Funbers 11

A double-dose of double-digits with the number 11! It has quite the infamous history with the good – the Armistice on the 11th hour of the 11th day of the 11th month, the bad – September 11th and the attack on the Twin Towers, and the ugly – conspiracy theories including the so-called ‘fake’ moon landing of Apollo 11, making it an interesting number to say the least…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

World Cup 2018: The Perfect Penalty Kick

 

The 2018 World Cup in Russia kicks off today and so I bring you a special double-edition of Throwback Thursday looking at the science behind the perfect penalty kick… Fingers crossed the England players listen/read my website and we don’t lose to Germany in a penalty shootout (though let’s be honest we probably will).

Live interview with BBC Radio Cambridgeshire looking at the ‘unsaveable zone’ and the best way to mentally prepare for a penalty.

 

And if that wasn’t enough, here’s a full description of the ‘Penalty Kick Equation’…

For all of the footballers out there who have missed penalties recently, I thought I would explain the idea of the science behind the perfect penalty a little further, and in particular the maths equation that describes the movement of the ball. On the radio of course I couldn’t really describe the equation, so here it is:

Screen Shot 2017-06-05 at 10.09.22

If you’re not a mathematician it might look a little scary, but it’s really not too bad. The term on the left-hand side, D, gives the movement of the ball in the direction perpendicular to the direction in which the ball is kicked. In other words, how much the ball curves either left or right. This is what we want to know when a player is lining up to take a penalty, because knowing how much the ball will curl will tell us where it will end up. To work this out we need to input the variables of the system – basically use the information that we have about the kick and input it into the equation to get the result. It’s like one of those ‘function machines’ that teachers used to talk about at school: I input 4 into the ‘machine’ and it gives me 8, then I put in 5 and I get 10, what will happen if I input 6? The equation above works on the same idea, except we input a few different things and the result tells us how much the ball will curl.

So, what are the inputs on the right-hand side? The symbol p just represents the number 3.141… and it appears in the equation because footballs are round. Anytime we are using circles or spheres in maths, you can bet that p will pop up in the equations – it’s sort of its job. The ball itself is represented by R which gives the ball’s radius, i.e. how big it is, and the ball’s mass is given by m. We might expect that for a smaller ball or a lighter ball the amount it will curl will be different, so it is good to see these things are represented in the equation – sort of a sanity test if you will. The air that the ball is moving through is also important and this is represented by r, which is the density of the air. It will be pretty constant unless it’s a particularly humid or dry day.

Now, what else do you think might have an effect on how much the ball will curl? Well, surely it will depend on how hard the ball is kicked… correct. The velocity of the ball is given by v. The distance the ball has moved in the direction it is kicked is given by x, which is important as the ball will curl more over a long distance than it will if kicked only 1 metre from the goal. For a penalty this distance will be fixed at 12 yards or about 11m. The final variable is w – the angular velocity of the ball. This represents how fast the ball is spinning and you can think of it as how much ‘whip’ has been put on the ball by the player. Cristiano Ronaldo loves to hit them straight so w will be small, but for Beckham – aka the king of curl- w will be much larger. He did of course smash that one straight down the middle versus Argentina in 2002 though…

So there you have it. The maths equation that tells you how much a football will curl based on how hard you hit it and how much ‘whip’ you give it. Footballers often get a bad reputation for perhaps not being the brightest bunch, but every time they step up to take a free kick or a penalty they are pretty much doing this calculation in their head. Maybe they’re not quite so bad after all…

Funbers 10

We’ve finally reached double figures in the form of the number 10! The reason that ten is the first number with two digits is precisely because we count in base 10. Computers count in base two (0 and 1’s) and 7-tentacled aliens probably count in base seven…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Funbers 9

We love the number 9 as humans – perhaps due to the 9 months we spend inside our mother’s womb before birth… There are also LOADS of fun maths tricks that you can do with the last single-digit number, with my two favourites explained in the video below.

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Funbers 8

The number of legs on a spider, tentacles on an octopus and planets in our solar system… Eight is also a big deal in Asia – listen below to find out why!

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire here.

Funbers 7

From the number of seas sailed by pirates, to the number of days in the week named after ancient Gods, seven is a popular number. It also happens to be the maximum number of circular items that can be bundled together securely. Now there’s something you don’t hear every day…

You can listen to all of the Funbers episodes from the series with BBC Radio Cambridgeshire here.

Funbers 2 Pi

Two times pi is such an important number in maths that it deserves its very own edition of Funbers… featuring angles, trigonometry and pie jokes.

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire here.

Funbers 6

The number of strings on a classical guitar, the number of points on a Star of David and the number of legs on an insect – which make up 80% of the world’s species! Six is also a perfect number: have a listen and see if you can work out the next three…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Funbers 5

As well as being a hit(?) boyband from the 90’s, five is also a number. We have five human senses, five rings in the Olympic symbol and five Platonic Solids. These are my favourite shapes and were believed by the Ancient Greeks to be the building blocks of the universe…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

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