Approach Length

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Equation / Last modified by mike on 2015/07/29 06:35
Rating
ID
Carol.Approach Length
UUID
8082ff96-c532-11e3-b7aa-bc764e2038f2

This equation calculates the Approach Length for a cutting operation as:

Approach Length = `sqrt(D*d-d^2)`

where D is the diameter of the cutter and d is the depth of the job

'pi'

ApproachLength-illustration.png

Notes

In the diagram, 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)`