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How would the shuttle cock change its position in air, if it were hit with a small force from a badminton bat?
Question Date: 2013-04-08
Answer 1:

I'm sure you have noticed that a shuttlecock (a.k.a. birdie) is much heavier on the bottom than it is by the feathers. The way the weight is placed makes a big difference in how we perceive its motion, but the same physical laws apply. When you swing a badminton racket and meet the birdie, it is essentially the same as when you throw a ball at a wall: it bounces back (unless the ball is flat!) In this case, the birdie is the "ball" and the strings on your racket are the "wall."

Newton's Third Law tells us that objects that interact (like a racket and shuttlecock) force each other equally and oppositely. The force from a hit comes from the change in velocity as well as the time it takes to make that change. In this case, the birdie is changing velocity. Remember that velocity has a speed (how fast?) and a direction (where?) part to it.

The birdie changes its position in air as a result of you putting a force on it through the racket. With a very fast camera and some estimations, we can figure out about what kind of force is put on a birdie.

Using this website as a guide: click here to see, please), I will estimate a few things:

Type of shot: Forehand smash (the awesome overhead one)
Incoming velocity: -15 meters / second
Outgoing velocity: 75 meters / second
(remember it's now going in the opposite direction!)

This means the change in velocity is (final - initial) = 100 meters/sec
Impact time: 0.004 seconds
Shuttlecock mass: 5 grams = 0.005 kilograms
Force is equal to mass*(change in velocity) / (impact time)

So, the force on a shuttlecock in a professional game is 125 Newtons. This is about the force of 30 pounds (three bowling balls), which doesn't seem like much, but remember how small the birdie is!

The acceleration on the shuttlecock is very large.
Acceleration is equal to (change in velocity) / (impact time) = 25,000 meters/(sec2) over 2500 times the acceleration of gravity (often noted as 2500 G, just meaning 2500 times Gravity).

For comparison, NASA's retired space shuttle reached 3 G's during liftoff. A scientist named John Stapp holds the record for maximum horizontal acceleration tolerated by a human:
46.2 G!

He had vision problems for the rest of his life as a result of this experiment.
click here to read about It's clear that a birdie can tolerate higher accelerations than a human.

Hope you have a better appreciation for how tough that little birdie is!

Thanks for the question! Here's a cool video of some badminton shots:
cool video

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