PHYSICS OF
SPORT
COPYRIGHT: The
following articles may be downloaded for personal use only. Any other use
requires prior permission of the author and, in the case of Am. J. Phys. and
The Physics Teacher articles,
the American Association of Physics Teachers.
R.C. Cross, The dead spot of a tennis racquet,
Am J Phys, 65, 754-764, (1997).
R.C. Cross, The trajectory of a ball in lawn bowls, Am. J. Phys, 66, 735-738, (1998)
R.C. Cross, The sweet spot of a baseball bat, Am. J. Phys. 66, 772-779 (1998)
R.C. Cross, The sweet spots of a tennis racquet , Sports Engineering, 1, 63-78 (1998).
R.C. Cross, The bounce of a ball, Am. J. Phys. 67, 222-227 (1999).
R.C. Cross, Standing, walking, running and
jumping on a force plate, Am. J. Phys. 67, 304-309 (1999)
R.C. Cross, Dynamic properties of tennis balls, Sports Engineering 2, 23-33
(1999).
R.C. Cross, Impact of a ball with a bat or racket, Am. J. Phys. 67, 692-702 August
(1999).
R. Cross, Effects of friction between the ball
and strings in tennis, Sports Engineering, Vol 3 Number 2, p85-97 (2000).
R. Cross, Flexible beam analysis of the effects of string
tension and frame stiffness on racket performance, Sports Engineering, Vol 3 Number
2, p111-122 (2000).
R.C. Cross, The coefficient of restitution for collisions of happy
balls, unhappy balls and tennis balls, Am. J. Phys. 68, 1025-1031 (2000).
R. Cross, C. Lindsey and D. Andruczyk,
Laboratory testing of tennis strings, Sports Engineering, 3, 219-230
(2000).
R. Cross, Response to ``Comment on the sweet spot of a baseball
bat", American
Journal of Physics, 69, 231-232 (2001).
R. Cross, Customising a tennis racket by adding weights, Sports Engineering, 4, 1-14
(2001).
R. Cross, Why bows get stiffer and racquets get softer when the
strings are added, Am. J.
Phys, 69, 907-910 (2001).
R. Cross, The dual function of sand on a clay tennis court, The Physics Teacher, 39, 330-331
(2001).
R. Cross, Measurements of the horizontal coefficient of
restitution for a superball and a tennis ball, Am. J. Phys. 70, 482-489 (2002).
R. Cross and R. Bower, Measurements of string tension in a
tennis racquet, Sports
Engineering, 4, 165-175 (2001).
R. Cross, Grip-slip behaviour of a bouncing ball, Am. J. Phys. 70,1093-1102 (2002).
R. Bower and R. Cross, Player sensitivity to changes in
string tension in a tennis racquet, Jnl of Science and
Medicine in Sport, 6, 120-131 (2003).
R. Cross, Measurements of the horizontal and vertical speeds of
tennis courts, Sports
Engineering,6, 95-111 (2003).
R. Cross, Oblique impact of a tennis ball on
the strings of a tennis racquet, Sports Engineering, 6, 235-254 (2003).
R. Cross, The physics of overarm throwing, Am J. Phys. 72, 305-312, (2004).
R. Cross, Center of
percussion of hand-held implements, Am J. Phys. 72, 622-630 (2004).
R. Cross,
Physics of ankle injuries, Medicine and Science in Tennis, 9, 7 (2004).
R. Bower and R. Cross, String tension effects on tennis
ball rebound speed and accuracy during playing conditions, Journal of Sports Sciences, 23,
765-771 (2005).
R. Cross, A double pendulum swing experiment: In search of a
better bat, Am. J.
Phys. 73, 330-339 (2005).
R. Cross, Increase in friction force with
sliding speed, Am. J.
Phys, 73, 812-816 (2005).
R. Cross, Bounce of a spinning ball near normal incidence, Am. J. Phys, 73, 914-920 (2005).
R. Cross and R. Bower, Effects of swing-weight on swing speed and racket
power, Journal of
Sports Sciences 24, 23-30 (2006).
R. Cross and A. Nathan, Scattering of a baseball by a bat, Am. J. Phys, 74, 896-904 (2006).
R. Cross and A. Nathan, Experimental study of the gear effect in ball
collisions, Am. J.
Phys. 75, 658-664 (2007).
R. Cross, Cue and ball deflection (or “squirt”) in billiards, Am. J. Phys. 76, 205-212 (2008).
R. Cross, Tennis physics, anyone? Physics Today, 61(9) 84-85 (2008).
R. Bower and R. Cross, Elite tennis player sensitivity to
changes in string tension and the effect on resulting ball dynamics, Sports Engineering, (2008).
R. Cross, Mechanics of swinging a bat, Am. J. Phys. 77, 36-43 (2009).
R. Cross and A. Nathan, Performance vs moment of inertia of sporting
implements, Sports
Technology, 2, 7-15 (2009).
R. Cross and G. Pollard, Grand Slam men’s singles tennis
1991-2009, ITF
Coaching and Sports Science Review, 16 (Issue 49), 8-10 (2009). Can download at
http://en.coaching.itftennis.com/home.aspx
R. Cross, Impact of a ball on a surface with tangential
compliance, Am. J.
Phys. 78, 716-720 (2010).
R. Cross, Enhancing the bounce of a ball, The Physics Teacher, 48, 450-452
(2010).
R. Cross, Impact forces and torques transmitted to the
hand by tennis racquets, Sports Technology, 3(2), 102-111 (2010).
R. Cross, Measurement of the speed and bounce of
tennis courts, Sports Technology, 3(2), 112-120 (2010).
R. Cross, Bounce of an oval shaped football, Sports
Technology, 3(3), 168-180 (2010).
R. Cross, The polar moment of inertia of striking
implements, Sports Technology, 3(3), 215-219 (2010).
R. Cross and G. Pollard, Grand Slam men’s singles tennis 1995-2009. Part 2:
Points, games and sets, ITF Coaching and Sports Science Review, 19
(Issue 53), 3-6 (April 2011). Can
download at http://en.coaching.itftennis.com/home.aspx
R. Cross, A double pendulum model of tennis strokes, Am. J. Phys. 79, 470-476 (2011).
See also http://twu.tennis-warehouse.com/learning_center/doublependulum.php for videos of double pendulum
action.
R. Cross, Launch of a vehicle from a ramp, The Physics Teacher, 49, 410-411
(2011).
R. Cross, The kick serve in
tennis, Sports Technology, 4, 19-28 (2011).
R. Cross, Rolling motion of a ball spinning about a
near-vertical axis, The
Physics Teacher, 50, 25-27 (2012).
R. Cross, Measuring the effects of lift and drag on projectile
motion, The
Physics Teacher, 50, 80-82 (2012).
R. Cross, Aerodynamics in the classroom and at
the ball park, Am. J.
Phys. 80, 289-297 (2012). See http://youtu.be/t-3jnOIJg4k and also the baseball movies in the
sports physics movie clips.
R. Cross, Elastic properties of plasticine, silly
putty and tennis strings, The Physics Teacher, 50, 527- 529 (2012).
R. Cross, Impact of sports balls with striking
implements, Sports Engineering 17, 3-22 (2014).
R. Cross and C. Lindsey, Measurements of drag and lift
on tennis balls in flight, Sports Engineering 17, 89-96 (2014).
R. Cross, Impact behavior of hollow balls, Am. J.
Phys. 82(3), 189-195 (2014).
R. Cross, Men’s tennis vs Women’s tennis, ITF Coaching
and Sport Science Review, Issue 62, pp3-5, April 2014 (download at
http://en.coaching.itftennis.com/home.aspx)
R. Cross and C. Lindsey, Measuring the drag force on a
falling ball, The Physics Teacher, 52, 169-170 (2014).
R. Cross, Comment on “An accurate determination of the acceleration of gravity for lecture hall
demonstration”, Am. J. Phys. 82(8), 803-804 (2014).
R. Cross, The footprint of a tennis ball, Sports
Engineering, 17, 239-247 (2014).
R. Cross, Oblique bounce of a rubber ball,
Experimental Mechanics, 54, 1523-1536 (2014).
R. Cross, Impact behavior of a superball, Am. J. Phys.
83(3), 238-248 (2015).
R. Cross, Physics of swinging a striking implement,
Physics Education, 50(2), 232-236 (2015).
R. Cross, Factors affecting the vibration of tennis
racquets, Sports Engineering, 18, 135-147 (2015).
R. Cross, Behavior of a bouncing ball, Physics
Education, 50(3), 335-341 (2015).
R. Cross, Effects of turbulence on the drag force on a
golf ball, Eur J. Phys. 37, 054001 (2016).
R. Cross, Physics of croquet, Eur. J. Phys. 38,
014001, (2017).
R. Cross, Impact of a ping-pong ball, Physics
Education 52, 033002 (2017).
R. Cross and C. Lindsey, Measurements of drag and lift
on smooth balls in flight, Eur. J. Phys. 38, 044002 (2017).
R. Cross, The slap shot in
ice hockey, The Physics Teacher, 56, 7-9 (2018).
R. Cross, Throwing accuracy, Physics Education 53(3),
035021 (2018).
R. Cross, Backward bounce of a spinning ball, Eur J. Phys. 39(4), 045007 (2018).
R. Cross and
P. Dewhurst, Launch speed, angle and spin in golf, Eur J. Phys. 39(6), 065003 (2018).
R. Cross, Elastic
deformation of a bouncing ball, Eur J. Phys. 40(3), 035002 (2019).
R. Cross and C. Lindsey, Topspin generation in tennis,
Sports Engineering, 22(1), (2019).
R. Cross, Effect of topspin on the apparent speed of a
tennis court, Sports Engineering, 22(1), (2019).
Olivia Cant, Stephanie Kovalchik,
Rod Cross & Machar Reid, Validation of ball spin estimates in tennis from
multi-camera tracking data, J. Sports Sciences, 38(3), 296-303 (2019).
R. Cross, Calculations of groundstroke
trajectories in tennis, Sports Engineering, 23(1), Article 9, (2020).
TENNIS
WAREHOUSE UNIVERSITY
R. Cross,
Physics of the tennis kick serve
http://twu.tennis-warehouse.com/learning_center/kickserve.php
R. Cross and
C. Lindsey, Which
strings generate the most spin?
http://twu.tennis-warehouse.com/learning_center/spinexperiment.php
R. Cross,
The double pendulum in tennis
http://twu.tennis-warehouse.com/learning_center/doublependulum.php
Racquet Tech
Articles (www.racquettech.com)
(ALL
articles are COPYRIGHT)
C. Lindsey
and R. Cross, String testing, (3.3 Mb pdf)
Racquet Tech, 25, 4-20, June 2000.
R. Cross and
C. Lindsey, String test results: what do they mean?
Racquet Tech, 25, 4-13, July 2000.
R. Cross, Do strings affect power? Racquet Tech, 10-16, Sept 2000.
R. Cross, String gauges: Are thin strings
softer or stiffer? Racquet
Tech, 26, 4-10, Feb 2001
R. Cross, Measuring string tension: Part 1, Racquet Tech, 26, 4-8, June 2001
R. Cross, Measuring string tension: Part 2, Racquet Tech, 26, 14-18, July 2001
R. Cross, Stretch Tests on Strings, Racquet Tech, 26, 12-19, Sept
2001.
C. Lindsey
and R. Cross, Swingweight calculator, Racquet Tech,
26, 6-10, Dec 2001.
R. Cross and
C. Lindsey, How stiff is a stiff racquet? Racquet Tech, 26, 13-21, Dec 2001.
R. Cross and
C. Lindsey, Frame vibrations, Racquet Tech, 26, 14-17, Dec 2001.
R. Cross, Dwell time, Racquet Tech, 28, 10-12, May 2003.
R. Cross,
Getting a grip on the ball, Racquet Tech, 28, 4-9, Oct 2003.
Racquet
Sports Industry Articles (www.racquetsportsindustry.com)
(ALL
articles are COPYRIGHT)
R. Cross, Racquet power and the ideal racquet weight, Racquet Sports Industry, 1, 53-57,
Feb 2004
R. Cross, The world's most efficient tennis
racquet.. sort of, Racquet
Sports Industry, October 2004, p36-37.
R. Cross, Racquet Acrobatics, Racquet Sports Industry, April
2005, p46-47.
R. Cross, The inch that changed tennis forever, Racquet Sports Industry, January
2006, p40-41.
R. Cross, Raw racquet power, Racquet Sports Industry, February
2006, p16-17.
R. Cross, Racquet Handle weighting and
maneuverability, Racquet
Sports Industry, April 2006, p36-37.
R. Cross, Wrist snap in the serve, Racquet Sports Industry, July
2006, p40-42.
R. Cross, Spin off the court and strings, Racquet Sports Industry, January
2007, p40.
R. Cross and C. Lindsey, Ball testing, Racquet Sports Industry, January
2007, p20-25.
(see also C. Lindsey, How a tennis ball is made, p.26-29)
R. Cross, Technology smokescreen, Racquet Sports Industry, September
2009.
OTHER ARTICLES
R. Cross, Why you miss putts, Australian Golf Digest, 46-50 Dec 2006.
H. Brody and R. Cross, Proposals to slow the serve in
tennis, Tennis Science and Technology, (Eds S.J. Haake and A. Coe), Blackwell Science, ISBN 0-632-05638X,
Published as the proceedings of the 1st International Congress on Tennis
Science and Technology, London, August 2000, pp. 261-268.