Event date : 28 September 2018

Golf performance explained by physics -The Ryder Cup, a golf trophy between Europe and the United States, starts this 28 September in Saint-Quentin en Yvelines (France). On this occasion, zoom on the physics of the golf ball, and the reasons for its curious structured form.

Few golfers know what the small dimples of their balls are for but without these irregularities, they would be much less efficient! This amazing effect was discovered as early as the 18th century, when golf was invented. The bullets were then made of leather, filled with sand. To be smooth and have less friction, the seams were arranged inside. But the players quickly realized that the worn balls, though rougher, went further. How was that possible?

It was not until the beginning of the 20th century to discover the explanation. This is due in particular to Gustave Eiffel (yes, the builder of the Eiffel Tower) who, at the end of his life, was interested in aerodynamics, the science of air flows. He tried to establish the "coefficient of drag" of balls in a wind tunnel. This coefficient indicates the faculty of penetration into the air of an object. This is the famous Cx coefficients of cars, which decreases with the aerodynamic of the vehicle. Eiffel measures the Cx of spheres, and finds a result very different from that of another researcher, the German August Föppl, and his director Ludwig Prandtl. A difference of almost double!

In a political context of strong Franco-German rivalry, Prandtl even claims that Gustave Eiffel was wrong in his calculations. Never mind: Eiffel begins again his experiments, but does not just test a single sphere, nor a single wind speed in the wind tunnel. By multiplying the experiments, he realizes that there are two values ​​of the drag coefficient. When the blower speed is low, or the sphere is small, it observes the same value as the Prandtl team. Conversely, for high speeds or large spheres, it finds its previous results, with a lower Cx. The threshold for switching from one regime to another depends solely on the product of the diameter of the ball by the blower speed.

This threshold is the Reynolds number. Highlighted in 1883 by the Irish physicist Osborne Reynolds, it characterizes the way fluids flow around an object. Beyond a threshold, called critical Reynolds, air no longer flows in a laminar, but turbulent manner around the object. It is this threshold that Gustave Eiffel has demonstrated experimentally. The turbulent regime decreases the wake behind the sphere, which reduces drag, a force that opposes movement. So in turbulent regime, the object undergoes less friction. "The case of the golf ball is atypical, however, says Bruno Chanetz, research master at Onera (Université Paris-Saclay), the French center for aerospace research. In general, turbulence slows the progress. There are indeed two components of drag, one due to the wake, the other due to friction at the wall. Turbulence reduces the first and increases the second. In the case of the golf ball, the resultant is a lower total drag force. "

What is the relation between these phenomena and the dimples of the golf ball? These dimples promote the transition to a turbulent regime. The ball is therefore less braked, and goes further. For the greatest pleasure of the spectators of the Ryder Cup!

8 Université Paris-Saclay researchers present their work at the Ryder Cup: find out more