The Approach Length calculator computes the approach length for a circular cutting tool (e.g. circular saw) based on the diameter of the cutting blade and the depth of the cut.
INSTRUCTIONS: Choose units and enter the following:
Approach Length (AL): The calculator returns the length in millimeters. However, this can be automatically converted to compatible units via the pull-down menu.
The formula for Approach Length for a cutting operation is:
`AL = sqrt(D*d-d^2)`
where:
In the diagram, the radius, half the diameter, is the hypotenuse of the right triangle which has side `delta = D/2 - d`.
Using the Pythagorean Theorem: `(D/2)^2 = delta^2 + "Approach"^2`
which implies: `"Approach"^2 = (D/2)^2 - delta^2`
`=>` Approach = `sqrt((D/2)^2 - (D/2 - d)^2)`
`=>` Approach = `sqrt(D^2/4 - ((D^2/4) -(2*D*d)/2 + d^2))`
`=>` Approach = `sqrt(D^2/4 - D^2/4 + D*d - d^2)`
`=>` Approach = `sqrt(D*d - d^2)`