Review of Tennis Ball Aerodynamics (Mehta, Alam, Subic, 2008)

Source file: Review_of_tennis_ball_aerodynamics.pdf.txt

Domain: biomechanics / ball-aerodynamics

Tier: reports/tier-1-high-value-gaps

Used in artifact: artifacts/reports/tier-1-high-value-gaps.md

Abstract

Wind-tunnel review of tennis ball aerodynamics. Drag coefficient CD = 0.55–0.65 for new balls (not 0.3–0.4 as earlier Cambridge). Fuzz contributes ~10% to drag. Critical Re ~85,000; serve regime 100k–200k. Quasi-steady state reached after ~10 ball diameters.

Key points

Drag coefficient CD = 0.55–0.65 for new non-spinning tennis balls.
Felt 'fuzz' contributes ~10% to drag — shaving the nap lowers CD.
Critical Reynolds number for a tennis ball is approximately 85,000.
Ball reaches quasi-steady aerodynamic state within ~10 ball diameters (~3% of trajectory).
Seam orientation has negligible effect on aerodynamic properties.

Raw dump (first ~1000 words)

Review of tennis ball aerodynamics DOI: 10.1002/jst.11 Review of tennis ball aerodynamics Rabindra Mehta1,�, Firoz Alam2 and Aleksandar Subic2 1 Sports Aerodynamics Consultant, U.S.A. 2 School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia Review The aerodynamics of a tennis ball are reviewed here with reference to several wind tunnel measurement efforts. Measurements for a wide variety of tennis balls, including the `oversized' balls, are presented. Flow visualization results have shown that the separation location on a non-spinning tennis ball occurred relatively early, near the apex, and appeared very similar to a laminar separation in the subcritical Reynolds number regime. The flow regime (boundary layer separation location) appears to be independent of Reynolds number in the range, 167,000oReo284,000. Asymmetric boundary layer separation and a deflected wake flow, depicting the Magnus effect, have been observed for the spinning ball. Aerodynamic force (drag and lift) measurements for nonspinning and spinning balls are reviewed for a wide range of Reynolds numbers and spin rates. Relatively high drag coefficients (CDffi0.6 to 0.7), have been measured for new nonspinning tennis balls. The observed (unexpected) behavior of the tennis ball drag coefficient is explained in terms of a flow model that includes the drag contribution of the `fuzz' elements. & 2008 John Wiley and Sons Asia Pte Ltd Keywords: . tennis . tennis balls . aerodynamics . coefficient of drag 1. HISTORICAL BACKGROUNDy The game of tennis originated in France some time during the 12th century and was referred to as jes de paume, `the game of the palm played with the bare hand'. As early as the 12th century, a glove was used to protect the hand. Starting in the 16th century and continuing until the middle of the 18th century, rackets of various shapes and sizes were introduced. Around 1750, the present configuration of a lopsided head, thick gut and longer handle emerged. The original game known as `real tennis', was played on a stone surface surrounded by four high walls and covered by a sloping roof. The shape of the new racket enabled players to scoop balls out of the corners and to put `cut' or `spin' on the ball. The rackets were usually made of hickory or ash and heavy sheep gut was *209 Orchard Glen Court, Mountain View, CA 9404, U.S.A. E-mail: rabi44@aol.com yA substantial part of this section `1. Historical Background' has been reproduced from Balls and Ballistics, In: Materials in Sports Equipment, ed: Mike Jenkins, ISBN: 1 85573 599 7, by kind permission of Woodhead Publishing. used for the strings. The old way of stringing a racket was to loop the side strings round the main strings. This produced a rough and smooth effect in the strings, hence the practice of calling `rough' or `smooth' to win the toss at the start of a tennis match. Only royalty and the very wealthy played the game. The oldest surviving real tennis court, located at Hampton Court Palace, was built by King Henry VIII in approximately 1530. The present day game of lawn tennis was derived from real tennis in 1873 by a Welsh army officer, Major Walter Wingfield. Balls used in the early days of real tennis were made of leather stuffed with wool or hair. They were hard enough to cause injury or even death. Starting from the 18th century, strips of wool were wound tightly around a nucleus of strips rolled into a small ball. String was then tied in different directions around the ball and a white cloth covering was sewn around it. The original lawn tennis ball was made of India rubber, the result of a vulcanisation process invented by Charles Goodyear in the 1850s. Today, the size, bounce, deformation and colour of the ball must be approved by the world governing body for tennis, the International Tennis Federation (ITF). Ball performance characteristics are based on varying dynamic and aerodynamic Sports Technol. 2008, 1, No. 1, 7�16 & 2008 John Wiley and Sons Asia Pte Ltd 7 Review R. Mehta, F. Alam and A. Subic properties. Tennis balls are classified as Type 1 (fast speed), Type 2 (medium speed), Type 3 (slow speed) and high altitude. Type 1 balls are intended for slow pace court surfaces, such as clay. Type 2 balls, the traditional standard tennis balls, are meant for medium paced courts, such as a hard court. Type 3 balls are intended for fast courts, such as grass. High altitude balls are designed for play above 1219 m (4000 ft). Tennis balls may be pressurised or pressureless. Today's pressurised ball design consists of a hollow rubber-compound core, containing a slightly pressurized gas and covered by a felt fabric cover. The hourglass `seam' on the ball is a result of the adhesive drying during the curing process. Once removed from its pressurised container, the gases within a pressurised ball begin to leak through the core and fabric and the ball eventually loses bounce. Pressureless balls are filled with microcellular material. Subsequently, pressureless balls wear from play, but do not lose bounce through gas leakage. As a costsaving measure, pressureless balls are often recommended for people who play infrequently. The tennis ball must have a uniform outer surface consisting of a fabric cover and be white or yellow in colour. Ball seams must be free of stitches. All balls must weigh more than 56.0 g and less than 59.4 g. Types 1 and 2 ball diameters must be between 6.541 cm and 6.858 cm; Type 3 balls must be between 6.985 cm and 7.302 cm in diameter. It was in fact the flight of a tennis ball that first inspired scientists to think and write about sports ball aerodynamics. Newton [1] noted how the flight of a tennis ball was affected by spin and he wrote `I remembered that I had often seen a tennis ball y describe such a curveline. For, a circular as well as a progressive motion being communicated to it by that stroke, its part on that side, where the motions conspire,