With the nation in a state of football fever, scientists at the University of Bath have been using software to study the art of "spin".

The element used by free-kick takers like David Beckham to score vital goals.

They have been measuring the flight of the ball and using MathSoft's Mathcad to develop mathematical models of its trajectory.

The findings may have significant implications for the design and construction of footballs in the future, as well as influencing the tactics teams adopt with a defensive wall.

Ken Bray, a visiting fellow, and Professor David Kerwin, head of the department, have developed mathematical models of the flight of a spinning ball and verified them using 3-D reconstructed digital video images of actual free kicks.

Their findings revealed only a couple of degrees variation in the kick, a slight tilt in the axis of the spin, or a marginal difference in speed, would put the kick into the wall or over the bar, making footballers who can manage and control all three elements a precious commodity.

The research revealed players who take free-kicks tend to divide into two categories.

The majority favour sidespin as it produces as much as three to four metres lateral deflection.

Liverpool's Danny Murphy is an excellent sidespin kicker.

Other players favour topspin, which is feared by goalkeepers as the ball arrives more quickly and then dips savagely in the latter portion of the flight. David Beckham is a supreme exponent of this technique.

The work showed why defending against direct freekicks used to be simple.

Attackers typically shot very hard at the defensive wall, hoping for a gap or a lucky deflection.

The old leather ball, which was prone to water absorption and weight increase, hardly swerved at all in flight and if the wall held, the goal was usually safe.

Technology has changed all this and the lighter, modern ball with its nonabsorbent surface, is very receptive to spin, shifting the tactical advantage decidedly to the attacker.

By using Mathcad to calculate solutions to multiple differential equations covering the three dimensional flight path and then fitting the results to real data to establish the aerodynamic constants governing the flight of a ball, it is possible to create an outstandingly accurate model.

Diane Ashfield, marketing manager at MathSoft, said:

"Mathcad has been used for calculations in all sorts of diverse projects, from ballet to outer space. It is likely the results of the studies may have a bearing on the design and construction of footballs in the future."