BMW801 and R-2800 BMEP figures

[kreighund]

To SEEKER,
The BMEP for the BMW801D was 196 lb/sq in

and the R-2800 was 208 lb/sq in

[wells]

You can calculate it by:

HP = PLAN / 33000, where

P = mean pressure in lb/sq in
L = length of stroke in feet
A = area of the piston in sq inches
N = number of power strokes per minute

So,

P = HP * 33000 / (LAN)

DB605A = 191 psi for 1475 hp @ 2800 rpm
Merlin = 239 psi for 1490 hp @ 3000 rpm
Jumo 213A = 203 psi for 1776 hp @ 3250 rpm
Napier Sabre = 200 psi for 2080 hp @ 3750 rpm
Bristol Centaurus = 226 psi for 2520 hp @ 2700 rpm
Homare 21 = 240 psi for 1990 hp @ 3000 rpm
Allison = 219 psi for 1425 hp @ 3000 rpm

[Seeker]

Thank you!

I must admit to being surprised by the R-2800's higher figure. That suggests that it's the more efficiently breathing design, which in turn would suggest a more stressed engine, and that would be at odds with it's reputation of withstanding damage and rough handling.

However, I've heard it said before that German engine design in the thirties and forties wasn't as refined as their engineering reputation would suggest, and Well's analysis seems to back that up. The Homare 21 would seem to be particularly efficient, is that the Niki engine?

[wells]

Well, my analysis might be a little misleading as far as efficiency goes, since you could push the Merlin up to 1650 hp and 265 psi at same rpm, or you could throw MW50 into the DB605A and get 1800 hp and 233 psi, and so on.  If you look at it on a per HP basis, that might give you a better idea of efficiency?  In that case, including kreighund's numbers for the BMW and R-2800, we'd get:

BMW 801D = 0.115
R-2800 = 0.104
DB605A = 0.129
Merlin = 0.160
Jumo 213A = 0.114
Napier Sabre = 0.096
Bristol Centaurus = 0.090
Homare 21 = 0.121
Allison = 0.154

[Seeker]

Thanks Wells.

I'm tryng to see which designs were most power efficient, because to an extent, poor design can be hidden with capacity.

However, your figures would seem to indicate the Centaurus was more efficient than the Sabre; and I've read the Sabre to be just about the ultimate in piston engines (if it didn't blow up first).

Any comments?

[wells]

The Sabre is great at getting lots of power from a small displacment because of it's cylinder dimensions and valve design.  Generally, long stroke engines are high torque, low rpm engines, since the area of the intake and exhaust valves is smaller with a smaller bore, which means that air has to be crammed into the cylinder faster (through a smaller hole).  There's a limit as to how fast air can go through those valves before you lose volumetric efficiency, just like the critical mach number for a wing.

The Sabre and Centaurus demonstrate this nicely.

Bore x Stroke for Centaurus = 146 x 178 (2700 rpm)
Bore x Stroke for Sabre = 127 x 120 (3700 rpm)

That doesn't mean it's more efficient though.  Overall efficiency would be an energy_out / energy_in formula.  We'd need to look at ideal fuel consumption vs power output and we'd need to know the manifold pressure and rpm to get the ideal fuel consumption.  I'll see what I can dig up but in the mean time, the efficiency of the otto cycle can be figured by:

e = 1 - 1/(compression_ratio)^0.4

So, higher compression engines should be more efficient, which doesn't help the Sabre vs Centaurus comparison since they have the same compression ratio of 7:1!  hehehe

[ 01-02-2002: Message edited by: wells ]

[wells]

Here's what I can figure...

Efficiency is based on a mixture ratio of 15.1 and air density of 1.225 g/L.  Energy content of the fuel (heat of combustion) is about 44 kJ/g.  It looks like the Centaurus is a wee bit more efficient than the Sabre and the Homare would seem to be the most efficient of the lot.

DB605A (109G2/G6, C.205)
Bore:  154 mm
Stroke:  160 mm
Capacity:  35.8 L
Compression Ratio:  7.50/7.30
Power:  1475 hp @ 1.42 ata @ 2800 rpm
Efficiency:  26.0 % (sea level)

BMW 801D (FW-190A)
Bore:  156 mm
Stroke:  156 mm
Capacity:  41.7 L
Compression Ratio:  7.22
Power:  1700 hp @ 1.42 ata @ 2700 rpm (sea level)
Efficiency:  26.7 % (low gear)

V-1650-7 (P-51D)
Bore:  137 mm
Stroke:  152 mm
Capacity:  27.0 L
Compression Ratio:  6.00
Power:  1490 hp @ 61" Hg @ 3000 rpm (sea level)
Efficiency:  22.6% (low gear)

V-1650-3 (P-51B, Spitfire IX)
Bore:  137 mm
Stroke:  152 mm
Capacity:  27.0 L
Compression Ratio:  6.00
Power:  1380 hp @ 61" Hg @ 3000 rpm (sea level)
Efficiency:  21.0 % (low gear)

P&W R-2800 (F4U)
Bore:  146 mm
Stroke:  152 mm
Capacity:  45.9 L
Compression Ratio:  6.70
Power:  2000 hp @ 54" Hg @ 2700 rpm (sea level)
Efficiency:  22.4 % (neutral blower)

P&W R-2800 (P-47)
Bore:  146 mm
Stroke:  152 mm
Capacity:  45.9 L
Compression Ratio:  6.70
Power:  2000 hp @ 52" Hg @ 2700 rpm
Efficiency:  23.3 % (sea level)

Napier Sabre II (Typhoon, Tempest V)
Bore:  127 mm
Stroke:  120 mm
Capacity:  36.5 L
Compression Ratio:  7.00
Power:  2030 hp @ +7 psi @ 3700 rpm (sea level)
Efficiency:  25.5 %  (low gear)

Bristol Centaurus (Tempest II, Sea Fury)
Bore:  146 mm
Stroke:  178 mm
Capacity:  53.6 L
Compression Ratio:  7.00
Power:  2520 hp @ +9.5 psi @ 2700 rpm (sea level)
Efficiency:  26.5 %  (low gear)

Allison V-1710 (P-38)
Bore:  140 mm
Stroke:  152 mm
Capacity:  28.0 L
Compression Ratio:  6.65
Power:  1425 hp @ 54" Hg @ 3000 rpm
Efficiency:  23.6 % (sea level)

Sakae 21 (A6m5)
Bore:  130 mm
Stroke:  150 mm
Capacity:  27.9 L
Compression Ratio:  7.00
Power:  1130 hp @ +300 mm @ 2750 rpm (sea level)
Efficiency:  26.5 % (low gear)

Homare 21 (N1K2-J)
Bore:  130 mm
Stroke:  150 mm
Capacity:  35.8 L
Compression Ratio:  7.00
Power:  1990 hp @ +500 mm @ 3000 rpm (sea level)
Efficiency:  28.0 % (low gear)

[gripen]

Interesting stuff Wells! Direct sea level comparison is a bit missleading because rated altitudes and  supercharger systems vary so generally this favors low altitude engines. BTW where did you find MAP values for the Ha-45?

gripen

[kreighund]

I got my map values from a guy from Japan a while back but I remember his web site.

Hey Wells, how we equate the Japanese measurement of mm to inches orf Hg or Lbs/sq in?

[ 01-02-2002: Message edited by: kreighund ]

[wells]

Standard pressure at sea level is 29.92" Hg, or 14.7 psi or 760 mm (There are 25.4 mm in 1" Hg.)

[HoHun]

Hi Kreighund,

>Hey Wells, how we equate the Japanese measurement of mm to inches orf Hg or Lbs/sq in?

The "mm" measurement is sort of incomplete since pressure was measured (long ago) either as mm Hg or as mm (or m) H2O. I'm sure Hg is meant here since a typical pressure in mm of water would result in a much larger number than mm of mercury :-)

Anyway, just as Wells pointed out, 1 inch = 25.4 mm.

Note that some measurements of manifold pressure are absolute (like the US inches of mercury or the Luftwaffe ata), while others are relative (like the British pounds-force per square inch or, apparently, the Japanese mm of mercury). This simply means that the US and the Luftwaffe recorded the exact value of pressure, while British and Japanese only counted the difference to the atmospheric pressure at sea level.

(Today, the international unit of pressure is Pascal. Atmospheric pressure at sea level is 1013.25 hPa.)

Regards,

Henning (HoHun)

[wells]

Ok, here they are again, but at critical height and/or high gear of the supercharger.  We should be able to see how demanding the different supercharging systems are.

DB605A (109G2/G6, C.205)
Power:  1355 hp @ 1.42 ata @ 2800 rpm @ 5700m
Efficiency:  20.8 %

BMW 801D (FW-190A)
Power:  1440 hp @ 1.42 ata @ 2700 rpm @ 5700m
Efficiency:  19.7 % (high gear)

V-1650-7 (P-51D)
Power:  1370 hp @ 61" Hg @ 3000 rpm @ 21400'
Efficiency:  17.7% (high gear)

V-1650-3 (P-51B, Spitfire IX)
Power:  1210 hp @ 61" Hg @ 3000 rpm @ 25800'
Efficiency:  15.1 % (high gear)

P&W R-2800 (F4U)
Power:  1650 hp @ 53" Hg @ 2700 rpm @ 21000'
Efficiency:  16.1 % (high blower)

P&W R-2800 (P-47)
Power:  2000 hp @ 52" Hg @ 2700 rpm @ 27000 ft
Efficiency:  18.9 % (27000' +)

Napier Sabre II (Typhoon, Tempest V)
Power:  1735 hp @ +7 psi @ 3700 rpm @ 17000'
Efficiency:  19.2 %  (high gear)

Bristol Centaurus (Tempest II, Sea Fury)
Power:  2225 hp @ +9.5 psi @ 2700 rpm @ 11000'
Efficiency:  21.6 %  (high gear)

Allison V-1710 (P-38)
Power:  1425 hp @ 54" Hg @ 3000 rpm @ 26600'
Efficiency:  19.2 % (26600'+)

Sakae 21 (A6m5)
Power:  980 hp @ +200 mm @ 2700 rpm @ 6000m
Efficiency:  22.3 % (high gear)

Homare 21 (N1K2-J)
Power:  1620 hp @ +350 mm @ 3000 rpm @ 6400m
Efficiency:  22.1 % (high gear)