TABLE FOR SPACING HOLES IN CIRCLES THE table on pages 284 and 285 will be found of service when it is desired to space any number of holes up to and including 32, in a circle. The number of divisions or holes desired will be found in the first column, the corresponding angle included at the center being given as a convenience in the second column. The remaining column heads cover various diameters of circles from 1 to 12 inches, and under these different heads and opposite the required number of holes will be found the lengths of chords or distances between hole centers for the given circle diameter. Thus, if it is required to space off 18 holes in an 8-inch circle, by following down the first column until 18 is reached and then reading directly to the right, in the column headed "Length of ChordDia. 8," will be found the distance 1.389 as the chord length for that number of divisions and diameter of circle. Or, suppose a circle of 12 inches diameter is to be spaced off for a series of 27 holes to be drilled at equal distances apart: Opposite 27 found in the first column, and under the heading, "Dia. 12," will be found the chord 1.393 as the length to which the dividers may be set directly for laying off the series of holes. If it is desired to lay off a series of holes in a circle of some diameter not given in the table, say 10 holes in an 11-inch circle, subtract the chord for 10 holes in an 11-inch circle, or, 3.399 from the chord in the "Dia. 12" column, or 3.708, and add half the difference (.154) to 3.399, giving 3.553 as the chord or center distance between holes. Or, if 24 holes are to be equally spaced in a 20-inch circle, all that is necessary in order to find the chord, or center distance, is to find opposite 24, and in the column headed, "Dia. 1o," the quantity 1.305 and multiply this by 2, giving a length of 2.610 inches as the center distance. TABLE OF SIDES, ANGLES AND SINES THE table on pages 287 to 291 is carried out for a much higher number of sides or spaces than are included in the preceding table and will be found useful in many cases not covered by that table. It was originally computed for finding the thicknesses of commutator bars and also for calculating the chord for spacing slots in armature punchings. In using this table the diameter of the circle is, of course, multiplied by the sine opposite the desired number of holes or sides. Assuming for illustration that a series of 51 holes are to be equally spaced about a circle having a diameter of 17 inches, opposite 51 in the column headed "No. of Sides," find the quantity .06156 in the column headed "Sine," and multiply this quantity by 17. The product 1.0456 is the length of the chord or the required distance between centers of the holes for this circle. Or, if 40 equidistant points are to be spaced about a circle 16 inches diameter, opposite the number of sides, 40, will be found the quantity .078459 which multiplied by 16 gives 1.255 inch as the distance between centers. MULTIPLY DIAMETER BY SINE TO GET LENGTH OF SIDE (Angle given is half of angle subtended at center) Angle Sides Deg. Min. Sec. 345678 Sine .8660254 No. Sides 52 9 ΙΟ II 20 .3420201 3-6-12.41 .0541388 18 .3090170 3-3-3.05 .0532221 16-21-49.09 .2817325 3 .0523360 .2588190 61 12-51-25.71 .2225208 63 15 12 .2079116 64 2-48- 45 .0490676 11-15 .1950903 65 2-46-9.23 .0483133 10-35-17.64 .1837495 66 2-43-38.18 .0475819 IO .1736481 67 2-41-11.64 .0468722 9 .1564344 69 2-36-31.30 .0455145 21 8-34-17.14 .1490422 22 8-10-54.54 .1423148 71 .1361666 72 .1305262 73 7-12 .1253332 6-55-23.07 .1205366 75 74 31 5-48-23.22 .1011683 80 2-15 .0392598 .0980171 81 .0950560 82 34 5-17-38.82 .0922683 83 35 5-8-34.28 .0896392 84 .0871557 85 .0848058 86 .0825793 .0804665 2-2-43.63 .0356923 |