Badminton
Studying aerodynamic forces on a badminton shuttlecock
Author:
Title 4
Learning objectives :
This activity allows students to discover how aerodynamic forces modify the trajectory of a badminton shuttlecock. It develops the ability to compare a theoretical model with real data.
Concepts covered
Aerodynamic; Drag forces; Non-parabolic trajectory; Interpolation of curves; Air resistance
What students will do :
The student analyzes the trajectory of a badminton shuttlecock using the FizziQ Kinematics module. After pointing out the successive positions of the steering wheel, the student draws the position-position graph and compares the real curve to a theoretical parabola then studies the evolution of the horizontal speed to highlight the influence of aerodynamic forces on the movement.
What is required :
Smartphone or tablet with the FizziQ application; 'Badminton' video from the FizziQ library; FizziQ experience notebook; Optional: spreadsheet for additional analysis
Scientific background :
The trajectory of a projectile in a vacuum is perfectly parabolic, described by the equations x(t) = v₀ₓt and y(t) = v₀ᵧt - ½gt², with a constant horizontal speed. However, in the air, aerodynamic forces can significantly modify this trajectory, particularly for light, non-spherical objects such as a badminton shuttlecock. The shuttlecock has a unique structure: a weighted hemispherical base extended by a conical skirt of feathers or synthetic material. This shape generates significant aerodynamic forces: 1) High drag, mainly due to the skirt which creates a large frontal area. This force is proportional to the square of the speed: F_drag = ½ρC_Dₐᵢᵣv². The coefficient of drag (C_D) of a shuttlecock is exceptionally high (0.6-0.7), much higher than that of a tennis ball (0.5) or golf ball (0.3). 2) Gyroscopic stabilization: during flight, the steering wheel naturally orients with its base forward, which contributes to its characteristic trajectory. The kinematic analysis reveals that the real trajectory deviates significantly from a parabola: it has a lower initial slope and a more vertical drop at the end of the course. The horizontal velocity graph shows an exponential decay due to aerodynamic drag, in contrast to the constant velocity of an ideal projectile. This rapid deceleration explains why the shuttlecocks only travel 13-14 meters even with a powerful strike, while their initial speed can exceed 300 km/h (world record: 493 km/h). This analysis perfectly illustrates the importance of aerodynamic forces in racket sports.