More Curling Physics

This weekend I was away at a curling competition and the television at the curling club was televising professional curling. As I was watching some of these curlers deliver their rocks I noticed that a couple of them actually picked the rock up off the ice, usually when they want a faster shot. I was curious about exactly how much further the stone would travel if the “backswing” delivery was used with the same initial velocity, because this delivery is high risk and requires more work to be done by the curler to lift the 20 kg stone. Norikazu Maeno determined that the coefficient of kinetic friction of a granite curling stone on a pebbled ice surface is 𝜇=0.004 in his paper titled “Dynamics and Curl Ratio of a Curling Stone”. Using the conservation of energy: ΔKE = -ΔPE + WNC, the process of throwing the stone with a “backswing” can be broken into two parts  and compared to a stone that was simply pushed down the ice. The average curling stone is delivered at 2.0 m/s and weighs 20 kg, and when a stone has “backswing” the stone is lifted about 0.3 m off the ice. The first calculation for the “backswing” is as follows:

(½)mvf2 - (½)mvo2 = -(mghf - mgho)

(½)(20 kg)vf2 - (½)(20 kg)(2.0 m/s)2 = -[(20 kg)(9.8 m/s2)(0 m) - (20 kg)(9.8 m/s2)(0.3 m)]

Vf = 2.8 m/s

This means that as the stone falls, it increases in speed by 0.8 m/s. By comparing the distances travelled by a stone with and without “backswing”, we can see that this 0.8 m/s makes a huge difference in the outcome of the shot.

Without “backswing”:

(½)mvf2 - (½)mvo2 = WNC WNC = 𝜇mgd

(½)vf2 - (½)vo2 = 𝜇gd

(½)(0 m/s)2 - (½)(2.0 m/s)2 = (0.004)(9.8 m/s2)d

d = 51 m

With “backswing”:

(½)mvf2 - (½)mvo2 = WNC WNC = 𝜇mgd

(½)vf2 - (½)vo2 = 𝜇gd

(½)(0 m/s)2 - (½)(2.8 m/s)2 = (0.004)(9.8 m/s2)d

d = 100 m

Through these simple calculations, you can see that the “backswing” is an extremely effective technique to almost double the distance the stone travels. Although the rotational motion of the stone was not accounted for in this calculation, the results are still significant enough to see that the “backswing” technique is high risk but also high reward.