iv | NewScientist | 7 July 2012

” One of the main effects of all-in-one swimsuits is to compact the body. This reduces drag in the water”

Fluid flow plays an important part in sport, with the most obvious example being a swimmer in water. For cycling, athletics and many other sports, the fluid is the air. While sports scientists seek to improve an athlete’s biological performance, sports engineers seek to reduce energy losses, particularly those that are the result of interactions with a fluid.

Probably the most important force to minimise is drag, which is controlled by a number of factors. It is proportional to the square of the speed, so doubling the speed means four times as much drag. It is also proportional to the density of the fluid. Water is almost 1000 times as dense as air, so a triathlete experiences far greater drag when swimming than running or cycling.

Another factor is the cross-sectional area of the body in relation to the fluid. Doubling the area doubles the drag force and this is why cyclists crouch when riding. One of the main effects of polyurethane all-in-one swimsuits is to compact the body. The smaller cross-sectional area reduces drag.

More subtle effects are important too. In the 1970s, Elmar Achenbach at the Jülich Nuclear Research Centre in Germany carried out a series of experiments on spheres in a wind tunnel. He showed that the roughness of a sphere’s surface influences the way that a fluid flows over it and thus affects drag. Even scratches a hundredth of a millimetre deep are significant.

One of the clearest examples of this is the dimples on a golf ball. In the late 1800s, golf balls were smooth, and because they were expensive players

kept them for as long as possible. It turned out that older balls travelled further as they accumulated more nicks and bumps. The roughness creates turbulence in the layer of air in contact with the ball. This actually stabilises the flow of air around the ball, allowing it to follow the ball’s contours and reducing drag. Thus, golf ball dimples were born.

The late fluid dynamicist Milton Van Dyke produced a beautiful book called An Album of Fluid Motion (Parabolic Press, 1982). It shows numerous examples of the way in which fluids can be coaxed to separate or attach to a body using geometry, steps and even trip wires. One of the clearest examples of good aerodynamic design in sport is the helmets used in cycling and the bobsled. The helmet’s main job is to direct the airflow along the back of the athlete and keep it attached to the body as long as possible, thus reducing the size of the wake and the drag.

AERODYNAMICS

Computational fluid dynamics helps to improve design and performance

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7 July 2012 | NewScientist | v

Sport is not just about maximising the performance of the athlete, it is also about minimising the energy that is lost as we run, swim or slide through the fluids around us. Engineers now know that understanding the forces that dominate a particular sport is crucial to performing well

THE PHYSICS OF SPORT

Sports equipment is often too complicated to analyse using mathematical equations such as those in Newton’s laws. But in the 1990s, increasingly powerful computers enabled Keith Hanna, of engineering company Fluent in Sheffield, UK, to show that sport could use numerical methods to improve design, including finite element analysis and computational fluid dynamics.

Both methods start with a 3D representation of the athlete or equipment, created either with

THE NUMBERS GAME a software design package or from a 3D body scanner. Finite element analysis breaks down a complex structure such as the handlebars of a bike into a large number of small elements, whose movements are easier to work out than the structure as a whole. A computer program analyses the forces acting on each element separately, then combines them to give an overall picture of what is happening.

Computational fluid dynamics is similar, though it is the fluid rather than the object that is split up into small elements. Large models can take hours or even days to run and require clusters of computers, lots of memory and many processors.

These numerical methods have, however, made it possible to gain insights about sporting equipment where experiments would be just too costly or difficult to do. And they have helped with the design of equipment as diverse as archery bows, America’s Cup yachts and golf clubs.

Newton’s laws of motion are the starting point for sports engineersLE

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Natural philosopher Isaac Newton realised that forces were important in sport, and said as much in a letter to Henry Oldenburg, the secretary of the Royal Society in 1671. Newton’s three laws of motion are still the basis for modern sporting analysis. Using them, physicist Howard Brody at the University of Pennsylvania in Philadelphia pioneered studies of the interaction between a tennis racket and a ball. He found that the best racket designs optimise three parameters. Mass is crucial because if the racket is too heavy players find it difficult to hold, if too light the racket transfers little momentum to the ball. The centre of mass must also be optimised – too far from the hand and the racket feels “head heavy”. Finally, the moment of inertia is a product of the mass of the racket and the square of the distance of the balance point from the hand. If it is too high, players cannot swing the racket fast enough to give momentum to the ball.

Newton also coined the phrase “coefficient of restitution” to describe the ratio of rebound to impact velocity of an object. Simply speaking, it quantifies the bounciness of sports balls and the effectiveness of most bats, clubs, rackets and sticks.

NEWTON’S INSIGHTS