The croquet shot

The split shot:

and the take-off shot:

are names for the two extremes of swing angle of the mallet for this stroke.

There's some interesting discussion on the Oxford Croquet site:
Aiming in Croquet Strokes - Not Half the Angle!
Mid-Point Aiming
Take-Offs: Where to Aim?

The general picture is:


  1. θ is the angle of swing of the mallet. Also called 'line of swing' and 'line of aim' in the figures above.
  2. φ is the angle at which the struck ball, 'R', takes off.

When θ is small, say less than about 20°, we're playing a split shot and φ is twice θ. This corresponds to the rule 'swing at the angle which bisects the direction in which you want the struck ball to go, and the line through the centres of the balls'. So the slope of the graph of φ as a function of θ is 2 near the origin.

When θ is slightly greater than 90° the shot is a fault because the croqueted ball does not move, φ = θ and the slope of the graph is 1.

But what happens when θ is slightly less than 90°? The graph must be continuous, and probably smooth because these are classical dynamics, so must follow some curve from (22.5, 45) to (90, 90), but what is that curve?

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