Cold Saw/Depth Blade Slot
What is a Blade Slot
The blade slot is an opening under the vise's mounting surface. This opening provides space into which the blade can descend.
The blade needs to descend more than the vise's mounting surface in order to fully cut material that is resting on the mounting surface.
If the blade slot is not deep enough, then the blade will cut into the vise.
So let's find out how deep to make the blade slot!
Maximum Depth Situation
The blade is circular, so the wider the cut, the deeper we have to make the slot.
In addition, the diameter of the circular blade also affects our required slot depth.
We want the blade slot to be as deep as the highest depth we're ever going to use. And if depth is determined by the width of the cut, then we have to figure out what is the widest cut we expect to perform on the Cold Saw.
A bit of insight at this point is that the widest cut that we perform is not solely dependent on the widest material we cut.
We also want to perform angle cuts, which span the material diagonally, hence are wider than straight cuts. The greater the angle away from 90 degrees (straight) cuts, the wider the angle cut (assuming that the entire angle range is within 180 degrees).
So it appears that the 3 variables we are working with are:
Required Slot Depth = D
Maximum Material Width = W
Maximum Cut Angle = A
Blade Diameter = B
Solving for Required Slot Depth in Terms of the Other Variables
From circle geometry, we know that the horizontal and vertical position of the circumference of a circle is dependent on each other and the radius:
x^2 + y^2 = r^2
We can put this equation in terms of our variables where applicable, and renaming where relevant.
1: (Cut Width/2)^2 + (Length of Blade Radius Over Vise Surface)^2 = (Blade Diameter/2)^2
Cut width is actually determined by the material width and the angle of the cut:
From trigonometry, we know that the cosine of an angle in a right triangle is equal to the horizontal side (the side touching the angle and right angle) divided by the hypotenuse.
cos(Cut Angle) = (Material Width/2) / (Cut Width/2)
cos(A) = (W/2) / (Cut Width/2)
Isolating Cut Width, we get:
2: Cut Width = W / cosA
Now we can substitute equation 2 into equation 1 to get:
(W/cosA * 1/2)^2 + (Amount of Blade Radius Over Surface)^2 = (B/2)^2
Isolating Amount of Blade Radius Over Surface,
3: Amount of Blade Radius Over Surface = (1/2) * sqrt[ (B^2) - (W/cosA)^2 ]
We know that Required Slot Depth = Blade Radius - Amount of Blade Radius Over Surface
D = (B/2) - (1/2) * sqrt[ (B^2) - (W/cosA)^2 ]
Maximum Cut Height
For a given cut width and assuming large enough blade slot, what is the maximum height of the material that can be cut?
We introduce a new variable here, the diameter of the blade supports (because they will stop the blade's descent when they touch the workpiece on the top).
Blade Support Diameter: S
Putting the Blade Support Diameter into the equation for Amount of Blade Radius Over Surface, we get:
Amount of Blade Radius Available to Cut With = (1/2) * sqrt[ (B^2) - (W/cosA)^2 ] - (S/2)
And finally to make things clear, note that the Amount of Blade Radius Available to Cut With = Maximum Cut Height