In article ,
Stephen Harding writes:
Time to do my share to improve the S/N ratio here at r.a.m,
or at least make a try at it!

It's easy to overlook. No exhaust pipes visible protruding
from the sheet metal around the Allison engines on the P-38.

Right. On all Lockheed Model 322s other than the RAF Lightning 1s,
the exhaust gas is ducted to the hot section of the turbosupercharger
in the tail boom.

Given that Lockheed, and Kelly Johnson in particular, paid
a lot of detailed attention in the design and execution of
the aircraft, I'm wondering why they never made an effort
to use exhaust thrust to squeeze a few extra hp/mph out of
the engines for this aircraft.

Because it was far more useful to use the energy in the exhaust to run
the 1st stage (Turbosupercharger) or the 2-stage supercharger setup on
the P-38. If that supercharger stage were run from a gear train from
the engine, it would eat up 150-200 Shaft Horsepower that would
otherwise go to the propeller. At speeds below about 400 MPH, you
gain more thrust by providing that power to the propeller, rather than
as jet thrust.
This is due to the Thrust-Power relationship.
Since 1 HP = 550 lb ft/sec, or 1 HP = 375 lb Miles/Hr,
1 HP = 1 lb (force) of thrust at 375 moh. At lower speeds, 1 HP
produces more thrust, and at higher speeds, less. Here's a table
showing thrust values for a 1000 HP engine at various speeds,
ignoring propeller efficiency.

SHP Speed, mph Thrust, lb
1000 50 7500
1000 100 3750
1000 150 2500
1000 200 1875
1000 250 1500
1000 300 1250
1000 350 1071
1000 400 938
1000 450 833

So, as you can see, thrust starts out quite high, and drops off as
speed increases. For a constant power output engine, such as a recip
or the propeller section of a turboprop, this number represents the
maximum amount of thrust that can be produced by the propeller.

Now, a constant thrust value will produce more Horsepower as the
airplane moves faster. Here's a table showing how much power is
produced by our nominal 100# of thrust from our 1000 HP engine.

Thrust,lb Speed, mph Thrust HP
100 50 13
100 100 27
100 150 40
100 200 54
100 250 67
100 300 80
100 350 93
100 400 108
100 450 120

At about 25,000', it takes about 150 HP to compress the air that the
turbosupercharger is taking in. So, I'll gin up another table,
showing the thrust produced by an 850 SHP engine, with 100# of jet
thrust, and the thrust that our 1000 HP engine would produce.

Speed, SHP Propeller Jet Total 1000 SHP 1000 SHP
MPH Thrust lb Thrust Thrust Thrust Thrust Advantage
50 850 6385 100 6485 7500 1015
100 850 3188 100 3288 3750 462
150 850 2125 100 2225 2500 275
200 850 1594 100 1694 1875 181
250 850 1275 100 1375 1500 125
300 850 1063 100 1163 1250 87
350 850 910 100 1010 1071 61
400 850 797 100 897 938 41
450 850 708 100 808 833 25
500 850 638 100 738 759 12

As you can see, not losing that 150 SHP to run the first supercharger
stage gives you a really big gain at low speeds. Which is where you
really need it - best climb for a P-38 was at around 150 mph, so
excess thrust in that speed range really pays off.

The Spitfire in particular, but I believe the P-51 as well,
all made use of exhaust thrust to gain a bit more speed. Given
the P-38 was designed in 1937-ish and didn't appear in person
until about 1939, perhaps the advantage of using thrust to
boost speed a little wasn't really thought of? Perhaps the
Allison at the time of design just didn't have the oomph for it?

It was, actually fairly well understood, (The N.A.C.A. had published
several papers on it before the XP-38 had ever flown)

Pretty much all inline-engined fighters from the late 1930s used
ejector exhausts to get a bit of jet thrust. Take a look at an Me
109, a P-40, or a Hurricane. Most radials used collector-type
exhausts, and that pretty much negated any thrust that you'd be able
to extract. Later A-20s, B-25s, the Fw 190, the A6M5, the A-26, and
the Centaurus engined Tempest and Sea Fury did end up with jet stacks.

Jet thrust is a product of Mass Flow (Pretty low, for a recip. and the
expansion ratio as the pressure reduces in the exhaust stacks from the
exhaust valve to atmospheric. Mass flow is a product of displacement
and RPM, so there's not much of a difference between a 1650 cubic
inch Merlin at 3000 RPM, and a 1710 cu. in. Allison at 3000 RPM.

In each case, you're getting "Something for free" - actually, it's
more like "Something you'd otherwise get no use out of" by choosing to
use either a gear-driven first supercharger stage (As in the later
(Post 1942) Merlin 60 series) and get more jet thrust, or a
turbine-driven auxiliary stage, like the Allison in the P-38, and not
gain the jet thrust. Depending on the propeller efficiency at high
speed, (Which we neglect here, because it's really, really,
complicated, and doesn't change the results much) It's possible to get
a slight gain in thrust by using the ejector exhausts - but only at
the very high end of the speed range, and at a substantial cost in
engine Shaft Horsepower.
The turbosupercharger gives you much more thrust a lower speeds, where
it really help to improve your climb rate, and excess power for
sustaining turns. It comes at a fairly large cost of weight and bulk,
There was just no way that an engine-turbosupercharger installation
like that of a P-38, with its ducting, intercoolers, extra
lubrication, and extra oil coolers, was going to fit in a small
fighter like a Spitfire, or a P-51. Look at the original XP-39. It
started out with a turbosupercharger, but all the various coolers &
ducts added so many lumps, bumps, and bulges, because they wouldn't
fit in the airframe, that it would never have made its performance
guarantees. In an airframe that was already going to be big, like a
P-38, or a P-47, it wasn't that much of a cost. It's all a matter of
tradeoffs, and what you're willing to spend in one area to gain in
another.

Also, exactly where does the P-38 engine exhaust exit the
engine? Seems to be a big, upward facing pipe in the vicinity
of the turbocharger, but never really knew if that was turbo
intake or an exhaust of some sort.

Yep, that's the turbine exhaust.
--
Pete Stickney
A strong conviction that something must be done is the parent of many
bad measures. -- Daniel Webster