How are the cams and pistons properly aligned mathematically

This has been puzzling me for some time now. Even my Mechanical Engineering teacher never gave me an answer on this. Taking for example a V8 or V6 4 stroke Engine 4 valve per piston. How is the firing sequence calculated and how is the camshaft aligned to the crankshaft with accordance to the 4 stages of the piston. Suction, Compression, Ignition, Exhaust. How did the Otto guy who invented the 4 stroke engine come up with this mathematically?

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Basically, the inlet cam opens the inlet valve throughout the inlet stroke; the exhaust cam opens the exhaust valve throughout the exhaust stroke. You also need to increase the duration to compensate for any slack in the system. You may choose to provide a small amount of overlap (where both inlet and exhaust valves are a little open at the same time) to flush the last of the exhaust gas out. You may also want to open the exhaust valve a little early (before BDC) and close the inlet valve a little late (after BDC).

The values you choose will have an impact on the performance of the engine (both power and economy). I don’t think these decisions are done mathematically, but on past experience of how different cam profiles produce different characteristics of engine performance.

 
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