# A Simulation of the Effects of Badminton Serve Release Height
## 1 Introduction  
In badminton, each rally begins with a serve. The server's feet are placed inside the service box, at a minimum distance of 1.98 m to the net, and the shuttlecock must land inside the diagonally opposite service box on the receiver's side after clearing the net height of 1.55 m. The game has evolved such that most serves in singles and, in particular, in doubles are short serves. In doubles, the server's feet are placed at the corner of the service box close to the middle of the court and close to the net, and the target of the serve is often the near corner of the receiver's service box; i.e., the shortest possible flight trajectory. The server will typically perform the serve with the arms extended in front of the body to approach the launch position to the net and further minimize the length of the flight trajectory. In this situation, the launch height becomes an important factor, with a larger height enabling a flatter serve and minimizing the opportunity of the receiver to attack the serve. Therefore, the classical rules of the serve constrain the position of the racket head at impact with the shuttlecock to be below the lower rib of the player. This means that taller players are able to launch the shuttlecock from a higher position than players of smaller statures. In 2018, the Badminton World Federation (BWF) decided to experimentally change the rules of the serve and introduced a new limitation formulated as follows: \"The whole of the shuttle shall be below 1.15 meters from the surface of the court at the instant of being hit by the server's racket\" [1]. To assist in the enforcement of the rule, the BWF also introduced anew apparatus by which the service judge can verify visually that the maximum launch height is not exceeded. This rule was put in place for the first time during the All England Open Badminton Championships 2018 and sparked much controversy among players. The frame of reference for the launch position changed from a relative measure with respect to the server's rib cage to an absolute measure with respect to the court. While no official explanation was provided, the rule change likely reflected a desire not to disfavor players with smaller statures. The new rule means that taller players must lower their launch position, while some shorter players can raise theirs, and the point of the controversy is whether a relative or an absolute measure is more fair. The serving situation, particularly in doubles, is stressful because it is easy to attack the serve, and so the serving team will often find themselves in a defensive situation; thus, the serving height influences the balance of the game. The purpose of this investigation was to provide quantitative measures for the influence of serve height. More precisely, we aimed to answer the following research questions:  
1. How much lower is the new launch position compared with the old one for a particular world-class female doubles player, for whom the rule change has required an unwelcome adjustment? 2. Can we quantify the effect of the change in launch position on serve quality? 3. Are there under-exploited serve strategies that may come into play in light of the new serve rule? As a by-product of the investigations, we also identified aerodynamic parameters for the numerical simulation of shuttlecock flight trajectory at Reynolds numbers typical for short serves. Previous works on shuttlecock trajectory simulation are limited but have successfully simulated flight trajectories. [PERSON] et al. [2] noted that the flight of a shuttlecock is influenced by drag and different from a theoretical parabola. The subject of different material choices (plastic versus natural feathers) has attracted some attention, and [PERSON] [3] developed a simulation based on aerodynamic measurements [4] for the flight of different types of shuttlecocks and found agreement with experimental results. [PERSON] and [PERSON] [5] investigated a variety of designs and simulated their trajectories based on aerodynamic measurements. [PERSON] et al.