Contact Sphere - Obstacle Calculation


A calculator for the point where a sphere on a plane - or a circle on a line - touches an obstacle at a certain height. The obstacle must be lower than the sphere radius, otherwise the distance from the contact point of the sphere to the plane is equal to the radius. Please enter two values, the third value and the chord length will be calculated.

Contact of a sphere with an obstacle

Sphere radius r:
Obstacle height h:
Distance to obstacle a:
Chord length c:

Round to    decimal places.

Example: a sphere with a diameter of one meter, so a radius of 50 cm, touches a 10 cm high obstacle. Then the distance of the sphere's center to the obstacle, projected to the plane, is 30 cm.

The calculation is:

Be γ the angle between the two straight lines from the center of the sphere to the touching points.
Be c the chord length between both touching points.
c² = a² + h²

If r and h are given: γ = acos( 1 - h/r )
If r and a are given: γ = asin( a/r )
c = √2 r² * [ 1 - cos(γ) ]

If a and h are given:
γ = 2 acos[ (a² + c² - h²) / (2ac) ]
r = c / sin(γ) * sin[ (π-γ) / 2 ] Webprojects | Imprint & Privacy | German: Berührung Kugel - Hindernis