What Is The Magnus Force?

[Applause] So I'm back at the University of Sydney with Rod Cross. Hi Derek! And today we're talking about the effects of air on projectiles.

We normally neglect these effects when I'm teaching students about projectiles. I tell them, "Forget about the air. Let's just talk about gravity," because it simplifies the problem. But air is real; it's heavy stuff, and it affects the flight of all projectiles.

All right, well, why don't we do a little experiment to show the effect that air can have? This is a surprising experiment that we've set up here. First of all, I'll show you what happens to a tennis ball when it rolls down this inclined ramp. Well, that falls exactly like I would expect—basically a parabolic path as predicted.

But let's try something a little bit lighter, such as this paper cylinder. Okay, it weighs only a gram or so. The effect of the air will be more important. Watch what happens this time.

Okay, wow! So the paper cylinder goes backwards. That doesn't make any sense! I mean, it was rolling forwards off that ramp.

No, it does it every time, and it's because of an effect known as the Magnus Force that's acting on the spinning cylinder. It acts on a spinning ball as well, and people who play sports know about it, but they wouldn't call it a Magnus Force.

Why is it called the Magnus Force? Because Magnus was the first guy who discovered it when he was investigating why cannonballs curve as they propagate through the air.

Aha! So what did he find out? What he found is that when a ball or any object is spinning like this, there's a force perpendicular to the spin axis. If it's spinning clockwise or has Top Spin, the force is down. If it's spinning anticlockwise (counterclockwise), the force is up.

So how do we get a Magnus force on a ball? As the ball's moving forward through the air, if it's spinning, the air is flowing around the ball from the front to the back. The ball is spinning in the same direction as the airflow at the top of the ball but in the opposite direction at the bottom. Because of friction between the air and the ball surface, air is dragged around the top of the ball downwards towards the back.

But at the bottom of the ball, the air flow and the ball are opposite directions. The air comes to a screeching halt fairly soon. Instead of being deflected upwards, the net result is air is deflected downwards. Due to Newton's third law, the air exerts an equal and opposite force on the ball, which is upwards.

So how would sports players take advantage of the Magnus Force? They make the ball curve through the air by a different amount than that due to gravity alone. A golfer will strike a golf ball with backspin that exerts a vertical force, a lift force on the ball, that keeps it in the air for a longer time, and therefore it travels further.

A tennis player will hit the ball with Top Spin that causes the ball to curve down onto the court after it clears the net. A baseball or cricket player will also do that, but in addition, they can make a ball curve about a vertical axis, in which case the ball will either curve to the left or to the right away from the batter, making it much more difficult to hit the ball. That's the object of the exercise.

I see. So are there any other air effects that we need to be aware of?

There's quite a few, actually. There's the buoyant force acting on a balloon, for example, or any object. There's a drag force acting backwards that slows the ball down, and if the ball happens to have seams, then there's a sod force acting on the ball.

Uh-huh! Well, that sounds like a whole other episode—balls with seams!

Yeah, that is. All right, well, stay tuned if you want to find out how air affects balls with seams!