The Effect of Hoop Upright Diameter on the Acceptance Angle of a Hoop
To save others scratching their heads on how to calculate the acceptance angle of a hoop the detail is given below. The answer is of current interest where it is planned that 3/4” diameter hoop uprights be used instead of the ‘normal’ 5/8” ones in an International competition.
The above diagram is the key for calculating the angle theta, Φ, which is the maximum angular deviation from playing face-on to the hoop where the ball will just pass through the hoop without touching the uprights.
The following variables are used:
The blue triangle is the route to the answer. From the diagram:
Standard relationships give cos Φ = adjacent / hypotenuse, hence
For a 5/8” diameter upright theta = ± 6.927 degrees, 13.854 degree opening
For a 3/4” diameter upright theta = ± 6.828 degrees, 13.656 degree opening
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