kerbal-space-program
In 1.0 there is a new part, the engine precooler.
The description says, it "improves jet performance" but not how or by what amount.
According to the stats it appears to be just a combined intake and jet fuel tank. Is that all it does or does it indeed affect the performance of jet engines in some way?
To answer #1 I constructed a test rig.
As you described, the outer-engines overheat faster than the inner one regardless of vertical placement. This means that the overheating is not a result of the heat emission map (which extends in a cone underneath the engine that drops off rapidly and is hotter than the engine itself). When I placed temperature gauges on the same rig it didn't overheat at all which inadvertently gives us our answer.
All parts have three config parameters relating to heat: maxTemp, heatConductivity and heatDissapation. By default conductivity and dissapation are set to 0.08 and they are never redefined in the config files. This means that all parts, even the tiny temperature gauge will receive heat from neighboring components at the same rate.
In our scenario the inner engine has four components with which to transfer heat via conduction but the outer ones only have one so they overheat faster. To prevent the outer-engines from overheating you could install a heat sink in the form of a few structural girders.
As for #2 the wiki states that:
As of 0.18.2, this tank does not transfer heat effectively. Engines attached directly to it and running at full throttle (especially Mainsails) will overheat.
I suspect this is a deliberate tweak in the coding since my usual trick of adding a small girder between the tank and engine reduces overheating by an approximate factor of 8 instead of a factor of 2 which you would expect from abusing the heat conductivity parameter as described above.
EDIT
Based on a comment by Philipp I re-checked the results of #1 and it turns out that the inner engine heats up at a slower rate by transferring heat upwards into the command pod, not across to the other engines as I assumed.
Your question is actually about how fast you are going to spend the fuel of your first stage: Are you using four or five engines simultaneously to convert it into speed? When you use all 5 engines but throttle down to 80% thrust, it's exactly the same as if you would use 4 engines at 100% thrust. To answer this question, we first need to talk about what forces affect a rocket during lift-off.
There are two forces which prevent your rocket from getting into orbit.
The first, gravity, is accelerating your rocket constantly downward until you have enough horizontal velocity to cancel it (achieved a stable orbit). The more time you spend affected by gravity, the more speed ("delta-v") does the gravity give you which you have to cancel by expending additional fuel. For that reason it is economically to accelerate early, so you get to your orbit faster and consume less acceleration from the gravity.
But there is also the second force: atmospheric drag. Atmospheric drag depends on atmospheric pressure and speed. The relationship with speed is quadratic. The faster you go, the more speed ("delta-V") you lose through air friction. That means it might not be so good after all to go too fast while you are still in the lower atmosphere.
So where do these two factors cancel out?
The ideal speed to balance atmospheric drag and gravity drag (assuming perfectly vertical ascent) is equal to the terminal velocity on the current atmospheric density. That speed depends on how aerodynamic your vehicle is.
When you go faster than this, you are wasting fuel on atmospheric drag. When you go slower than this, you are spending unnecessary fuel to fight gravity.
To get back to your initial question "what's better: serial staging or parallel crossfeed staging": It depends on your total thrust-to-weight ratio in the lower atmosphere. But my general experience is that a rocket gets higher with cross-feeding.
But what when you are already in orbit?
The truth is, it doesn't matter. The amount of delta-v you get per liter of fuel depends on the total weight of the ship and the average fuel-efficiency (Isp) of the engines you use. It doesn't matter how fast (through how many engines) you spend it. All that matters is to avoid having more mass than necessary (get rid of fuel tanks when they are empty). An orbital transfer stage with less engine power is more efficient, only because it tends to have a lower overall mass. This, however, is bought with longer burn-times to get the same amount of delta-v. Longer burn-times can sometimes mean less efficient burns because you can't hit your maneuver nodes that exactly, but this only matters in situations where a burn is very time-critical.
Best Answer
Looking at the parts.cfg file for the engine precooler (
Kerbal Space Program\GameData\Squad\Parts\Aero\engineNacelle\engineBodyRadial.cfg), the part has three functions, which isThe whole part is mostly a copy&paste from the engine nacelle (
Kerbal Space Program\GameData\Squad\Parts\Aero\engineNacelle\engineNacelle.cfg). The only non-cosmetic differences are price and the lower "emissiveConstant" which is relevant to heat transfer between parts. So when the part gets really hot for some reason, nearby engines overheat a tad bit slower with the engine precooler than with the engine nacelle. That's everything. Nothing which directly alters the performance characteristics of attached jet engines.tl;dr: no, it does not enhance performance besides providing intake air and fuel.