Fluid mechanics: Teaching the Bernoulli principle

If you are a secondary school or college PE teacher, there’s a pretty good chance that the concept of biomechanics teaching has crossed your mind. Perhaps you’ve taught it at GCSE or A-level or perhaps you’ve heard conversations about how hard it is and how people avoid teaching it. 

Regardless, I wanted to share some of my experiences teaching biomechanics. I’ve been teaching the discipline for over 20 years and I was lucky enough to learn the subject from the absolute best, Graham Thompson. Back in the pre-2008 specification change days (there have been subsequent changes since then, of course) my team and I used to teach biomechanics as an entire option instead of sports psychology on OCR A-level PE. Back then, students had five options of second-year study and they had to select three:

Compulsory:

• Exercise physiology

One further scientific option from:

• Sport psychology
• Biomechanics

One sociocultural option from:

• Historical studies
• Comparative studies

For a little while, we used to decide for the students and our decision was always biomechanics above sport psychology and history over comparative. But, as our team progressed, we started to offer options and students could select any combination. It helped that we were working at the biggest sixth-form college in the country and that we had over 300 A-level PE students at any one time but, as you can imagine, I got to teach a lot of biomechanics. 

I love teaching biomechanics. I mean, I LOVE IT! I honestly believe that I would choose to do it above any work-related activity and above some non-work-related ones too. It goes to my heart. I think it’s because the learning is conceptual and eureka moments are pretty common compared to, say, sports psychology, where models and frameworks need to be memorised. Within my biomechanics teaching, the sections I enjoyed the most were the fluid mechanics sections and, specifically, the teaching of the Bernoulli principle and Magnus forces. It’s such a cool thing to teach and exemplify for young people. 

This is what this week’s blog post is about. I want to share my love of biomechanics teaching and, specifically, my enjoyment of these two super-cool concepts and don't miss the huge biomechanics resources pack available to download below.

The Bernoulli principle

It’s got a crazy-sounding name. But what is it? The Bernoulli principle describes the relationship between air speed and air pressure. In essence, it tells us that the slower the air moves, the more pressure it exerts and vice versa. Therefore, fast-moving air exerts relatively low pressure. Like this:

Therefore, if a projectile in sport can experience different air speeds occurring at different parts of the projectile, a pressure differential can be created and the projectile can deviate in its flight path.

So far this has been theoretical. Let me put this into practice for you:

Basic example 1

Take a look at this image:

What does your intuition tell you will happen when you blow through the straw? Do you think the paper will open out to the left and right? When you ask this in a classroom context, most students will answer that this is their belief. But, if we apply Bernoulli’s principle to it:

You should now know exactly what happens: the air inside the tunnel beneath the paper is travelling relatively fast compared to the air on the outside of the paper, so the pressure in the tunnel is relatively low compared to the external air. Therefore a pressure differential is created and the paper is forced together, closing the tunnel. If you don’t believe me, give it a try. 

Basic example 2

This is actually my favourite one. Again, look at the image:

Once again, I ask you (the students normally): What does your intuition tell you will happen to the paper? Without knowledge of Bernoulli, students tend to say it will stay down and bent when, in reality, it does exactly the opposite. It moves upwards toward the horizontal, almost as if it is floating. Why? Simply because the air above the paper is fast-moving and low-pressure compared to the air below the paper. A lift force is created. Now, what would happen if we applied this to a javelin in flight or a discus or even a ski jumper? We’ll come to this.

Basic example 3

Take a look at this strange scenario:

When the fan is switched on, what do you think will happen to the balloons? Before you answer, think about a different question: what does Bernoulli’s principle tell us will happen to the balloons? You may find your two answers are different. But, once again, Bernoulli will always win because the principle is utterly consistent (on earth). The balloons will move together and, if set up correctly, will actually strike one another. 

Last bit of Bernoulli theory

I’m over three pages of writing in and we haven’t got to any application to sport. We will, I promise. But just before we do, I want you to be aware of a Venturi meter:

You’ll see that air in the wider parts of the channel is moving more quickly. Therefore, its pressure is relatively high. Within the narrow part of the chamber, the air is squeezed and has to speed up. Therefore, the pressure it applies to the chamber walls decreases. This is the Bernoulli principle in a nutshell. 

Actual Venturi meters look like this:

Notice that a pressure differential is created. It is this differential that can be exploited in sport when projectiles move through a fluid (air or water). Let’s see how:

Javelin throwing and the Bernoulli principle

This is a javelin. No surprises there! The aim of javelin throwing is to achieve the maximum horizontal displacement (if the word displacement worries you, just think distance + direction). We want to lob it as far as possible. 

So, how can this floaty, pressure-differential, force thing help? Put simply, a javelin thrower will aim to release the javelin with an angle of attack that promotes a lift force on the javelin. Once it is in the air, the following will occur:

Notice the following:

Normally, when I teach this, a student will ask why on earth does the air need to meet at the other end of the javelin at the same time. The student has a point, right? How does the air know to do this? Well, of course, it doesn’t. In fact, the air isn’t moving at all. It is the javelin (a uniform object moving at a set velocity in a specific direction) that displaces the air. Even though we illustrate the air moving, it is, in fact, the javelin moving past the air. This is another one of those eureka moments. 

With all this considered, if we were to sketch the flight path of a javelin thrown with and without an angle of attack, it might look like this:

The angle of attack, created at the point of release, is essential for a javelin to experience an extended flight path. 

Discus throwing and the Bernoulli principle

Put simply, discus throwing uses the same principle:

Notice the angle of attack. And here’s the completed version:

We could write the same table as we did for the javelin:

So, two different discus thrown with and without an angle of attack, might look like this:

Some of you may have noticed that another way of describing an angle of attack is to describe the presentation of the javelin or discus as an aerofoil. This is absolutely correct. An aerofoil is defined as an object that requires air to travel further above the object than below. You may not be surprised that this is the principle by which aeroplane wings are designed to create lift. 

Ski jumpers and the Bernoulli principle

I may well be labouring the point by now but ski jumpers apply exactly the same principle. Like this:

The flight technique is specifically developed to promote lift and, therefore, extend horizontal displacement. You may also notice that the closer the jumper can get their chin to their skis, the greater the pressure differential because the air will have less and less distance to travel beneath the skis.

Inverted aerofoils and downforce

But, in sport, we don’t always want to create the Bernoulli lift force UP. No! Sometimes, performers need to achieve a Bernoulli lift force DOWN. I know it sounds a little counterintuitive, but all that’s required is to turn the aerofoil around. We, once again, present an angle of attack but this time we want to cause the force to act downwards. Creating downforce has a few uses in sport but the main one to be aware of is the capacity to be able to turn bends at higher speeds. Take a look at this example:

This is an image of Bradley Wiggins circa 2012. You will undoubtedly recognise the aero position that he is holding on his time-trial bike. He is tucked down with his forearms narrow on the aerobars. But this is not our focus for today. Rather, I want you to notice how little distance the air that goes above his helmet and back has to travel. Therefore, it travels relatively slowly compared to the air that passes the greater horizontal distance below. This creates a pressure differential and a Bernoulli lift force DOWN. Whilst the cyclist is travelling in a straight line, this has little impact but it is crucial as the rider takes bends and corners. Because of the extra downforce, cyclists can maintain high speeds whilst turning without slipping off the road (or track). 

Take a look at the same image with airflow included:

Consider other performers who need to achieve similar things. A speed skater will tuck in the bends, so that air above them can travel less distance and more slowly. A racing car that travels a very twisty track such as the road track in Monaco, will carry a huge rear wing (inverted aerofoil) to maximise speed in bends. 

The Monaco Grand Prix features a highly twisting circuit, meaning that racing teams carry very large rear wings to maximise downforce and, therefore, turning speeds. 

Now consider a track such as Spa in Belgium:

Monaco features 19 turns to achieve the 360°, whereas, at Spa, Belgium, the same 360° is turned in 11 total turns, with far more parts of the course being straight and requiring greater top speed. 

You may also be interested in this question that we posed in our OCR A-level PE National Mock Exam Paper 1 2023:

With the mark scheme looking like this:

When I teach the Bernoulli principle, I try to get students excited about materials and product design in sport. I’ve worked with many students who, at A-level, consider themselves to be non-academic or non-scientific, yet are studying PE and DT or graphics. I like to engage these students in conversations about marginal gains in elite sport. 

I will leave Part 1 here, as the post has already reached 15 pages of content. I always start these posts with the intent of keeping them short and then I get stuck in and –let’s be honest– carried away. On the basis that 15 pages of content is more than enough for anyone, I will include Magnus forces in Part 2.

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 for reading (so far).

James