Vertical Acceptance Window and Mile High Tennis

In order to hit the ball over the net and have it land on or before the far baseline, the ball must leave the racquet within a certain "vertical window".  From simulations done by Howard Brody (Tennis Science for Tennis Players, pp 99-100) I noticed that this window gets cut in half (shrinks by 50%) as you increase your initial ball speed from 56 mph to 67 mph for balls hit at sea level.  That means if you avoid the sidelines, good advice in rally situations, you more than double your chances of getting the ball in if you hit the ball 56 mph rather than 67 mph.  A 67 mph shot is getting pretty fast for most people, but it's not crazy fast.  I can hit a ball over 80 mph and I'm not a big hitter at all.  Most juniors around here can hit forehands 90 or 100 mph.  Yet, I see almost nobody at my mile-high altitude sustaining rallies in the 60 mph range.  Why not?  Do we suck?  Hardly.

Our air is less dense than air at sea level, 0.84 compared to 1.00 roughly.  To compensate for this, the ITF allows us balls with reduced compression, 9% less than standard balls.  That means the balls bounce a bit lower and come off the racquets a bit slower.  So they make it harder to hit the ball 56 mph or 67 mph in the first place.  But the balls are otherwise the same as low-altitude balls, same size, mass, and nap.  So once we hit them, they do not slow down as quickly in our air.

A ball with an initial velocity of 47 mph in Denver will have the same vertical acceptance window as a 56 mph ball struck at sea level.  A ball struck at 56 mph in Denver will have the same vertical acceptance window as a ball struck at 67 mph at sea level.  Our vertical acceptance window gets cut in half at relatively slow ball speeds.  It's just not that hard to hit a ball 56 mph.  Almost anyone can do that.  But due to our dramatically reduced vertical acceptance window, very few people can control a rally at that speed at high altitude.

The window shrinks even more quickly as the speeds get up over 67 mph at low altitude or 56 mph in Denver.  Very, very few people can sustain a rally with initial ball speeds over 70 mph at low altitude. I have timed many rallies between very good players (tour and college level men and women) and in those rallies, initial ball speeds above 70 mph were rare.  None of those 70 mph rallies were at high altitude.

It makes sense then that good players in Denver would have enormous trouble sustaining rallies with ball speeds above 60 mph.  No wonder tour pros avoid high altitude.  They're not good enough to play here!