Race and high performance road car engines often have a higher number of cylinders in relation to overall capacity, compared to engines designed to optimize cost and reliability over ultimate performance.
The reasons multiple cylinder engines produce more power for the same cubic capacity are:
- Smaller bore x stroke = smaller pistons + smaller connecting rods + lighter crankshaft = less mass to accelerate on each stroke = quicker revving/higher max R.P.M. = more power = higher top speed + faster acceleration.
- More cylinders = more valves = higher rate of fuel throughput = greater power output.
Downsides to multi-cylinder engines include:
- Greater complexity of manufacture.
- Greater expense.
- Increased difficulty of servicing and shorter intervals between services.
- Greater complexity and difficulty of setting up and tuning engine to optimize performance.
- Reduced reliability and robustness.
Nowadays there are fairly stringent reliability regulations in Formula 1 and there are penalties for teams who have to replace too many engines in one season in order to control costs, but as a general principle the ideal racing car engine is one which disintegrates immediately after crossing the finish line!
Of course it's impossible to design an engine that precisely, but historically you'll find that racing engines are extremely strong when used within their intended design envelope (eg full rebuild every few dozen miles, scrapped after a few thousand miles) but tend to blow up spectacularly if they exceed the envelope by even a small amount. (eg if under serviced, over-revved etc.)
The reason for this is a combination of weight saving + trying to extract the absolute maximum power output and also a result of the compromise between those two goals and reliability. Racing car success can depend on the tiniest of margins. If your car is consistently 0.1 of a second faster than its nearest rival on a particular track, then that equates to a 5 second lead at the end of a 50 lap race. That is why racing car designers will attempt to use any possible means available to them in order to make their cars just that little tiny bit faster.
Weight is also incredibly important on a racing car. You might think that saving 1 gramme of weight on one component wouldn't make any difference, but if you can save 1 gramme on each of a car's 1000 components, then you've saved a total of 1 Kilogram, which on a lightweight racing car, can make a measurable performance increase. On a racing car, a V16 engine, may well be more expensive, more complicated and less reliable than the same capacity V8, but all other things being equal, if it weighs 2% less and produces 2% more power and is still reliable enough to finish races, and the team have the budget to build and run it, then (regulations permitting) they're going to use it.
The engine is not the only component on a racing car, but it's one of the most important for determining the car's ultimate performance. In Formula 1, the added cost and complexity of multiple cylinder engines is far outweighed by their performance advantage over a same capacity straight 4 for example.
In modern Formula 1 there are many complex regulations, governing engine design, reliability, energy recovery, fuel consumption, overall weight of cars, etc etc. and the number of cylinders and layout allowed may sometimes be defined by regulation rather than performance, but in general, a well designed and built many-cylindered engine will out perform one of the same capacity, but with fewer cylinders.