Sports Safety Netting

Trajectory Analysis

Three Dimensional Modeling of Golf Shots.

Two dimensions are not enough!

Errant balls travel in unexpected directions, rising higher, curving more, and heading off-line.
Ball trajectories are important because an effective barrier has to intercept the balls that are likely to reach the "at risk area". Barriers have to be positioned correctly and be at a suitable height

What 3D simulations can demonstrate ...

Best locations for golf ball barriers If we understand the: *impact points* of the balls,with and without barriers, to determine which balls it is most important to stop, and *flight* *paths* of the golf balls in three dimensions, so that we can work out the best size and shape of barrier to interrupt the flight. Golf “ballistics” has a long history, and many mathematicians have studied the problem. So the forces acting on a golf ball & the aerodynamics of golf ball flight are well documented. Our challenge is translating these studies into reliable models that will come close to “real” golf ball flight paths. Good simulations show you the options based on the design constraints: No undue interference with “fair” golf play. Suitable protection for the At Risk zone (a major road may need 99% protection, a waterway 90%).
Best height & shape for barriers With 3D trajectory studies, all types of ball flights can be examined, with a full understanding of the effects of different: Locations for the net. Heights of net. Wind conditions. To test positioning and height, we use flexible models that can : perform multiple simulation runs for many golf shots, under numerous different wind conditions. show "At risk zones" locations in 3D. for a player perspective, transfer to a more visual 3D model
Simulated impact patterns are then calculated for the "at risk zone", and transferred to the map for a decision about its true extent. Sometimes, neighbouring properties that were initially thought to be unaffected, are shown to be "in the zone"
Will it work? Now, differing wind conditions allow a few balls over.
This happens when: Headwinds (shown right) slow balls that would otherwise overfly the zone, or "balloon" the flight and balls are both higher than expected, and drop sooner. Crosswinds carry balls across into the zone. Tailwinds increase the carry of balls that would usually fall short, and these cross into the zone. Transferred to sketch to show the locations.

Ball Tracking

Ball-tracking radars can collect information about the 3D path of the ball are our preferred research tools. This data is used to derive a model that reflects the “real flight paths”.

Developments from military radar technology (phased array radar) are being adapted to sporting analysis. These are currently expensive, but are used in fields such as TV commentaries to show ball flights (“Hawkeye” in tennis, cricket) where the cost can be justified.

The same technology is now being applied to golf for club fitting, and this equipment can track the flight path of a golf ball over about 200m.

Measuring golf ball flight

In principle, the physics and mathematics of golf ball flight is relatively well understood. In reality, conditions like wind gusts and currents will change ball trjectories in short order. Measuring and understanding the range of values of all the main variables complicates the development of a useable model.

Some can be readily measured from the launch of the ball:

1. Ball velocity

2. Angle of Launch (from the ground)

3. Azimuth (angle on ground from North)

Others can also be measured from the launch of the ball, but not as easily:

4. Spin rate

5. Spin angles

The last 3 variables can be only measured at a point in time and a particular place

6. Wind speed

7. Wind direction

8. Air density

Winds can gust even during the flight of the ball, and humidity/ air density sometimes varies with height above ground. Other variables, such as the rate of spin decay (how quickly the spin slows) remain unknown, except for rough estimates.