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Dr Ian Plummer

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Technical
Analysis of Video showing Pull

Bob Kroeger writes:
I wanted you to see Howard Holdsclaw's croquet swing machine in action.  Howard is a retired physicist having served in the US Army Corps of Engineers. He did 60 degree drive shots with his machine and explains the setup of it in this video.  He actually did several shots but there is a video of just one: http://www.youtube.com/watch?v=sPR97qw9vdo  At the end of the shot you'll see a graph he created showing all his results.  Please choose the HD playback option using full screen - it will be easier to see the graph with the coloured balls.

12/01/2011


Observations on Swing Machine Results

  1. More energy goes into the croqueted ball, (~60%, 1:1.6, assuming distance proportional to energy).
  2. The ratio scroqueted/sstriker, where s is the distance travelled, is quite large but not correlated with distance.
  3. Both balls end up closer to the aiming line than expected by the initial geometry.
  4. The croqueted ball moves proportionally closer to the aiming line than the striker’s ball for an equivalent distance travelled.
  5. The striker’s ball does not travel in a straight line (the path of the croqueted ball was not visible).

Comments

A). Energy Distribution

From the Howard Holdsclaw's graph (below) of a number of trials (a-h), the lengths of travel of the balls were measured (arbitrary units) and their ratio, scroqueted/sstriker,calculated. The ratios varied from 1:1.29 to 1:1.88 as shown in the following table.

Trial

scroqueted

sstriker

scroqueted/sstriker

a

100

61

1.64

b

102

79

1.29

c

113

60

1.88

d

122

84

1.45

e

186

101

1.84

f

188

115

1.63

g

175

108

1.62

h

189

116

1.63

Average

1.6

If we were dealing with the classical ice pucks and striking exactly between the expected paths we would expect both pucks to travel the same distance.  Here we find a ratio of ~1.6. It does not seem to be due to the coefficient of restitution, since when the balls are initially struck there is solid contact between the balls and they can be treated as a single entity. Being of equal mass they should share the total input energy equally. Perhaps the striker’s ball is making multiple transits between the croqueted ball and the mallet, or it is a solely mallet-ball interaction, e.g. possibly the mallet rubbing on the ball causing back spin, or rubbing the striker’s ball into the turf.

Bob Kroeger's Graph - click for larger image

Howard Holdsclaw's distance/position graph. Click for larger image

B). Reproducibility of Measurements

There was no trend in the ratio of distance travelled by both balls with the strength of the shot (see table above) so this suggests experimental scatter.  Scatter could be due to the balls being not quite in contact, variations in the balls or the terrain conditions. This latter could be debris on the route, wind or wear. It has been noted previously when a ball is rolled down a ramp and its track measured, its track gets longer and longer with each successive trial as the grass gets progressively flattened.

Striker's ball position over time

C). Pull Demonstrated

The final positions of the balls deviate from the simple (school level physics) projection of their initial paths. They lie on the dashed lines not the solid lines in Howard's graph. They move, as folk-law on pull predicts, towards the aiming line.

D). The Croqueted Ball Pulls More than the Striker’s

For the same distance travelled, the croqueted ball ‘moves in’ around twice (1.92x) the distance of the striker’s ball from the geometrically predicted paths.  Clearly the croqueted ball gets more of whatever is causing pull than the striker’s.  If, as conventional wisdom suggests, it is spin about a vertical axis then one can imagine that the interaction of the striker’s ball with the mallet face could decrease the spin.  It would be interesting to try the same stroke with the mallet faced with emery paper or Teflon film to change its grip on the striker's ball.

E). Pull Results in Curved Tracks?

(... for the striker’s ball at least!)  I put plastic film over my monitor and plotted the ball positions of the striker’s ball with respect to the marking strings from the video.  I moved the film to compensate for the frame jitter which shifts the image. The curved track is shown in the diagram (right).  The green lines are just to guide the eye, the red spots are the data. Clearly there is a perspective effect due to the angle of view which affects the scaling of the image but the string (blue lines) shows that this is marginal. Further tests would be needed to be sure that this was repeatable and not say, due to bias on the ball.

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Updated 28.i.16
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