Given criteria (see post), what's the best radiator arrangement for a single seat/single engine fighter?

As for the original question, IMHO the Mustang pretty much nailed it, with possible LE radiators a close second. The Mustang style IMHO slightly edges out due to ample space for a big radiator core with diffuser inlet producing low velocity over the core => low drag + the jet outlet. I'd think the Mustang style also wins over a LE installation in terms of servicability and maintenance, and I'd guess a smaller target to hit as well.
LE is attractive in the sense it provides a 'free lunch' in terms of reducing frontal area. But that might be a simplistic argument, I'd need to know more about aerodynamics to say for sure. E.g. to which extent LE radiators reduce(?) the lift of the wing eating up that free lunch?

Obviously difficult to compare single to twin engine fighters like this, but it's worth noting that the DH Hornet was able to pretty much match the performance of the P-51H with ~150 less hp per Merlin using wing radiators. It's higher wing loading may have been part of that, though whether that's enough to balance out having to force a pair of engine nacelles through the air, I can't say.

As far as maintenance is concerned, I can't really say — I've never heard of any problems with the Mosquito, but that doesn't mean much — however you're definitely right that vulnerability to combat damage is a bit of a sore spot for the wing radiator. This was in fact, precisely what killed the Hawker attempts at it — performance was found to be stellar, but with the end of the war in europe and the advent of the jet, the air ministry determined that the Tempest (and the prospective Fury) were to serve primarily in the ground attack role going forward. The wing radiator was deemed too vulnerable to ground fire for that role, so Tempest I orders were changed to Tempest VIs, with the same engine but with the old chin radiator, while Fury I orders were cancelled entirely. Hawker also experimented with a Mustang-style radiator in the P.1027, which was to be the Rolls-Royce Eagle-powered follow up to the Tempest/Fury, however they seem to have returned to wing radiators when that design was further enlarged as the P.1030. Ultimately neither design made it off the drawing board so far as I know.

One argument I don't understand is how leading edge radiators were more vulnerable to ground fire vs a chin or annular radiator. All solutions were located near the front of the aircraft, and IMO equally as vulnerable.

Not to mention that all liquid cooled engines were vulnerable to ground fire without a ton of armor around the engine or the radiators, or the coolant/oil lines, irrespective of location. And IMO even radials didn't have the advantage they did early in the war on account or durability/resilience against ground fire. Often times, rifle caliber pea shooters were replaced by 20mm or larger flak in Germany, and the same with the British and the allies.

BarnOwlLover said:

One argument I don't understand is how leading edge radiators were more vulnerable to ground fire vs a chin or annular radiator. All solutions were located near the front of the aircraft, and IMO equally as vulnerable.

Not to mention that all liquid cooled engines were vulnerable to ground fire without a ton of armor around the engine or the radiators, or the coolant/oil lines, irrespective of location. And IMO even radials didn't have the advantage they did early in the war on account or durability/resilience against ground fire. Often times, rifle caliber pea shooters were replaced by 20mm or larger flak in Germany, and the same with the British and the allies.

Click to expand...

I think it boils down to the size of critical 'target areas' on the plane where a substantial hit (as in, proper flak caliber and not pea shooter like you say) would bring the plane down. With a chin or annular radiator two such critical target areas are more or less merged (as in, a substantial hit might destroy both the engine and the radiator, but so what, either one is fatal), meaning that the place where the radiator otherwise would be (wings, ventral, whatever) might not be as critical. And additionally there would be much shorter very vulnerable coolant lines to and from the engine.
For wing mounted vs Mustang style ventral radiator, I think the Mustang style would have a small advantage in that the wings are relatively thin, meaning that the radiators need to be pretty wide, thus presenting a larger critical target area, whereas on the Mustang the radiator is relatively compact and thus presents a smaller target (and in a turnfight style situation the airframe itself might shield the radiator from direct hits).
As for the durability of radials, there is certainly anecdotal evidence like radial engines making it back to base with an entire cylinder shot off. However I'm not sure how representative such situations are, in a major war with thousands of planes shot down there are bound to be a number of freak occurences. Like an infrantry officer headshotting a pilot with his pistol, I'm sure something like that could have happened, but it certainly doesn't mean that a pistol is a useful AA weapon.

I searched and found a few previous discussions on this site wrt the merits, or lack thereof, of annular radiators. One of these discussions had this attachment of a 1945 RAE report on an annular radiator installation on a prototype Tempest: https://ww2aircraft.net/forum/attachments/napier-annular-pdf.674007/ .

Wrt vulnerability in combat it notes that
"As regards vulnerability in combat, the unique design of the radiator is valuable in that its face lies in the direction of a frontal attack, rather than at right angles to it consequently the matrix is much less vulnerable to this form of attack than the conventional type of matrix. The cowling design lends itself to a simple form of protection for the radiator collector tank. It can be produced as a thick light alloy casting or forging which forms an effective bullet deflector."

In that same discussion thread is also attached a copy of a Flight magazine article from 1946 where one can see the annular radiator installation. One can see how the radiator is slanted to better align with the airflow, and as a side effect also provides a smaller frontal area which the above quote refers to. https://ww2aircraft.net/forum/attachments/napier-engine-testing-1946-pdf.247236/

That report also contains a comparison of the cooling drag of various radiator installations, with the annular providing substantially less drag than the chin mounted, leading edge, or the Centaurus powered radial engine cooling drag. In particular vs. LE radiators, it quotes another RAE report stating that
"Thus, we see that 8-9 sq.ft. of radiator would be required to keep the percentage cooling drag at all comparable with present day v[UNCLEAR]. The ring radiator installation is the only scheme devised to date which provides such a large radiator without unduly high tare drag". Indeed if you look at pictures of the Tempest Mk I prototype with the LE radiators, those radiators are rather huge and chunky and I can certainly believe they cause a lot of drag.

In light of the above I think I should revise my opinion above such that after a Mustang style radiator installation, my second preference would be the annular one.

z42 said:

Indeed if you look at pictures of the Tempest Mk I prototype with the LE radiators, those radiators are rather huge and chunky and I can certainly believe they cause a lot of drag.

Click to expand...

How does that corroborate with the notion that 'proof is in the pudding'?

tomo pauk said:

How does that corroborate with the notion that 'proof is in the pudding'?

Click to expand...

Hmm, well that RAE report linked above shows results from wind tunnel tests with different radiator arrangements for the Tempest, and the per those tests the LE installation does have pretty high drag, in fact not much less than the chin radiator.

But yes, aerodynamics seems to be one of those topics where results can be highly unintuitive, and one should be very careful about making sweeping generalizations.

z42 said:

Hmm, well that RAE report linked above shows results from wind tunnel tests with different radiator arrangements for the Tempest, and the per those tests the LE installation does have pretty high drag, in fact not much less than the chin radiator.

Click to expand...

Unfortunately, the RAE report does not note how much the drag from the wing section behind the LE radiator was decreased due to the LW radiator taking the brunt of the slipstream now. IOW - it is abut total drag of the aircraft, not just how much drag this or that installation imparts.

z42 said:

But yes, aerodynamics seems to be one of those topics where results can be highly unintuitive, and one should be very careful about making sweeping generalizations.

Click to expand...

FWIW, the fastest Hawker fighters were the ones with LE radiators.

tomo pauk said:

Unfortunately, the RAE report does not note how much the drag from the wing section behind the LE radiator was decreased due to the LW radiator taking the brunt of the slipstream now. IOW - it is abut total drag of the aircraft, not just how much drag this or that installation imparts.

Click to expand...

Hmm, I'm not sure how you could meaningfully measure the radiator in isolation, if that's what you're saying? I'm no aerodynamicist, but the way I'd setup an experiment like this is that I'd have a baseline airframe without any radiators at all, and measure the drag of that. Then the cooling drag of the various radiator variants would be the difference between said airframe with a particular radiator arrangement and the baseline.

I am sure other nations did it too, but the US would build a model of the general shape of the aircraft (wing size and fuselage shape and tail) and then add or subtract "details" to see how much each detail was worth.

However when you start playing with radiators thigs get complicated real quick. With a short radiator duct you are gaining certain things and giving up others while a long radiator duct reverses a few things.
Trying to figure out the drag the 300-400mph airflow through an interior duct pretty much means you need a full scale model of the duct.
You need a longer duct than needed just for cooling to get the Meredith effect work but a long duct means more drag from both the external and internal airflow.
The DH Vampire was designed the way it was to minimize losses in the ducts.

That was also the reason that sticking the engines out under the wings or inside the wings was popular.
Now with both jets a Meredith effect you have the duct acting somewhat like a RAM jet. You not only have the air causing friction in the inlet/s but the early jets had really crappy compression ratios. Some times under 4 to 1 and the speed of incoming air made a difference to the total thrust. Slow it down too much and the engine wasn't burning quite as much air and was making less power. Same thing on the exhaust end. A long pipe slowed down the jet exhaust and hurt power.
Getting the right balance on the radiators was tricky. A smaller duct might not give you as much thrust but it might have less drag. The big duct could give you more thrust but it was also going to create more drag.
Where was the "happy" point?

For reference (for even better photos, you'll need an account and probably buy them), but Boeing does have photos on one of their media sites that has some detail photos of the P-51, A-36, and XP-51B radiator developments, as well as the final Merlin Mustang (P-51B/C/D/K) radiator. Not much on the P-51H's radiator in particular, but it does have some good action/inflight and ground shots of it and the F-82 if you're curious.