With high compression, you will need to run higher boost pressures to create similar power to a low compression equivelent engine as you will need to wind back the ignition timing loads (and run your engine very hot) as you will have a vastly increased dynamic compression ratio.
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In turbocharged engines there is a fine balancing act when it comes to making a lot of power on low octane fuel. In most cases, ignition timing must be retarded as the boost pressure rises above a critical point and finally there reaches a further point where the engine simply loses power. If the timing was not retarded with increasing boost, destructive preignition or detonation would occur. Normal combustion is characterized by smooth, even burning of the fuel/air mixture. Detonation is characterized by rapid, uncontrolled temperature and pressure rises more closely akin to an explosion. It's effects are similar to taking a hammer to the top of your pistons.
Most engines make maximum power when peak cylinder pressures are obtained with the crankshaft around 15 degrees after TDC. Experimentation with increasing boost and decreasing timing basically alters where and how much force is produced on the crankshaft. Severely retarded timing causes high exhaust gas temperatures which can lead to preignition and exhaust valve and turbo damage.
We have a hypothetical engine. It's a 2.0L, 4 valve per cylinder, 4 cylinder type with a 9.0 to 1 compression ratio and it's turbocharged. On the dyno, the motor puts out 200hp at 4psi boost with the timing at the stock setting of 35 degrees on 92 octane pump gas with an air/fuel ratio of 14 to 1. We retard the timing to 30 degrees and can now run 7psi and make 225hp before detonation occurs. Now we richen the mixture to 12 to 1 AFR and find we can get 8psi and 235 hp before detonation occurs. The last thing we can consider is to lower the compression ratio to 7 to1. Back on the dyno, we can now run 10psi with 33 degrees of timing with an AFR of 12 to 1 and we get 270 hp on the best pull.
We decide to do a test with our 9 to 1 compression ratio using some 118 octane leaded race gas. The best pull is 490 hp with 35 degrees of timing at 21 psi. On the 7 to 1 engine, we manage 560 hp with 35 degrees of timing at 25psi. To get totally stupid, we fit some larger injectors and remap the EFI system for126 octane methanol. At 30psi we get 700hp with 35 degrees of timing!
While all of these figures are hypothetical, they are very representative of the gains to be had using high octane fuel. Simply by changing fuel we took the 7 to 1 engine from 270 to 700 hp.
From all of the changes made, we can deduce the effect certain changes on hp;
Retarding the ignition timing allows slightly more boost to be run and gain of 12.5%.
Richening the mixture allows slightly more boost to be run for a small hp gain however, past about 11.5 to 1 AFR most engines will start to lose power and even encounter rich misfire.
Lowering the compression ratio allows more boost to be run with less retard for a substantial hp gain.
Increasing the octane rating of the fuel has a massive effect on maximum obtainable hp.
We have seen that there are limits on what can be done running pump gas on an engine with a relatively high compression ratio. High compression engines are therefore poor candidates for high boost pressures on pump fuel. On high octane fuels, the compression ratio becomes relatively unimportant. Ultimate hp levels on high octane fuel are mainly determined by the physical strength of the engine. This was clearly demonstrated in the turbo Formula 1 era of a decade ago where 1.5L engines were producing up to 1100 hp at 60psi on a witches brew of aromatics. Most fully prepared street engines of this displacement would have trouble producing half of this power for a short time, even with many racing parts fitted.
Most factory turbocharged engines rely on a mix of relatively low compression ratios, mild boost and a dose of ignition retard under boost to avoid detonation. Power outputs on these engines are not stellar but these motors can usually be seriously thrashed without damage. Trying to exceed the factory outputs by any appreciable margins without higher octane fuel usually results in some type of engine failure. Remember, the factory spent many millions engineering a reasonable compromise in power, emissions, fuel economy and reliability for the readily available pump fuel. Despite what many people think, they probably don't know as much about this topic as the engineers do.