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Slot Punch and Drift Geometry

*** DO NOT TRUST MY BLACKSMITHING MATH I NEED TO TEST THIS***



While touring the Philadelphia Museum of Art I came across a very cool 15th Century Italian fire dog.

I noticed that this piece was designed to be broken down for transport by way of a series of end user attachable fasteners. 
Think 15th century Ikea. 


Here is basicly a cotter pin that was inserted through and any local smith would simply bend the pins over.
Unfortunately due to a ban on flash photography I was unable to get clear photos of the bottom.



I really liked the slotted wedged tenon they used to hold the uprights on.



Doing this type of slotted wedged tenon is simple in wood since you take a sharp chisel an remove the wood to make the slot.
Making the slotted wedged tenon in iron requires a little creative math.


PLEASE NOTE I HAVE NOT TESTED THIS YET

If you have a bar and you want to create a slot with no bulges you will need to have a matched set of drift and punch.
The metal to either side of a punched hole is moved out horizontally and a negligable amount of steel is removed during the punching process.
I am Discounting the thickness of the bar since that will be same at the beginning and end of this project and does not affect the math.

Now for some blacksmithing math.


this is the total steel for the sides of the slot that area of steel will remain the same when the slot is drifted longer.
Variables
Wb Width of bar
Wd Width of drift
Ld Length of drift
Lp Length of punch
Ao area of affected origional bar bar
Ad cross section area of drift
Af final cross section area

Ao= Wb * Lp  

Ad= Wd * Ld


The new total area will sum of the old area plus the cross section of the drift. 


Af = Ao + Ad = Wb * Ld

OR

Wb * Ld = Wb * Lp + Wd * Ld




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