Soccer and Physics

Ben, an adult amateur player, asks:

Why does the air pressure affect the distance the ball travels?

Answer

Interesting question – ready-made for an answer chock full of equations and lots of physics, but we’ll I’ll rein in our enthusiasm and try not to get technical.  The answer depends on what the ball is traveling on.

When the ball is in continuous contact with the surface of the pitch (i.e., it is rolling), the pressure of the ball determines the rigidity of the surface of the ball (higher pressure = more rigidity) which in turn has a measurable though not easily visible effect on the total surface area of the ball that is in actual contact with the ground’s surface.  At higher pressures, the area of contact is smaller (because the ball is “rounder”) and thus there is less friction on the passage of the ball across the pitch surface.  There is a smaller, secondary effect at higher pressure caused by a somewhat greater “lift” that makes the ball ride a bit higher on the pitch surface.  Remember, a ball is, in effect, a type of balloon – the more air there is in it, the lighter it is and, as with “roundness,” this reduces slightly the contact surface area.  In short, a higher pressure produces a speedier ball, all other things equal.

However, the other medium on which a ball travels is the air.  Here, again, air pressure acts similarly (see above).  A rounder ball (a function of air pressure)  encounters less “drag” while in the air and has greater buoyancy.  There is a third factor regarding a ball traveling in the air that is not found when a ball is rolling on the ground and that is the fact that, inevitably, a ball in the air comes down and makes contact with the ground.  Holding all other factors equal, a higher ball pressure makes for a higher bounce (a factor that you can often actually hear by listening to the sound of the contact – a ping rather than a thud in extreme cases!).  Now, however, something else comes into play (no pun intended) and that is the angle at which the ball is traveling just prior to contact with the ground.  It isn’t speed as such (as is the case with rolling) but it does directly affect distance – which, in a soccer game, may be just as important as the speed of the ball.  With higher air pressure comes greater bounce when the contact occurs – the more acute the angle, the greater the distance for any given air pressure as a result of the bounce effect.

So, the higher the pressure (within the range permitted by Law 2, of course), the greater is the rolling speed and the greater the rolling speed, the longer is the distance the ball will roll (assuming someone from the other team doesn’t stop it!).  This generalization also assumes a relatively constant consistency in the surface (one of the reasons why, again all other things equal, soccer balls travel faster on artificial surfaces relative to grass, and faster on short grass than taller grass).  Further, for a ball launched into the air, the higher the pressure is, the greater the distance traveled both before and after “the bounce” for contact at any angle of less than 90 degrees behind the ball (disregard all forms of spin … it gets too complicated).

There — not a single formal physics lecture and no equations!  Instinctively, though, a home team which has been coached to engage in fast play will likely provide the Referee with game balls at the upper end of the allowable pressure range.  A different team, which may not like or be used to fast play, is likely to provide game balls at the lower end of the pressure range.  It is not the Referee’s job to deliberately favor one team or another by changing an allowable ball pressure up or down based on personal preferences.  If it is in the allowable range, leave it alone.  If it is not, give it to the home team (it’s their ball anyway) for correction but be sure to check a corrected ball again and, again, leave it alone if it is in the allowable range.