The Field Practice of Laying Out Circular Curves for Railroads ... |
Other editions - View all
Popular passages
Page 152 - E, is equal to twice as many right angles as the figure has sides, less four right angles.
Page 147 - Let the angle abd be 1 20°, how far from b must we begin, at a or d, to lay out a curve and, of 2865 feet radius ? Here, half of the angle abd= 60°, which taken from 90° leaves the angle * ca = 30°.
Page 156 - That is, from the square of the radius subtract the square of half the chord, and take the square root of the remainder from radius, for the middle ordinate.
Page 141 - ... &c., as before, to the end of the curve. Finally, in order to pass from the end of the curve at...
Page 147 - ... must be put in at every angle, or often the whole direction of the line changed. Without stopping to explain the compound curve, reversed curve, or any of the intricacies of location, it is thought advisable simply to give a rule for inserting a curve at any of the angles of intersection. Suppose it is required to find the point A or D at which to commence a curve of a given radius. RULE. — Subtract half the angle A 3 D from 90°, the remainder will be the angle B c A or B c D.
Page 141 - Bs, is called the tangential angle, as being that by which the curve is connected with the tangent AD ; but inasmuch as the others are all equal to it, they also are called tangential angles.
Page 141 - METHOD 1. To lay out a Curve by means of Tangential Angles. IF from any point B, fig. 1, in a straight line AD, we lay off any number of equal angles, as DB s, s B t, t...
Page 140 - Tangents, &c., are read upwards, from the bottom of the page, using the corresponding column of minutes. To find the sine of an angle exceeding 90°, subtract the angle from 180°, and take out the sine of the remainder — because the sine of an angle, and that of what it wants of 180°, are the same.
Page 139 - Tables in common use, must have frequently experienced the embarrassment which attends the inaccuracies to which they are all subject. So long as a Table is known to contain a single error, the position of which is not ascertained, its employment is attended with doubt in every instance in which we are obliged to refer to it.
Page 156 - Rule 2. — Subtract the tabular cosine of the tangential angle from 1, and multiply the remainder by the radius. Example. — Same as foregoing; namely, radius 819 feet, angle of deflection 7°, to chords of 100 feet.