How compression ratio effects power output of an engine

Since I need new pistons in my non voluntary engine rebuild I’m considering upping the compression ratio to extract more power.
But how much more HP can I expect by going from stock 9.7:1 CR to 11:1 CR which is the most sensible aftermarket option at the moment for the MZR L5.

There are a lot of  “x amount of CR increase = y amount of HP” out there that varies from around 2-5% depending on where you look.

I think this video by Engineering Explained is a good introduction to what actually happens:

The long short version:

Raising CR will increase thermal efficiency of the engine.
Thermal efficiency is the percentage of heat created in the air/fuel mixture during the compression stroke that will be converted to pressure during the combustion in the power stroke.  It’s the pressure of the combustion that is driving the piston down = power.

The formula for thermal efficiency in an otto engine is:


CR=compression ratio
K = specific heat ratio of air.  This is 1.35 during the combustion (750C)

This formula can be found on numerous other articles on the web as well but often with a different K value of 1.25 or 1.4 resulting in a different outcome.

So, if I go from 9.7 to 11:1 CR my theoretical thermal efficiency increase is

1-(1/11^(1.35-1))  -  1-(1/9.7^(1.35-1))) = 56.7% - 54.8% = 1.9 %

If I understand this correctly a set of shiny new 11:1 CR pistons on a 100hp engine will give an extra 1.9 hp at the same AFR.  Not impressed.

But I didn’t take boost into consideration.
Of all the threads and articles I googled online I found Bob Cross explanation to be relevant:

Static vs. Effective compression: Why does higher effective compression not require higher octane gas?

The formula for calculating CR under boost, or “Effective Compression Ratio” is:

<pre style="background-color: #eeeeee; border: 0px; color: #222222; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, sans-serif; font-size: 13px; margin-bottom: 1em; max-height: 600px; overflow: auto; padding: 5px; width: auto; word-wrap: normal;">ECR = sqrt((boost+14.7)/14.7) * CR</pre>For my current CR of 9.7  and 9 psi this equates to:
sqrt((9+14.7)/14.7) * 9.7 =  12.3:1  CR

For 11 CR pistons this is:
sqrt((9+14.7)/14.7) * 11 = 14:1 CR

If we put those numbers into the thermal efficiency formula we get… even less raise in E :
1-(1/14^(1.35-1))  -  1-(1/12.3^(1.35-1)))  = 1.8 %

If this ECR calculation is correct the 12.3 ECR with the 9.7:1 pistons is already quite high for 91 octane or the Norwegian 95 RON.  WI will fix that but the 14:1 ECR with the 11:1 pistons is the same as the current SkyActive engines with DI and other magic tricks.

Based on the ECR I would think that 9.7 is not that bad as 91 is still an option even without WI.
The theoretical power increase of just ~ 2 % might not be worth the hassle of being closer to detonation.

At the time of writing the only aftermarket piston options for the L5 are 9, 11 and 12.5:1 CR. Going down from 9.7 to 9 seems like a bit of waste as you need even more boost including the MP62 heating it to get to the current power level. 10:1 would be perfect. Even 9.5:1 would be great.
I could always just go for new stock pistons but then I’ll need to find the definitive answer to my engine problems.

Some other interesting things about CR that I found googling:

The Carnot theorem, or how the speed of the compression (RPM) will influence the  energy released during combustion:

Pressure ratio and how higher CR will reduce pumping losses:


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