Davin Johnson
Are You Inclined to Putt?
Background, Purpose, Hypothesis
I decided to do my science fair project on something related to golf because it is my
favourite sport. I decided to study the putting aspect of golf because for many golfers it is the
most challenging part of the game. Even professional golfers have difficulty judging the strength
of hit required for uphill or downhill putts. From watching golf on television, it appeared to me
that golfers had more trouble judging putting distance on fast, dry green surfaces. I wondered if
there was some way I could investigate this with a science fair project.
The purpose of the project was to try to investigate the relationship between the strength
of a putting stroke and the degree of inclination and the speed of the green. It was assumed that a
typical putt could be studied from the physics standpoint. The ball would have an initial velocity
(which could be measured with a motion sensor), a final velocity (which would be zero since a
putt stops), and a displacement (which one could measure). Acceleration could be calculated
using this data. The degree of inclination could be easily controlled and measured with a ramp
system. Different green surfaces (fast or slow) could be simulated with different carpet remnants.
Some preliminary research suggested that the primary frictional forces would be those of rolling
friction, which is far less in magnitude than conventional sliding friction. It was hoped that this
approach would allow a quantitative assessment of putting.
The hypothesis was that faster green surfaces would be more sensitive to variations in the
inclination of a putt. This means that putting speed would have to be adjusted more for downhill
and uphill putts on a faster green than on a slower green. This hypothesis was supported by a
theoretical analysis of the physics of a rolling sphere.
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Davin Johnson: Are You Inclined to Putt?
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Procedure
A putting machine was designed and built. It was divided into three parts: the putter
swinger, a ramp, and an inclination adjuster. The putter swinger was a putting club mounted as a
pendulum. The 8 foot (2.5 meter) ramp was double-sided and had a slow carpet surface on one
side and a faster surface on the other. A stimpmeter (which measures green speed) was used to
verify that the slow and fast carpets mimicked real green conditions (with readings of 8 feet and
14.5 feet, respectively). The inclination adjuster held the foot of the ramp and could be adjusted
to give different slopes. Balls were hit on both surfaces with different inclinations. Varying
velocities gave putts ranging from 0.5 to 2 metres. The initial velocity of the ball was measured
with a motion sensor, and the distance of the putt was documented. The results were analyzed.
Results/Observations and Conclusions
A lot of interesting data was generated. The graphs of experimentally measured distance
versus initial velocity gave relatively straight lines that shifted as inclination changed. The
calculated acceleration (actually deceleration) versus initial velocity also gave largely linear
relationships that again shifted as inclination was modified. Analysis of this experimental data
allowed the determination of the initial velocity required on different inclinations (and different
green speeds) to achieve putting distances of 1 and 2 metres.
From the physics standpoint, the results verified that deceleration of a golf putt depends
on at least three factors: green surface, green inclination, and the initial velocity of the putt.
Slower greens have a greater deceleration (when inclination and initial velocity are kept
constant). Deceleration increases for uphill putts and decreases for downhill putts. Interestingly,
deceleration is fairly uniform for all initial velocities on a faster green but deceleration increases
as initial velocity increases on a slower green. This may be because the harder hit on the slower
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Davin Johnson: Are You Inclined to Putt?
Page 2 of 5
green causes some initial bouncing and sliding which increases the friction. This effect is much
less on a faster green where one does not need to hit the ball as hard.
The results seemed to prove the hypothesis in that it showed that more compensation was
required for inclination on fast surfaces (with less friction) than for slow surfaces (with more
friction). This means that a golfer putting on fast greens must hit downhill putts really softly and
uphill putts much harder compared to a level putt. On a slower surface, there would be less of a
variation on the strength needed to hit uphill or downhill putts compared to a level putt.
Acknowledgement
I would like to thank my mom and dad for financing the materials used in the project and
also for advice during construction of the apparatus. Also thanks goes to my dad for operating
the putter swing, as it was necessary for two people to be present at all the trials (one to operate
motion sensor, one to swing the putter). Finally I would like to thank Victoria East Golf Club in
Guelph for lending me the stimpmeter so that I could quantify the green speeds.
References
Barry, Maurice et al. (2002). Physics 12. Toronto: Thomson Canada Limited.
BMS Europe Ltd. (n.d.) Stimpmeter- Greens Speed Measurement Tool. Retrieved November 3,
2002 on the World Wide Web: http://www.greenkeeper.co.uk/products/golf/stimpmeter/
Kurtus, Ron. (2001 October). Rolling Friction and Automobile Tires. Retrieved November 3,
2002 on the World Wide Web: http://www.school-forchampions.com/science/frictionrolling 2.htm
Putting Physics. (n.d.) Retrieved November 3, 2002 on the World Wide Web:
http://www.geocities.com/Augusta/Fairway/5090/linkslsgloss ary.html
Rolling Friction. (n.d.) Retrieved November 3, 2002 on the World Wide Web:
http://webphysics.davidson.edu/faculty/dmb/PY4 30/Friction/rolling.html
The United States Golf Association. (n.d.) The Stimpmeter. Retrieved November 3,2002 on the
World Wide Web: http://www.cyberturf.co.za/pages/interests_thestimpmeter.ap
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Davin Johnson: Are You Inclined to Putt?
Page 3 of 5
Distance vs. Initial Velocity for Putt on Slow Green
2.5
Inclination
2.4 degrees
down
Distance (m)
2.0
1.2 degrees
down
1.5
level
1.2 degrees
up
1.0
2.4 degrees
up
0.5
3.6 degrees
up
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Initial Velocity (m/s)
Distance vs. Initial Velocity for Putt on Fast Green
2.500
Inclination
1.2
degrees
down
Distance (m)
2.000
0.6
degrees
down
1.500
level
1.000
1.2
degrees up
0.500
2.4
degrees up
0.000
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
Initial Velocity (m/s)
Acceleration vs. Initial Velocity for Putt on Slow Green
Acceleration vs. Initial Velocity for Putt on Fast Green
Initial Velocity (m/s)
0.000
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
0.000
0.000
2.000
Initial Velocity (m/s)
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
Inclination
-0.100
-0.100
Inclination
-0.200
1.2 degrees
down
-0.300
0.6 degrees
down
-0.400
level
-0.500
1.2 degrees
up
-0.600
2.4 degrees
up
Acceleration (m/s2)
Acceleration (m/s2)
-0.200
-0.300
-0.400
2.4 degrees
down
1.2 degrees
down
level
-0.500
1.2 degrees
up
-0.600
2.4 degrees
up
-0.700
3.6 degrees
up
-0.700
-0.800
-0.800
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Davin Johnson: Are You Inclined to Putt?
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Effects of Inclination and Green Speed on Straight Putts
1.800
Initial Velocity of Golf Ball (m/s)
1.600
1.400
2m Fast Putt
1.200
2m Slow Putt
1.000
1m Fast Putt
0.800
1m Slow Putt
0.600
This graph shows experimentally determined initial
velocity required for one or two meter putts on
variably inclined slow and fast green surfaces. Note
that the curves for the fast greens are steeper.
0.400
0.200
0.000
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
Angle of Inclination (degrees)
Compensation Required for Inclined Putts on Fast and Slow Greens
Compensation (Percentage of Level Incline Hit Required)
140
Fast Green
130
120
Slow Green
110
Downhill (-1 degree) Putt
1m
2m
1m
2m
100
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90
80
1m
2m
1m
2m
Uphill (1 degree) Putt
Slow Green
70
60
50
Fast Green
40
Davin Johnson: Are You Inclined to Putt?
Page 5 of 5
This bar graph shows relative initial
velocity (compared to a level putt) that is
required to roll the ball one or two
meters for a downhill or uphill putt.
Note that there a much higher percentage
adjustment required for faster greens.