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# Acceleration of reciprocating piston with respect to crank angle

## Description

A piston is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod. The motion of a non-offset piston connected to a crank through a connecting rod (as would be found in internal combustion engines), can be expressed through several mathematical equations. The acceleration of the reciprocating motion of the piston with respect to crank angle (angle domain) can be calculated by the rod length, the crank radius and the crank angle. ( It’s second derivative, using the chain rule and the quotient rule).

Related formulas

## Variables

 ap Acceleration of the piston (in) r The crank radius (distance between crank pin and crank center) (in) A The crank angle (from cylinder bore centerline at top dead centre) (degrees) l The rod length (distance between piston pin and crank pin) (in)