The three methods generally used to find the dimensions of a sheet metal blank are the tentative, the gravitative, and the mensurative-probably, as a rule, more time is spent in experimenting to obtain the proper diameter of a blank than it takes to manufacture the tools.

There are many experienced toolmakers who can design and manipulate the tools for producing almost any shaped article in a press that one cares to place before them, yet cannot form any idea by calculation as to what size blank is required from which the article is to be produced. These mechanics usually work by the tentative method, either giving a rough guess based upon their past experience, and trying over and over again until they have arrived at the proper size or thereabouts, or they look over the patterns of previous work that has been done in the workshop, and select that blank which they think will work out approximately correct.

The gravitative method is often used when a sample of the work to be done is supplied, and this method is particularly useful in the case of stamping or raising sheet metal articles where no drawing or extending of the metal is to take place. The sample of work is carefully weighed and its thickness noted, after which a piece of sheet metal measuring one square inch in area and of the same gauge or thickness as the particular sample is also weighed. Then the weight of the sample or finished article, divided by the weight of the one square inch of sheet metal, will give the number of square inches to he contained in the blank for producing an article to sample. For example, suppose the toolmaker is supplid with a sample brass stamping which weighs {avoirdupois) 1 lb. 4 oz. 6 drms. = 326 drms., and it is found that the weight of one square inch of sheet metal {measuring in thickness exactly the same gauge as sample) is 1 1/2drms., then the number of square inches to be contained in the area of the required blank will be 326 / 1.5 square inch = 217.333 square inches. This will be the exact area of metal contained in the sample, and assuming that the article is not to be clipped after being stamped, then a blank containing the 217.333 square inches would be correct. On the other hand, should it be necessary to clip the article after it has been stamped, as is frequently the case, then a few square inches must necessarily be added to the area of the blank, the amount added being according to the shape, size, and nature of the stamping.

The mensurative method consists in finding the exact area that is contained in the surface of the article to be produced; the blank is then cut out a certain size, so that it will contain the same area in square inches as the sample. The sample may be an actual finished article, or a sketch may be supplied showing the exact outline and size of the article to be made-in either case it is a question of mensuration.

Anyone having an elementary knowledge of mensuration of surfaces may, by exercising a little care and judgment, obtain fairly reliable results by means of finding the area of an article, and then fixing upon the proper diameter and shape for the required blank. But, even though a tool-maker may be able to deal with the mensuration of curved surfaces, it is not an easy matter to fix upon the diameter of a blank when dealing with articles which have to undergo a large number of processes, such as re-drawings or extensions, as, for instance, would be necessary in producing the brass cases for quick-firing ammunition. This is an instance where the pattern sample shelf often comes in useful to the tool-maker.

It may be truly stated that the usual methods taught by mathematicians for obtaining the areas of curved surfaces of peculiar outline often introduce formula containing the differential and integral calculus. This makes it absolutely impossible for the practical mechanic or toolmaker to follow the reasoning necessary to work out the equations. When, however, such surfaces of unusual outline have to be measured, they may be readily dealt with in comparative ease (if the article be measured up in sections). The few selected common shaped articles illustrated from fig. 268 to fig. 280, together with their formula;, will enable the student to follow the application of mensuration to sheet metal processes. The examples have been reduced down to ordinary figures, so that the working may be more readily followed by the practical mechanic in the workshop, who may, perhaps, not understand a simple algebraical equation. Some useful notes on mensuration of surfaces will be found in The Practical Engineer Pocket Book, besides tables of areas and circumferences of circles, squares and square roots, and decimal equivalents of fractional parts of an inch, all of which will greatly assist the workman to follow the examples. Fig. 268, Cylindrical flat-bottomed vessel:

Fig. 268.

Fig. 269.

Area = π d h + d2π /4

= 3.1416 x 2 x 1 + 4x3.1416 /4

= 9.4248 square inches, or 7r(2 + l)=37r = 9.4248 square inches.

Then, to obtain the diameter of the required blank, multiply the square root of the area contained in the figure by 1.12838.

Thus the diameter of blank

= √ 9.4248 x 1.12838 = 3.464 inches.

Fig. 269, Cylindrical vessel spherical ended:

Area = π d h +d2π / 2

= 3.1416 (2 x .75) + 6.2832

= 4.7124 + 6.2832 = 10.9956 square inches.

Diameter of blank = √10.9956 x 1.12838 = 3.7416 inches.

Fig. 270.

Fig.. 270, Sphere:

Area = d2π

= 4 x 3.1416 = 12.5664 square inches.

Diameter of blank '= √12.5664 x 1.12838 = 4 inches. Fig. 271, Conical vessel:

Area = -π D+d /2 S + d2π /4 when S = the slant height of vessel.