I have read on another forum of club racers that people are looking closely at going to a smaller capacity engine on the basis that the smaller engine will provide a wider power band for the given restrictor size in their class.
The engines are production based 4 cylinder turbo engines, but that's trivial as they're fundamentally quite similar. Is their theory flawed or is there an optimum restrictor size for a given engine capacity?

Yes.

Actually, what you meant is there an optimum engine size for a given restrictor? (The optimum restriction for a given engine capacity is zero, har.) The answer is not really/it depends. In most all rules regimes & engines the optimum displacement is maximum allowed, I have to think. Especially with a turbo. However, as with many things in life you can do it the wrong way and still come out ahead. A little birdie told me there is a V10 production racer in Europe running on 8 cylinders to great effect, and this comes on good inside authority from a person not totally crazy. (This is one of those stories that makes perfect sense or is completely ridiculous once you really look at it, or both. Like freon in your tires.) For the Viper (oops, I blabbed) there might be tangential considerations including tire and fuel management.

However, the optimal way to match the engine to the air restrictor is with port volumes and valve timing etc while keeping the displacement at legal maximum. That is a complicated engine-specific process that can only be worked out experientally, really. And from there, matching the engine's internals to its true loadings rather than its hypotheticals. There is no sense designing an engine to handle 800 hp and 10,000 rpm if the restrictor will only allow 500 hp and 6000 rpm. Consequently some of these air-restricted engines now look like jewelry on the inside, with dainty little recip and rotating parts to minimize friction and intertia. (Just as with rev limter engines.) People would be shocked to see what one current GT engine looks like disassembled... resembles bicycle parts. As with all rules, with air restrictors eventually you breed a race of freaks.

For normally aspirated engines:

The way the restrictor works to limit power, is that the airflow will go sonic at a certain mass flow and 'choke' meaning the mass flow is constant from that point onward. Power is proportional to mass flow, and the mass flow of the engine is proportional to rpm (given a constant VE).

So, a smaller capacity engine chokes the restrictor at a higher rpm than a larger capacity engine. Seems to me the 'wider power band' mentioned above must in fact mean a wider rpm range. If it referred to the torque curve then the larger capacity engine has the advantage as it develops peak power over a larger rpm range.

As long as the gearing can be adjusted accordingly then I would favour the larger capacity engine revving lower. You would need to extract less BMEP from the engine for equal performance, meaning less stress internally.

Add a turbo and you can approach a constant power engine, as seen in the WRC, by choking the restrictor constantly at all rpm's. But you still need a higher BMEP for a smaller capacity engine, and the system mass flow is still dictated by engine capacity, so I see no reason why this changes anything.

Regards, Ian

But the frictional losses in the engine increase as you increase the swept volume, and speed, of the engine. So there is still a tradeoff.

So far as the powerband goes, in percentage terms (ie as a proportion of max power rpm) there must be some subtle interaction with engine size, but it doesn't spring out at me.

Any idea how these two scale? I doubt friction is precisely linear with either capacity or rpm, but I wouldn't know what relationship to use in an analysis. All I can say is an engine has an 'easier' time at lower BMEPs which suggests capacity not rpm is better. Witness the trend in LMP to build large capacity engines whether turbocharged or not, both gasoline and diesel.

Regards, Ian

SAE Paper 2002-01-3362 goes somewhat into this subject, although the primary focus is naturally aspiranted engines vs. turbocharged engines in endurance racing (Le Mans).

In general, with restrictor equipped engines it's advantageous to use a small low speed engine to reach the desired output. Since the airflow through the engine is restricted by the restrictor, the only possible methods to increase performance is to increase the output in relation to the air consumption (by for example friction reduction measures) and/or to increase the rpm range over which a high engine output is given.

In the case of endurance engines, a low fuel consumption and high reliaility tend to be the focus and this require an engine designed not to run that much beyond choke while an engine designed for maximum performance, as a WRC car, tend to use engine speeds much beyond choke. A WRC car for example begin to choke the restrictor at about 3000 rpm, but maximum engine speed is usually closer to 8000 rpm. As a WRC car is turbocharged, much of the work is focused around getting boost at low speed and then gradually decrease the boost as engine speed increase so the restrictor can be kept at choke for the widest rpm range possible. Naturally, to reduce losses are of great interrest too.

Due to the nature of the restrictor, restrictor fitted engines tend to use mild cams.

In LMP, Audi (and Peogeot) decided to use a larger displacement engine for the diesel. This was not because it was the best option, but it was the safe option. Using a smaller engine would suggest very high (untested) bmeps and that would result in high piston temperatures and so on, making the design of the engine a much more difficult task from a reliability perpective.

On the other hand, if we look at Audis earlier LMP engines (gasoline), they were on the small side using a displacement of only 3.6 litres but also a rather low maximum engine speed. As paper 2002-01-3362 suggests, it's an advantage to use a small low speed engine. And remember that not only engine speed and bmep increase the load on the engine, but also displacement as pistons, rods etc gets heavier. In general the stress caused by high speed is the highest, followed by displacement and bmep.

Bmep is also not related to engine speed; in general a small high speed engine tend to use a similar bmep as a large slow speed engine. If the regs allow that is.

In addition to this we should not forget the effect on engine weight, size and cooling requirement. A small engine have in general an advantage when it comes to the two earlier, and in particular engine size (as some mass must be added to make the engine stronger), but a turbocharged engine generally has some disadvantage of the latter, as charge air cooling requires a lot of cooling air, and the amount increase with specific output (engine boost).

RCE did a small article (advertisment) about this using the Bosch engine sim program and incorporated the lapsim program (with different gross weights for each engine type).
I don't remember which issue it was, but it was last year sometime. The Bosch site should have it. I don't know anything about engines so I don't know how realistic the sim program is.

Flicking through Heywood I get the impression that there is enough info in it to give some guidance. The first thing you'd have to do is come up with a SOLID definition of powerband, and then what tradeoff you are prepared to make with power, until you do that you'll never be able to decide.

Interesting, thanks to everyone. I guess my use of 'powerband' was a bit ambiguous but ultimately the goal is still the same - tractable power delivery and a faster lap time.

McGuire, yes I have heard of that Viper being raced in the VLN. Definitely an anomaly for a couple of reasons - I believe it is to do with the Viper violating max capacity rules and then how many racing series would let you race with 8/10ths capacity and then everything else like non-homologated crank, etc?

I think with any given combination of displacement limit and restrictor orifice you are liable to encounter, displacement will win out over crank speed with respect to powerband or operating range... key factor in chasing the efficiencies around being pumping losses.

So that is the story. I was pretty sure I was being hosed, just didn't know how... my contact was implying it was a big secret when actually they would just rather not talk about it.

Nah, I distinctly remember my cynicism when the commentator announced it during the Nordschleiffe 24hr .
I don't know whether it has custom crank/cams/firing order/etc but common sense tells me it definitely would.

An engine builder that I worked with played around with this. He said gave some reasonable numbers, but felt that there was a bit of hand-waving involved in producing those numbers. He said the inputs couldn't possibly give you the amount of data that the output produced. He also said that, "This looks like an engine simulation that was done by a chassis guy." I believe this was an entire true observation.

The trick is going to be to keep the restrictor at it's maximum airflow rate for as much time as is possible, right? In naturally aspirated form, that means the biggest engine that you're allowed to run. In turbo form, that mean keeping the boost as high as possible. Getting high boost at low-ish RPM isn't an easy thing to do. There just isn't the energy or volume of exhaust to make it happen.

I can see how a small, boosted engine could have some advantages, though. First, you'd have to run it at high boost pressures to be competitive in terms of HP. If you can turn it up, then you can turn it down. This may allow you to reduce boost in low gears for better driveability or reduce boost in high gears for fuel mileage. At a place like Lemans, this could mean an extra lap which could be more of an advantage than the higher HP and lower lap time.

This game is not always about getting more 'plusses'. Sometimes the 'minuses' can be more of an advantage.