Fluid mechanics: Teaching the Magnus force

This week, I am going to complete my writing from last week, where I tried to give clarity about the Bernoulli principle for teaching within PE courses. I want to take things further and move on to Magnus forces.

Before we get started, in case you missed it in last week's post, click below to download our huge biomechanics resources pack!

What’s the difference between Bernoulli and Magnus?

The difference between the Bernoulli principle and Magnus forces is that Magnus forces describe the deviating flight paths of spinning objects, such as table-tennis balls. Magnus force is based on the same logic and fluid dynamics as the Bernoulli principle. In fact, Magnus force can be considered an applied Bernoulli lift force but specifically applied to spinning projectiles.

I am a big lover of table tennis. I have played the sport my entire life and have coached to a reasonable level too. My elder daughter (you know, the one from “Can A-level PE Lead to a Degree in Medicine”-posts) is a good player and I’ve stayed in touch with the sport all the way through her playing days too. 

Creating spin

So, let’s start with a ball:

If this ball is struck with a force away from the centre of mass of the ball (an eccentric force), the ball will spin around its axis. For example, look here:

Notice that the orange vector does NOT pass through the centre of mass. Rather, the ball has been hit below the CoM. We would call this a slice, a chop or even a push in table tennis. In other words, backspin is being applied to the ball and the ball will both travel through the air and spin around its axis like this:

Now, what I am about to write here is VERY important when it comes to Magnus forces because, without grasping it, the concept is not understandable. Here goes: the surface of that ball is very, very rough! It may feel smooth but it really isn’t. The molecules that form the mixture of gases that is the air are absolutely tiny and, as a result, when the ball spins, it carries a boundary layer of spinning air with it:

Going back to our Bernoulli principle, it is worth noting that the table-tennis ball is a uniform shape. It is round. Therefore, presenting an angle of attack/creating an aerofoil is not possible. Rather, the table tennis player, in our example, can use spin to create a pressure differential:

Notice how the airflow below and above the ball are now at different speeds. Therefore, a pressure differential is created because of the backspin and a Magnus lift force is created:

Because of this lift force, the flight path of the table-tennis ball is extended horizontally:

Notice the following about the shot with backspin:

👉 It travels lower over the net…
          …causing the opponent to have to lift the ball to some degree.

👉 It travels deeper on the table…
          …pushing the opponent back.

👉 It travels more slowly through the air (not visible in the image)...
          …allowing the player time to recover their position.

Therefore, we can begin to understand why a table tennis player would use backspin:

• It produces a defensive shot.
• It’s chosen when a player is out of position.
• The ball travels low over the net.
• It causes the opponent to need to lift the ball over the net.
• The ball travels slowly through the air.
• It allows the player more time to recover before the ball comes back.
• It is also considered a controlling shot or a more accurate shot because the ball travels more slowly.
• It can help to change the cadence of a rally. In sports like tennis, topspin can dominate to such a degree that most shots are hit with similar pacing. Introducing backspin can add variety.
• It is excellent for drop shots because of the effect of backspin on the bounce. 

Other than describing other types of spin to you, there are two more places I could take you:

1. Backspin and bounce;
2. Hitting a ball that already carries backspin.

Both of these are fascinating areas of conversation but I will leave them out of this post and will add them in if colleagues request me to do so. Those of you who taught A-level PE between approximately 1998 and 2016 (like me) will remember teaching both of these ideas. 

Topspin

Topspin has the same mechanics as backspin but in reverse:

Notice how the topspin is caused by, once again, an eccentric force but, this time, causing the ball to rotate around its axis in the opposite direction:

As you already know, the ball spins with a boundary layer. Therefore, we can describe how topspin is achieved like this:

As a result, a Magnus force down is created and the ball deviates from its flightpath:

Notice the following about the shot with topspin:

👉 It travels higher over the net…

          …meaning there are fewer unforced errors by hitting the net.

👉 It has a shorter flight path…

          …meaning it can be hit harder without the fear of missing the back of the table.

👉 It travels more quickly through the air (not visible in the image)...

          …allowing the player time to attack an opponent who is out of position.

Therefore, we can begin to understand why a table-tennis player would use topspin:

• It produces an attacking shot.
• It’s chosen when an opponent is out of position.
• The ball travels high over the net.
• It’s unlikely to hit the net.
• The ball travels quickly through the air.
• It allows the opponent little time to respond.

These principles apply equally to tennis as to table tennis. 

…and, finally, sidespin.

I’m not going to take you through the full process of how to create sidespin. The process is identical to that of backspin and topspin except that the eccentric force is applied to the left or right of the vertical/longitudinal axis of the ball. Sidespin causes a ball to deviate in flight. Somewhat like this:

Notice how a ball hit with hook (draw) allows a ball to deviate to the left (for a right-hander). This can be really helpful for a golfer, say, who might need to avoid an object or even play a shot to counteract a strong wind from the left. Likewise, the slice (fade) shot allows exactly the same in the opposite direction. If a golf hole is structured like these:

The hook (on the par 4) and slice (on the par 5) could be very useful. Equally, a footballer wishing to curl (hook) or swerve (slice) a ball around an object such as an opponent or even a defensive wall can use the same principle to cause the ball to deviate:

Conclusions

So, there you have it, my friends. Two significant posts containing lots and lots of drawings and conceptual understanding. I hope you have enjoyed reading them. 

In order to help colleagues take these ideas further, I wanted to share with you a broadcast that I did back in 2017. I was young and thinner and I only had one chin. Anyhow, it's a really nice webinar session and I encourage you to watch it. 

Thanks again and have a lovely day. 

James