In the first part of this article we let maths set the scene for a free kick. Now we continue the drama, tracing the trajectory of the ball throughout the milliseconds it takes it to reach the goal line.

A new mathematical analysis of how to hit a winning serve shows that spin is the thing. Perhaps there's still time for Murray's coach to include some maths in his preparations for the match today...

Runners and cyclists can tolerate heat and cold but the thing they dislike most is wind. They know it produces slower times. Can we show them why?

What makes a perfect football? Anyone who plays or simply watches the game could quickly list the qualities. The ball must be round, retain its shape, be bouncy but not too lively and, most importantly, be capable of impressive speeds. We find out that this last point is all down to the ball's surface, the most prized research goal in ball design.

Last month leading researchers in sports technology met at the Royal Academy of Engineering in London to demonstrate just how far their field has come over recent years. The changes they make to athletes' equipment and clothes may only make a tiny difference to their performance, but once they're added up they can mean the difference between gold and silver. In this podcast we talk to some leading sport engineers.

Last week leading researchers in sports technology met at the Royal Academy of Engineering in London to demonstrate just how far their field has come over recent years. The changes they make to athletes' equipment and clothes may only make a tiny difference to their performance, but once they're added up they can mean the difference between gold and silver.

Andy Green, Royal Air force pilot and Oxford maths graduate, is gearing up to break his own land speed record in Bloodhound SSC, a supersonic car designed to reach speeds of up to 1000mph. He tells Plus about the challenges — and the maths — behind this engineering adventure.

In 1997 Andy Green was the first to break the sound barrier in his car Thrust SSC, which reached speeds of over 760mph. Now he and his team want to push things even further with a car called Bloodhound, designed to reach the dizzy heights of 1,000mph, about 1.3 times the speed of sound. Ben Evans explains how maths is used to build this car.

Chuck Gill caught the space bug as a child when watching Alan Shepherd launch into space. Since then he's worked as a US Air Force navigator, a satellite operator, and in the US intelligence service. These days he's busy reducing carbon emissions and preparing London for the 2012 Olympics. Plus went to see him to find out more about his career.

Phil Trinh discovers how maths helps solve the mysteries of flight and love.

Learn about the aerodynamics of footballs and perfect your free kick.

One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the Navier-Stokes equations.