 does not, or should not.  D-40 should be 2600 on WEP I think.  My books are packed up so I'm going off memory here.

Razorback models may be a little more streamlined, but the extra horsepower of the later D's, N's, and M make up for it.  The biggest reason our D-11 is faster is because it doesn't have wing pylons or rocket rails, more so than the "fastback" fuselage.  The only difference in weight from the D-11 to the D-25 is basically the wing pylons and more fuel capacity (bigger main tank).

[moot]

Suppose I wanted to make an animated bar graph of a couple of planes' acceleration to their top speeds at a couple of different altitudes.  What specifications would I need to calculate the figures to feed into that animation?

[Widewing]

Suppose I wanted to make an animated bar graph of a couple of planes' acceleration to their top speeds at a couple of different altitudes.  What specifications would I need to calculate the figures to feed into that animation?

You would need to calculate total thrust in pounds. This can be done with a simplified formula.

375 x Prop Efficiency X Horsepower / Initial Speed 

You need to calculate total drag in pounds. This is more complicated as you need data from which to make the calculation.

With these two data points, you can then calculate acceleration.

One can calculate a reasonably close rate of acceleration if we can determine several unknowns. These are propeller efficiency and drag. We can use a constant for the the prop, but may have to estimate drag.

We can calculate the approximate thrust available at a given speed. To do this, we must estimate the efficiency of the propeller. If we begin at 150 mph, a typical WWII prop will demonstrate approximately 70% average efficiency over its normal speed range (can vary from 60% up to just over 80% and back down again). If this is applied to all examples, it becomes a fair, if not perfectly accurate method. Note that 2,400 hp in the Tempest is at 11 lb boost.

Thus, for the Tempest:

375 x .7 x 2,400 / 150 = 4,200 lb of thrust.

For the Spitfire Mk.XIV:

375 x .7 x 2050 / 150 = 3,588 lb of thrust.

Now that we know the available thrust, we can calculate acceleration in feet per second, per second. Of course, we need to know what the total drag is. This can also be calculated or obtained from a reliable source. In this case, I'm going to use what I believe are close estimates.

Total drag for the Tempest: 1,350 lb

Total drag for the Spit XIV: 990 lb

Thus, thrust - drag / mass (in slugs) = initial acceleration in feet per second, per second.

Tempest: 4200 (thrust) - 1350 (drag) / (11480/32.2) = 7.99 feet per second, per second.

Spit XIV: 3588 - 1090 / (8500/32.2) = 9.46 feet per second, per second.

Let's toss in the P-51D for comparison. I am calculating based upon an empty rear aux fuel tank (always burned off first on climb-out)

P-51D: 3010 - 845 / (9611/32.2) = 7.25 feet per second, per second.

Results, initial acceleration rate in g:

Spitfire Mk.XIV: 0.294 g
Tempest Mk.V: 0.248 g
P-51D: 0.225 g

Initial acceleration in the game, full load except for P-51D with 75% fuel. Time to accelerate from 150 mph to 200 mph at 100 feet ASL.

Spitfire Mk.XIV: 8.12 seconds (18 lb boost)
Tempest Mk.V: 8.16 seconds (10.5 lb boost)
P-51D: 10.81 seconds (67 in/hg boost)

The relationship between the Spitfire XIV and P-51D is reasonably close to the calculated acceleration (30% calculated vs 33% actual testing)

However, the difference between the Tempest and P-51D is much different (10% calculated vs 32% actual testing). In short, the AH2 Tempest appears to accelerate much faster than it should for the given boost and horsepower, at least in theory. Even if I reduce the Tempest's drag by 200 lb, it still should not accelerate as fast as it does in the game.

Dean published drag figures for most American fighters in his book, America's Hundred Thousand.

Note that acceleration is not going to be linear as propeller thrust decreases as speed increases. Also, you would have to know the available power at the various altitudes to calculate for each increment. There is also a gradual rise in drag as speed increases, which means an increasing error as speeds rise. All of these variables make accurate data over a speed and altitude range very difficult to pinpoint.


My regards,

Widewing

[Hooligan]

Wingnutt:

The observations I made concerning M performance are from the graphs on page 282 of "America's Hundred Thousand".  On the deck, p-47M top speed and climb (with WEP/without WEP) are approximately:  365/335  3600/2600.  The AH 51D comes in about 370/355  3450/3000.  Acceleration and climb are close to proportional because they are both closely related to thrust/mass (the drag which affects the two is somewhat different).

And you completely missed my point about speed and acceleration.  P-47s have good top speeds for the MA but because of their poor acceleration, they can't use that top speed to pursue or escape effectively starting from a low E condition.  A high top speed just isn't that useful if acceleration is poor compared to the competition.

[moot]

Widewing - So, to make a thoroughly accurate simulation, we're missing PropEff at a range of speeds (150-~400 IAS) and a number of altitudes (say SL, 5k, 10k, 15k), Drag in that same range of speeds and altitudes, and engine Power at those altitudes?
Or does drag behave the same through a range of indicated speed, at any two different altitudes?

I don't mind researching (all this info is available in public records, right?), but all things considered, it's faster and more accurate to record the accelerations in the game (since that's what we're after here), and then try and find the numbers for the 47M (since that was part of the original purpose of this) to see how it's expected to compare.

[bozon]

From what I've read recently, weight doesn't mean much for top speed.  It's important for acceleration, obviously (F=MA).  You mentionned the M's prop was something special?  Can you quantify exactly how the D-11 is more slippery than the others?

Just realized that I misread the charts.  Disregard my comment on the D-11's powerloading.. Do you know exactly how much power our D-11's engine makes? 2535hp is what I've found, but it's not specified for which D model that is.  And our N does make 2450hp, doesn't it?
This page says it used the R-2800-21, making 2300hp @ wep.

The D11 is both lighter than all other model and has less drag. The reduced drag is both due to the razorback vs. bubble canopy and the lack of wing pylons. In addition the razor back adds lateral stability, perhaps the reason the D11 feels better near the stall than the bubbles. This is offset by the lack of paddle blade prop on the D11 (all other models are modeled with it) that knocks off 500-800 fpm from the climb rate (and suppose to add 2-4 mph to top speed). Essentially all razorback that did not come out of the factory with this prop had it installed in the field. The most common and significant Jug configuration in the ETO is a razorback with a paddle blade prop.

All jug engines give 2000HP at mil power. The main difference is the WEP that adds ~100HP for the D40 and is like injecting the engine with cocaine in the M,N.

[moot]

Thanks Bozon, I was just thinking about this...  What about exhaust thrust?  Because the 152 would really have to be aerodynamically miles ahead of the 47N/M to match their speed there with (IIRC) only ~1300 HP versus their 2800 HP.

[Krusty]

Super giant radial frontal area = tons of drag.

[moot]

Still.. a ~1200 HP bird like the 152 vs a 2800 HP model like the 47N up in the thin air of 30k..  I'm not seeing such a huge amount of extra drag to cancel out 1600 HP.  That's huge!
The question I'm asking though, is whether exhaust thrust plays a non-negligible part in overall thrust, and how difficult it'd make what I had in mind - crunching out accurate enough numbers for the 47M, to compare with what we have already.

[Karnak]

Still.. a ~1200 HP bird like the 152 vs a 2800 HP model like the 47N up in the thin air of 30k..  I'm not seeing such a huge amount of extra drag to cancel out 1600 HP.  That's huge!
The question I'm asking though, is whether exhaust thrust plays a non-negligible part in overall thrust, and how difficult it'd make what I had in mind - crunching out accurate enough numbers for the 47M, to compare with what we have already.

My understanding of exhaust thrust is that it equals approximately 10% more power.  I don't know if that changes with altitude though.

[moot]

Well there's got to be more to it than that.. I mean, the 152 makes 2050 HP @SL and only a bit over 1000 at 35k, while the R-2800 puts out 2800 at all altitudes.  And yet the 152 and 47N both have roughly parallel speed curves.  So there's something amiss because everything else being equal, the 152 ought to be getting less competitive with rising altitude.  Drag is constant (comparatively between the two planes), the 152 has a falling engine power whereas the 47 has constant engine power, and the speed curves (the "bottom line" tally of it all) are nearly identical.  So, somewhere in there is something that compensates for the 152's dropping engine power. 

The two of them can't have proportionally constant exhaust thrusts.  If you take the 47 as the benchmark, its performance is consistent with the 152 having lots of ET with rising altitude; but where's the 47's exhaust thrust?  I know I've read (IIRC) Frenchy say that exhaust thrust was a big factor for the jugs at altitude.  Either the 152 has immense exhaust thrust (very strange when you've got the engine wheezing out like that, but then I'm no gearhead), or the 47N has very little. 
I guess I'll only know when Widewing or Stoney, or someone who already knows this solves this riddle for me.  I don't think I can figure this one out knowing so little.

Incidentally... The AH charts show that the 152 only does ~460 @ ~31kft...  What the heck??


edit - Apparently the Jumo 213E still made 1740HP @ 40k thanks to GM-1.  That's still one thousand HP (+60%) difference.

[Stoney]

Well, a couple of other factors that may or may not impact the discrepancy.  We'd have to do some more detailed analysis to see:

Ta-152 has an aspect ratio of around 9.5 compared to the Jugs 5.5.  At those altitudes, with dynamic pressure getting so low, induced drag goes through the roof.  Especially with a 2,000-4,000 pound weight difference between the two aircraft.  That high-aspect ratio wing on the Ta-152 will be much more efficient at that altitude. 

Exhaust thrust may be important, but it can't account for that big of a difference.

The P-47 probably has a larger parasitic drag coefficient, but I don't know enough about the 152 design to know for sure.  Just because it has a radial motor doesn't really mean its automatically higher.  I keep coming back to the weight difference, because induced drag at those altitudes can be a killer.

[hitech]

I never understand why anyone wishes to calculate Acceleration. Climb rate is much easier to test and is a 100% linear equation with acceleration.

HiTech