Sporting chance - modelling techniques for high-performance equipment

Materials World magazine
4 Jun 2011
Finite element modelling of tennis racquet

New modelling techniques offer the chance of radical improvements in the design of high-performance sporting equipment. Dr Tom Allen, Sports Engineering Researcher from Sheffield Hallam University, UK, highlights the developments.

Sports equipment is big business – the global market is worth around US$80bln. Sports brands invest heavily in R&D to gain an advantage in this highly competitive market. Over the last 20 to 30 years, sports equipment has developed to become a highly technical and specialist industry.

Equipment can be vital to enjoyment, success and injury prevention for both elite athletes and budding amateurs. Sports engineers often have a mechanical engineering background and aim to apply the most advanced tools and techniques to understanding the physics of sports equipment. Finite element (FE) modelling is one such state-of-the-art engineering tool.

Simulating a response

Testing sports equipment typically requires dynamic FE models to represent events such as a baseball strike, for example. This type of modelling allows a variety of designs to be tested without the cost and time associated with producing prototypes, although highly trained operators are required to ensure accurate results, and licence costs for commercial FE packages can be high.

The larger organisations with vast R&D budgets were the first to apply FE modelling to sports equipment testing. For example, FE modelling is used widely in Formula 1 to maximise driver safety in the event of a high-speed crash. Adidas uses FE modelling when designing running shoes and footballs, whilst Ping applies the technique to improve the performance of golf clubs. Universities working in sports equipment testing are frequently involved in the development of FE models and methods. Smaller organisations, without large R&D budgets, are often forced to rely on consultants or universities for specific projects.

Playing ball

In recent years, advanced materials have led to massive improvements in sports equipment. In particular, the influx of composite materials has had a huge effect on tennis racquet design and how the game is played. Composite racquets are lighter and have larger heads than traditional ones. Modern players focus on powerful groundstrokes from the baseline as opposed to the serve-and-volley tactics that dominated the wooden racquet era. However, despite advances in racquet design, relatively little is known about how specific changes in material composition may affect a typical shot.

Prince Sports, a global racquet maker based in Bordentown, USA, has formed a partnership with Sheffield Hallam University in the UK to discover a better method for understanding the key design parameters, such as constituent materials, and how these can be manipulated. The team has embarked on a project with the objective to create the world's best tool for understanding the physics behind the tennis racquet.

The commercial FE code Ansys/LS-Dyna, which is widely used in automotive crash scenarios, has been selected for this project as it is optimised for simulating impacts. Model development has been achieved in three stages – the ball, the stringbed and finally the entire racquet. There is often a degree of uncertainty due to simplifications and assumptions in geometry and material properties, so FE models should be compared with experimental data to check their accuracy. The Sheffield team has compared the model against experimental data collected in a laboratory at the key development stages and found that the model matches real-life data.

Challenging requirements

The two main requirements when producing an FE model are material properties and computer geometry. Material properties can pose a major challenge when simulating sports equipment. The materials are often viscoelastic, which means that their properties are dependent on the speed of the impact. A tennis ball is only in contact with the stringbed for about 0.005 of a second during a shot, which results in very high strain rates.

The scientists have used a rubber material model that was ideal for simulating the viscoelastic core of the tennis ball. Bespoke tests help obtain the strings’ material properties at the correct strain rates.

Modelling geometry is often simpler than modelling materials, particularly as recent developments in FE packages have focused on usability and direct connections to CAD packages.

The Sheffield team has modelled the racquet’s interwoven stringbed using the Pro/Engineer CAD package and imported the geometry directly into Ansys/LS-Dyna. It has conceived a bespoke method for tensioning the strings and securing them to the frame of the racquet.

However, it is often necessary to produce FE models of sports equipment without the original geometry data, for example, when comparing an FE model of an old wooden field hockey stick with a modern composite stick. To cater for this possibility, the researchers used a non-contact laser scanner to replicate the geometry of the racquet.

In motion

Sports equipment testing must relate to how the item will be used by the athlete. So the scientists have compared their model with shots of elite players collected at a Wimbledon qualifying tournament. Following this, the model has been used to identify mass distribution as the key racquet parameter. Composites allow manufacturers to control the distribution of mass in the racquet. The mass at the point where the ball is impacted can be tailored to give the greatest transfer of momentum to the ball, in the form of speed and topspin. Professional players often use lead tape to further customise their racquet’s masses to their specific style of play.

It is vital to understand how an athlete interacts with his or her equipment to maximise performance and reduce the risk of injury. Relevant player geometry could be obtained using a scanner and incorporating it into the model. This would aid racquets to be customised to certain players or playing styles.

This type of model could also be used to explore the connection between racquet properties and tennis-related injuries. Once the design of the tennis racquet has been optimised, R&D could focus on manufacture.

Modelling in sports testing

Finite element modelling is already used to test sports equipment, mainly by global brands and research institutes. As the software becomes more userfriendly and accessible, the technique will be used more widely, especially by smaller organisations. There are implications in relying solely on a single technique, such as FE modelling. Therefore, FE modelling should be complemented by existing mechanical and biomechanical tests. In particular, the FE models must be representative of how the equipment will be used by the athlete.

One of the greatest challenges for sports brands is ensuring high quality during mass production. Greater use of FE modelling, in combination with more classical testing methods, would further the understanding of sports equipment and help manufacturing. In particular, equipment could be designed for specific manufacturing methods.

An increase in FE modelling in sports equipment testing should lead to better customisation for individual athletes. It also has great potential for sports broadcasting – a real-time FE model could provide extra information, such as a comparison of different players’ shots in tennis or penalty kicks in football.


Further information

Centre for Sports Engineering Research, Sheffield Hallam University Collegiate Campus, Sheffield, S10 2BP, UK. Tel: +44 (0) 114 225 3996. Email:

Golf club head images courtesy of Ping