Badminton

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.

In most ball sports, the trajectory of the projectile closely follows a parabolic arc, the hallmark of motion under gravity alone. Badminton is a striking exception. Despite being launched at speeds exceeding 300 km/h in professional play, the shuttlecock travels a remarkably short distance before plummeting almost vertically to the ground. This dramatic trajectory distortion is caused by the shuttlecock's unique aerodynamic properties: its large frontal area and conical skirt of feathers create an exceptionally high drag coefficient, roughly ten times that of a tennis ball. The resulting air resistance decelerates the shuttlecock so rapidly that its horizontal velocity can drop by 90% within a fraction of a second. This makes badminton an ideal sport for studying the effects of aerodynamic forces on projectile motion, offering a visible and dramatic contrast with the idealized parabolic trajectory taught in physics courses. Using FizziQ's kinematic analysis module, students can quantify this deviation and explore the physics of drag forces in a real-world sporting context.

Learning objectives:

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.

Level:

High school

FizziQ

Author:

Duration (minutes) :

40

What students will do :

- Analyze the trajectory of a badminton shuttlecock using video-based kinematic analysis in FizziQ
- Compare the real trajectory with the theoretical parabolic trajectory of an ideal projectile
- Observe the decay of horizontal velocity due to aerodynamic drag
- Understand the role of drag coefficient and frontal area in determining air resistance
- Apply curve fitting tools to characterize the deviation from parabolic motion

Scientific concepts:

- Aerodynamic
- Drag forces
- Non-parabolic trajectory
- Interpolation of curves
- Air resistance

Sensors:

- Camera (video recording for kinematic analysis)
- FizziQ Kinematics module (frame-by-frame position tracking)

What is required:

- Smartphone or tablet with the FizziQ application
- 'Badminton' video from the FizziQ library
- FizziQ experience notebook
- Optional: spreadsheet for additional analysis

Experimental procedure:

Open FizziQ and navigate to the Kinematics module. Load the 'Badminton' video from the FizziQ resource library.
Before starting the analysis, identify a reference scale in the video (e.g., the height of the net, the court markings, or a player's height). Set the scale in FizziQ.
Set the origin of the coordinate system at the point where the shuttlecock is struck by the racket.
Begin frame-by-frame tracking by clicking on the shuttlecock's position in each video frame. Start from the moment of impact.
Track the shuttlecock through at least 15-20 frames covering the entire flight from hit to landing.
Adjust the interframe interval if needed. An interval of about 1/30 to 1/15 second (every 1-2 frames) usually gives good results for a badminton shot.
After completing the tracking, examine the position-position graph (y vs. x) in the FizziQ notebook.
Note the shape of the trajectory. It should show a steeper descent compared to a symmetric parabola, with the shuttlecock falling more vertically at the end of its flight.
Use the FizziQ curve fitting tool to fit a parabola (y = ax² + bx + c) to the data. Observe how well or poorly the parabola matches the real trajectory.
Now examine the horizontal velocity (vₓ) as a function of time. For an ideal projectile, vₓ should be constant. For the shuttlecock, it should decrease significantly over time.
Plot the horizontal velocity graph and note the exponential-like decay characteristic of a velocity-dependent drag force.
Compare the actual trajectory with the ideal parabola and identify the regions of greatest deviation. Explain the physical reasons for the differences.

Expected results:

The position-position plot should reveal a clearly asymmetric trajectory: the ascent phase may approximate a parabola, but the descent is much steeper, with the shuttlecock dropping almost vertically. A parabolic fit will show significant residuals, especially in the second half of the flight. The horizontal velocity graph should show a rapid, roughly exponential decay from the initial value (which could be 20-50 m/s depending on the shot) to near zero by the time the shuttlecock reaches its apex. The vertical velocity will also be affected: the upward deceleration is faster than free-fall alone, and the downward acceleration is slower than g due to drag. Pointing errors of ±1-2 pixels are typical and will introduce scatter in the velocity calculations, particularly for closely spaced points.

Scientific questions:

- Why does the shuttlecock's trajectory deviate so dramatically from a parabola, while a basketball's does not?
- How does the drag coefficient of a shuttlecock compare to that of other sports projectiles?
- What would the trajectory look like if there were no air resistance? Sketch the theoretical parabola for comparison.
- Why do badminton shuttlecocks have a conical skirt of feathers rather than being solid spheres?
- How does the initial speed of the shuttlecock affect the shape of its trajectory?
- What is the terminal velocity of a badminton shuttlecock, and how does this relate to the observed trajectory?

Scientific explanations:

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.

Extension activities:

Frequently asked questions:

Q: The tracked positions seem noisy and the velocity graph is erratic. How can I improve the analysis?
R: Ensure you are clicking precisely on the same point of the shuttlecock in each frame (use the base rather than the feathers). If the video resolution is low, increase the frame step to reduce the number of closely spaced points. Smoothing tools in FizziQ can also help reduce noise in derived quantities like velocity.

Q: I cannot find a suitable scale reference in the video. What should I do?
R: If no standard reference is visible, you can use the known height of the badminton net (1.55 m at the edges, 1.524 m at the center) or the court dimensions (13.4 m long, 6.1 m wide for doubles) if court markings are visible. Even an approximate scale will reveal the qualitative features of the trajectory.

Q: Why does the parabolic fit work reasonably well for the first part of the trajectory but not the second?
R: At the beginning of the flight, when the shuttlecock is moving fastest, drag is strongest but the trajectory has not yet deviated significantly from a parabola. As the horizontal velocity drops due to drag, the flight path becomes increasingly vertical, diverging dramatically from the symmetric parabolic prediction.

Q: The video is blurry and the shuttlecock is hard to see. Any tips?
R: Use slow-motion playback to identify the shuttlecock more easily. Focus on frames where the shuttlecock is against a contrasting background. In the FizziQ library videos, the resolution is optimized for tracking.