What kind of welding math do I use to figure the dimensions of a square so that it fits inside a circle?
And when would you ever need to do that?
The first application that comes to mind is for building a square frame that supports a round part.
The round part might be a table top, a fixture, a base to a turntable...doesnt really matter.
In aircraft tooling, many of the fixtures are round.
And the easiest and most efficient way to build a stand or a cart for a round object is to make it square.
Usually, this would be a simple stand with casters. But sometimes, there would be some storage areas for tooling, spare parts, etc.
Its a really simple little formula. The only tedious part is converting fractions to decimals and then back to fractions again if you are in the USA and using imperial measurements.
In fact, just as a side note, I noticed while I was doing this video, that my tape measure had metric increments....It probably would have been easier for me to just use them. But when you are accustomed to using inches and fractions, you just roll with it.
With all the conversion charts available these days, it took me seconds to do the conversions.
So the diameter of my sample round piece was 13 5/8"
I converted the 5/8" to .625" just by dividing 5 by 8. ( I already knew that 5/8" was .625" but went thru the exercise anyway)
Then I multiplied 13.625 by .707
I came up with 9.633"
Not to use my tape measure again, I needed to convert .633 back to a fraction.
There are numerous conversion charts available I like engineeringtoolbox.com
There are all kinds of conversion charts there.
Actually, I didnt even need to look at a chart because .633 is only .008" more than .625"
Just to illustrate the application further, I cut 4 pieces 9 5/8" long with 45 deg miters.
And as you can see, it fit exactly within the circle piece I used for demonstration.
One more use I can think of for a formula like this is to quickly calculate what size square you could cut out of a round drop.
Sometimes, round drop pieces can be had pretty cheap because they are a common by product of cnc plasma cutting operations.
For example, if you needed some 12" square plates, what size round pieces would you need to be able to cut a 12" square out of them?
In this case you would actually use the number 1.414 because what you are actually doing is figuring out the hypotenuse of a right isosceles triangle.
By multiplying 12" by 1.414, you would quickly know the minimum diameter of a circle that would yield a 12" square.
12 x 1.414 = 16.968"
So it takes a circle almost 17 inches in diameter to yield a 12" square