# Maths

posted by
**Karl Haxell**
.

The distance from TDC (top dead centre) for the pin is given by x when the crank is

at angle . Hence :

i) Give an equation for x in terms of the other variables (r, L and ).

ii) If the crank rod is rotating at a constant value of ω calculate the speed of the

piston

i.e. calculate

dt

dx

in terms of ω, r, and L

iii) Hence calculate the x value when the speed of the piston is at a maximum.

iv) If L is 1 metre, r is 0.25 metres and the crank is rotating at 5,000 rpm

calculate the maximum velocity of the piston in m/s.