Course rating volunteer Goldsborough tackles ball speed query

  A Golf Association of Philadelphia course rating at Morgan Hill Golf Course seemed like business as usual on Sept. 4. Jack Hoffman, the organization’s 2015 Volunteer of the Year, and his team set out to accurately measure the layout and to account for obstacles that affect its playing difficulty.

  Morgan Hill’s 12th hole, a drop par 3 that measures 196 yards from the tips, prompted a group discussion different from the rest. Sure, typical items such as bunkers and recoverability served as topics, but the hole’s elevation triggered a curiosity beyond the normal banter.

  If a 7-iron is hit to a green 100 feet below the tee, and the golf ball, at its’ apex, is 160 feet above the green, what is the velocity of the ball striking the green? That’s what Ed Brzezowski, a GAP Executive Committee member and staple on Hoffman’s team, wondered. And he knew the right person to ask.

  “Ball marks were huge and your name came up as someone who could figure it out,” Brzezowski wrote in an e-mail to Glenn Goldsborough, a GAP course rating volunteer of 10 years and physics teacher at Pennsbury High School of 18 years.

  Goldsborough, with an easygoing attitude to match a mathematical mind, obliged.

  “Just for fun, I figured I’d do a quick calculation,” he said. “To actually calculate how fast it would go would be extremely difficult. This calculation would be how fast the ball would go if it was launched on the Earth and there was no air on the Earth, which is obviously not a realistic situation. If we wanted to do a realistic situation, there would be a lot of calculus and a lot of integration because the rotation of the ball provides lift and because of air resistance there is air drag. This does not come close to being what it would actually be.”

  Maybe not, but Goldsborough’s calculation warrants notice. Spoiler alert: the ball’s velocity as it lands on Morgan Hill’s 12th green is 117 miles per hour. The details behind that number make up the juicy plot here.

  First, Goldsborough plucked a pair of figures — ball speed and launch angle — from the LPGA tour averages, which closely resemble those of the average amateur golfer. The ball speed used in Goldsborough’s calculation is 104 miles per hour, or 152.533 feet per second; the launch angle is 19 degrees.

  Next, he sketched a right angle, with the initial height of 100 feet (the tee-box) at the top and final height of zero feet (the green) at the bottom. Goldsborough broke the golf ball’s initial velocity into a horizontal and vertical component to continue.

  “That’s important because horizontally the speed doesn’t change at all,” he said. “For example, if you’re traveling straight in an airplane and take a tennis ball and throw it straight up in the air, that tennis ball is going to come straight back down into your hands, unless you’re taking off or landing. That means the horizontal speed of the ball and you are the same. It doesn’t change at all. But if you had somebody that was standing outside of the plane and watching it, it would take a parabolic path.”

  In a scenario without air lift or resistance, the horizontal speed remains constant, so Goldsborough, for the Morgan Hill hypothetical, marked it at 144 feet per second squared. The ball’s vertical speed, however, changes because of gravity. Goldsborough determined it to be 49.85 feet per second.

  With those variables established, a physics tool entered the picture: a UAM (Uniformly Accelerated Motion) equation. Layman’s terms please.

  “If you dropped a ball off of a building, you could roughly calculate how fast it’s going when it impacts the ground if you knew the height of the building,” Goldsborough, 45, of Norwood, Pa., said. “If you have a dragster or a car that has a constant acceleration, you can calculate how long it takes to go from 0-60 (miles per hour). Initial velocity, final velocity, acceleration, distance and/or time … you need three of four variables to find the fourth.”

  Find the fourth he did. Goldsborough determined the acceleration downward due to Earth’s gravity: 32 feet per second squared. He multiplied it by the amount of drop-off on Morgan Hill’s 12th hole: 100 feet. Add it to the ball’s vertical speed squared, and Goldsborough acquired the vertical velocity, a figure essential to the formula.

  Enter another physics staple — the Pythagorean Theorem. Goldsborough calculated the ball’s vertical velocity at 8,868 feet per second squared. Square the ball’s horizontal speed to establish 20,800 feet per square second. Add both figures to arrive at 29,688, the square root of which is 172 feet per second.

  Convert that into miles per hour, and one arrives at 117.

  Crunching numbers and applying physics to golf is in Goldsborough’s wheelhouse. However, he rarely computes while playing.

  “I try to soak in the atmosphere more than anything. I love being outside and on a golf course,” Goldsborough said. “If I start thinking too much, it’s a bad thing.”

  The Association’s course raters know who to turn to when they start thinking physics.

  “Glenn is a valuable member of our course rating team. His mind works differently than the rest of ours and he processes things in a manner that most of us just simply couldn’t comprehend,” John Manos, GAP Director of Course Rating, said. “The course rating charts can be very confusing but they’re child’s play to Glenn given what he deals with on a daily basis. Glenn brings a different mindset to our ratings and makes our team that much stronger because of it.”

Golf Association of Philadelphia
  Founded in 1897, the Golf Association of Philadelphia (GAP) is the oldest regional golf association in the United States and serves as the principal ruling body of amateur golf in its region. Its 151 Full Member Clubs and 57,000 individual members are spread across parts of Pennsylvania, New Jersey, Delaware and Maryland. As Philadelphia’s Most Trusted Source of Golf Information, the Golf Association of Philadelphia’s mission is to promote, preserve and protect the game of golf.