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Dinan has a good article on BMWs and Dynos that showed a 11HP increase for a stock M3 just from switching from AKI 91 to AKI 93 gasoline.
Stock E46 M3 Ignition Timing Adaptations
Figures #23 and #24 below are taken directly from the BMW factory diagnostic tool, demonstrating how ignition timing adapts to different fuel octane ratings. The same car is represented here, the only difference being the octane rating of the fuel. If you were to add 1° of ignition advance, the engine management system would detect it and retard the timing 1°. You can see that adding timing in the engine management software or "power chip" is futile because the computer will negate the change, as sufficient octane does not exist. However, you can see that adding higher octane fuel is like adding a "power chip" as the system adapts to the better fuel, making more power.
You will see with the 91 octane gas, cylinder 1 has a knock adjustment of MINUS 4.99 degrees, with the 93 octane the adjustment changes to just MINUS 2.47 degrees, or in other words it advanced the timing by about 2.5 degrees based on the octane.
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