It is always convenient and frequently necessary to know the exact amount of stock required to make a given piece of work. There are four general methods used for determining this. The first and most accurate method, if it can be used conveniently, is mathematical calculation. Taking as an example the bent piece illustrated in Fig. 53. If the outside of this is measured, it would seem as though 16 inches of stock were required. If the inside is measured, 14 inches would seem the proper amount. It has been found by experiment that if a piece of straight stock is taken and a line drawn on it through the center, and this piece of stock then is bent and the lengths of the inside, center, and outside lines be measured, the outside line will lengthen considerably as the piece is bent. The inside line will shorten correspondingly, while the center line will remain comparatively unaltered in length. This is universally true, and the proper length of stock required for making any bent shape may always be obtained by measuring the center line of the curve or bend. To return to the first example: In this case, if the center line of the stock be measured, 7 1/2 inches will be the length for each leg, thus making a total of 15 inches of stock required to make that particular bend. This is a universal rule which should always be followed when measuring stock, to take the length of the center line.

Fig. 63. Diagram for Calculating Stock in Bent Piece.

Fig. 54. Diagram for Calculating Stock in Ring.

## Circles

On circles and parts of circles the length of stock may be easily calculated. The circumference, or distance around a circle, is found by multiplying the diameter by 3 1/7 or, more accurately, 3.1416. As an illustration, the stock necessary to bend up the ring in Fig. 54, would be calculated as follows: The inside diameter of the ring is 6 inches and the stock is 1 inch thick. This would make 7 inches the diameter C of the circle made by the center line, which may be called the calculating diameter, and the length of stock required would be 7X3 1/7 or 22 inches.