The piston crown refers to the top of the piston.
A piston can generally be divided into two sections (though the piston is a single piece). The lower part of the piston is called the skirt. The upper part, including the top of the piston that faces the valves and must handle the combustion of the fuel-air mixture, is called the crown. The piston crown must have the mechanical strength to withstand the forces of combistion, and must be made of materials that will withstand the heat of combistion. All this must come in a package that has limited thermal expansion so that the tolerances within the engine are tighter and performance is maximized.
The upper face of a piston assembly is called the crown or piston crown. It is the top surface of the piston that comes into contact with the combustion gases during the engine's operation.
The central part of the top of a piston, often raised in some engines.
Piston crown burn is typically measured by visually inspecting the piston crown for signs of scorching or discoloration due to heat exposure. The extent and severity of the burn can be assessed by measuring the size and depth of the affected area. Additionally, analyzing the material composition and structure of the piston crown through microscopic examination can provide further insights into the cause and severity of the burn.
Piston crown is the top, skirt is the side below the ring lands (ring grooves). The as you say, the skirt often has cut aways to clear the counterwieghts on the crankshaft.
A larger piston skirt to cylinder wall contact raises piston cooling. With turbo motors, they have piston oilers, they spray oil on the underside of the pistons, cooling the piston /crown.
Hottest part is the piston crown....
cracked oil ring on piston
Piston protrusion is typically measured by placing a dial indicator on the top of the piston while it is positioned at Top Dead Center (TDC). The measurement is taken from the piston crown to the deck surface of the engine block. This measurement is important for ensuring proper clearance and compression ratio in an engine.
compression rings.. while the bottom ring is known as oil ring .
rising piston compresses air/fuel mixture , then ignited at top, heat raises pressure, pressure on piston crown creates force, force over stroke = work
pre ignition , example : carboned up piston crown retains heat from previous burn and combined with compression , self ignites before firing point tending to stall rising piston
You can find an inexpensive tool at your local auto parts. This works best.