Reverse an equation

[Helvetosaur]

Hi all,

I have the following formula for calculating the “scallop height” (h) with a spherical cutter of radius ®, given the “stepover” (x).

h=r-\sqrt{r^2-(x^2/4})

With my remnants of high-school algebra, I tried to “reverse” the formula to solve for x given a desired h. However, my formula does not give me an accurate result, so I must have done something wrong…

x=\sqrt{8*h*r-h^2}

So, does anyone know how to do this correctly?

TIA, --Mitch

[Dancergraham (Graham Knapp)]

Hi Mitch,

I get \sqrt{4(r^2-(r-h)^2)} - does that make sense? It seems to work.

Simplifies to \sqrt{4h^2 -8rh}

[DanielPiker]

Wolfram Alpha can be quite handy for this sort of thing
solve h=r - sqrt(r^2-x^2/4) for x

[emilio]

BTW … Taking a more ‘geometrical’, step by step, approach :

t = r - h
y = \sqrt{ r^2 - t^2 }
x = 2 * y

FWIW …

[Helvetosaur]

Thanks guys !!!