Thursday, 23 May 2013

# Diving into basic mechanics

Hurdle step

Max height of step

I taught the mechanics of solids to mechanical engineering students for around 15 years.  When it came to exams, we always tried to include examples from the real world that would stretch the most able of the students – I even had a question relating the bending of beams with the deflection of springboards during a dive.

Funny, then, that I should return to it more than a decade later to model a vibrating diving board for an Olympic coach based in Sheffield.  The idea was to use the model in conjunction with high-speed video to get an understanding of the physics of the board and to use it to enhance the coaching.  It was surprising to see how far you could get with simple 1st year mechanics once you understand what is going on.

Initial contact

Max deflection

Final contact

Max height of dive

Second rotation

Final rotation

Let’s take a typical male diver and an example dive with two and a half turns and one and a half twists.  What you see by eye is a blur of diver and speedos running to the end of the board, bouncing up in the air once, then slamming down on the tip of the board before being propelled high into the air.  During his free flight, he rotates faster than my eyes can take in before ‘plopping’ into the water leaving only a dome of boiling water and the gentle decaying bounce of the board.

The first thing to understand is the boundary conditions of the board i.e. how it is held in place.  Effectively it is a pin jointed cantilever with a pivot near its middle so that the board deflects downwards from the pivot when the diver stands at its tip.  The position of the pivot along the length of the board is the only thing that can be adjusted and is done so using a large wheel.

The dive is a beautiful example of the exchange of energy from one form to another and the first jump of this particular dive – officially called a hurdle step – is used to give the diver potential energy (i.e. height).  This is converted to kinetic energy on impact with the tip, which is then converted to strain energy of the board as it deflects to its maximum position.  The strain energy is released to propel the diver high into the air to allow him to carry out his gymnastic manoeuvres.

The easiest way to understand what the board does is to listen to the noise;  this tells you that there are vibrations interspersed with bounces of the board on the pivot (try it next time you watch diving).  Between the hurdle step and the main impacts , while the diver is in the air, the board rotates up about the pin and bounces down onto the pivot twice.

When it’s on the pivot, it vibrates as a short beam with a relatively high frequency (about 22 Hz).  Conversely, when it’s not on the pivot it vibrates as a long beam with a relatively low frequency of about 8 Hz.  After the 2nd rebound of the board, the diver is on the way back down and coordinates his feet to impact with the board – and this is where it gets interesting.  The board is slightly raised off the pivot, rotating slightly first up and then back down.  Superimposed on top of this is the 8 Hz oscillation which at the tip appears to cancel out rotations so that the end of the board – where the diver is about to land – appears almost stationary in the air.

Getting the board to do this seems to be a combination of setting the pivot in the right place,  and jumping the right height during the hurdle step to get the landing time right.  A successful dive depends upon having enough time in the air to execute the rotations and twists before hitting the water.  This can be done by bouncing really high off the springboard, which in turn is a function of the strain energy stored in the board.  The diver intuitively sets the deflection of the board by altering the stiffness of the board using the pivot (which also affects timing).

The tip of the board was modeled using simple beam theory and damped harmonic motion - something a 1st year in engineering could put together - and gives a pretty good description of reality.  So, when you watch the diving at the Olympics this summer, listen to the noise of the board and think about the rudimentary mechanics involved – it may just be appearing as an exam question.

• As I diving coach for the past 30 years in the States, I enjoyed reading your article. There is one area I wanted to comment on in regards to the success of the dive depending upon having a enough height to complete the number of rotations and twists required. There is an important fact about gaining the height needed to completion. The higher the diver tries to go the slower they will rotate on their horizontal axis (the waist area). Therefore a most important aspect of making a successful dive is to create the rotation needed through angular momentum and the throwing of the arms to create speed before the divers feet leave the board.If the diver stays with board as it comes back up, the board will throw them high enough to give the needed height. It is the speed of the spin that diver needs to make a higher degree of difficulty dive successful. I also like your mention of the board bouncing against the fulcrum twice while the diver descends to the tip of the board from the hurdle. The best divers will listen to the board hit the fulcrum twice and if they only hear it bounce once they will make an adjustment so the can gain the timing back they need for a good take-off. Well done article.

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• A great article - but nothing would tempt me to put it to the test.

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• I hope you never stop! This is one of the best blogs I’ve ever read. You've got some mad skill here, man. I just hope that you don’t lose your style because you are definitely one of the coolest bloggers out there. Please keep it up because the internet needs someone like you spreading the world..

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