What is the primary purpose of supplying a rich mixture to the cylinders during takeoff and climb?

Supplying a rich mixture to the cylinders during takeoff and climb primarily serves to cool the charge temperature and prevent detonation. During these phases of flight, the engine operates under high loads and elevated manifold pressures, which can increase the temperature of the air-fuel mixture significantly.

A rich mixture contains a higher proportion of fuel relative to air. This additional fuel evaporates and absorbs heat, helping to lower the overall temperature of the mixture entering the combustion chamber. By maintaining a cooler charge, the risk of detonation—an unwanted and potentially damaging premature combustion due to excessive pressure and temperature—is greatly reduced. Detonation can lead to engine knock and serious engine damage, hence it's critical during high-stress phases like takeoff and climb.

The focus on preventing detonation is particularly important in aviation, where engine reliability and performance are crucial for safety. Although other factors such as thermal efficiency, volumetric efficiency, and excess power are important considerations for engine operation, the prevention of detonation through a rich mixture during takeoff and climb is the primary concern.