US866152A - Templet for drawing transition spirals. - Google Patents

Description

, No. 866,152. PATENTED SEPT. 17, 190v.-

J. A. MERRITT.

TBMPLET FOR DRAWING TRANSITIONSPIRALS.

APPLICATION FILED MAY 15. 1907.

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TEMPLET FOR DRAWING TRANSITION SPIRALS. APPLICATION FILED MAY 15. 1907.

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PATENT OFFICE.

JAMES ALFRED MERRITT, OF BALTIMORE, MARYLAND.

TEMPLET FOR DRAWING TRANSITION SPIRALS- Specification of Letters Patent.

Patented Sept. 17, 1907.

Application filed May 15,1907. $erial No. 373,745.

To all whom it may concern:

Be it l mown that I, JAMES ALFRED MERRIIT, a citizen ol the United States, residing at Baltimore, in the county of Baltimore City and State of Maryland, have invented a new and useful Templet for Drawing Tran sition Spirals, of which the following is aspecification.

in modern railway practice it is no longer usual to connect two angularly related lines of road by a simple curve, and transition or easement curves are now employed in order to gradually change the direction of travel of the train. A transition curve or easement curve, as it is sometimes called, is a curve of varying radius used to connect circular curves with tangents for the purpose of avoiding shock and disagreeable lurch of trains due to instant change in the relative positions of cars, trucks, and draw bars, and, also, to a sudden change from level to inclined tracks.

The primary object of the transition curve is to effect smooth riding when the train is entering or leaving a curve.

The generally accepted requirement for a power transition curve is that the degree of curve shall increase gradually and uniformly from the point of tangent until the degree of the main curve is reached, allowing the super elevation to increase uniformly from zero at the tangent to the l'ull amount at the con-' nection with the main curve, and'yet to afford at every point the appropriate super elevation for the curvature.

The field engineer in laying out a line determines first the degree of curve which will best meet the requirements of cut and fill and such other conditions as may be necessary, and the question of transition curves, or transition spiral, as it may more properly be termed, used to connect the angularly related lines and circular curve, are then determined. In plotting these transition curves either for new trackage, or for the correction ol' old tracks, considerable difiiculty is experienced in laying out curves that are mathematically correct, and the present practice, which will be entered into in detail hereinafter, is only approximate and requires con siderable skill and time to work out.

The principal object of the present invention is to provide a novel form of templet, so shaped and so graduated that given a curve of any predetermined degree, the transition spiral may be drawn without further difficulty, and with out any mathematical calculations whatever and with the utmost accuracy.

I11 the accompanying drawingsz-Figure l is a plan view of a templet constructed in accordance with the invention. Fig. 2 is a transverse sectional view of the same on the line 2-2 of Fig. 1. Figs. 3, 4, 5, 6, 7, 8, 9, 10 and 11 are diagrams illustrating the outlines of templets of different contour all embodying the invention.

Figs. 12 and 13 are diagrams more particularly referred to hereinafter.

Where .two roads, such as F G, are to be united by a curve, the engineer will, of course, try to employ a curve of the largest radius, but conditions are frequently such as to limit the choice, such, for instance, as the cost of property to be acquired, the conditions of cut and fill, and the like, so that a curve of comparatively small radius must sometimes be used. One of the methods at present inuse consists in projecting the lines F and G to a meeting point D, and then the point at which the curve begins is determined by the previously noted conditions, and these points, A O, are pricked, after which perpendiculars are drawn to the lines A D, D C, from the points A and C to a meeting point 0, this forming the center from which the curve B is struck. The degree of curve is measured in the usual manner by drawing a chord of one hundred feet across an,arc of the curve and measuring the angle between the radii which connect the ends of the chord to the point 0.

In determining the points H M at which the circular curve ends, considerable clifliculty is experienced. One of the ordinary methods is that followed in topographical work in polyconic projections, that is, by marking off the x values or latitude from A K on the line A D, andthen the g values from K to H, after which the point H is pricked, and marks the commencement of the circular curve. The transition spiral must then be drawn by using the proper number of curves to complete the distance A H, there being usually a separate curve for each 93 value. This method is very slow and expensive, and is correct only .in so far the points measured are concerned, while the drawing is imperfect owing to the difliculty in properly joining the different curved lines. Another method is to lay off or calculate the course from a meridian, (or in a straight line, that is north and south, and going out on it a distance A H, the angle K A H being measured by a protractor and being only approximate.

In Fig. 12 the dotted line S represents a simple circular curve connecting the lines F G, the curve being, say, a five degree curve. This simple curve is no longer used in railroad engineering, and in the laying out of a new line, or in the correction of an old line, the curve is moved out, as indicated by the line T, and its ends are connected to the lines F and G by the transition or easement spirals, each of which must be separately calculated.

The transition spiral is a curve whose degree of curve. increases directly as the distance along the curve from the point of spiral. Thus, if thespiral is to changeat the rate of ten degrees per hundred feet, at ten feet from the begining of the spiral the curvature will be the same as that of a one degree curve; at twenty-five feet, as of a two degree thirty minute curve; at sixty feet, as a six degree curve; at eighty feet, as an eight degree curve, etc. A spiral curve of this type would be known then as a ten degree spiral.

Where a five degree circular curve is to be connected to two straight lines by a two degree thirty minute transition spiral the engineer usually plots from the point A to the point K in measuring the at values or latitude, and then by known rules calculates the y values or departure from the point K to the point H.

In order to overcome the various difiiculties of the -method and to provide a simple method of drawing the transition spiral and locating the points of connection of the transition spiral and the circular curve with the utmost accuracy, I have provided an improved templet which may. be used after the two points A C and the degree of the circular curve have been determined upon, no further measurements or calculations being necessary. The templet 10 is formed of a strip of celluloid, ivory, wood or any other material, and preferably has its drawing edge beveled from both sides, as shown in Fig. 2, so that it may be reversed. The templet is shaped to correspond to the degree of the spiral or volute to be drawn, the one in the present instance being calculated for a one degree spiral, that is to say, a spiral which at the end of a chord of one hundred feet from the point of the spiral is on a curve of one degree, and at two hundred feet, a curve of two degrees, and so on, the scale followed being marked up to one thousand feet, where the curvature corresponds to that of a curve of ten degrees. If the circular curve to be used is a five degree curve, the templet is laid along the line D G with its straight edge u v in alinement with A G, and the zero mark opposite the point A. The pricker is moved along to the five degree mark, and the point H is pricked, the point H being thus located without any further measurements or calculations, and at this point the spiral will be of the proper curvature to merge into a five degree curve. The same operation is repeated on the line F D to locate the point M, and then the two points H M are connected by the five degree circular curve. It will be seen that a train passing from the straight line G to the circular curve will gradually change its position to the extent of one degree for each hundred feet, so that when it finally reaches the circular curve, there will be no disagreeable lurch, and the running will be as smooth as on a straight track. If the circular curve were six, seven, or eight degrees, or any other degree marked on the scale, the pricker would be stopped at the proper point to join with such circular curve. The transition spiral to be used to connect the straight lines to the curve is determined by property lines and the requirements of cut and fill, so that to make a complete set of measurements, it is desirable to employ templets curved to correspond to volutes of different degrees.

In Figs. 3 to 11, which are more or less diagrammatic in form, are illustrated the outlines of templets for spirals of different curvature, that shown in Fig. 3 being for a spiral which curves at the rate of twelve minutes or one-fifth of a degree for each one hundred feet; in Fig. 4 the curvature is fifteen minutes, or onefourth of one degree; in Fig. 5 the curvature is thirty minutes or one-half of one degree; in Fig. 6 the curvature is forty minutes, or two-thirds of one degree; in

Fig. 7 the curvature is forty-eight minutes or fourfifths of one degree; in Fig. 8 is shown the one degree curve illustrated in Fig. 1; in Fig. 9 is shown a one degree fifteen minute curve; in Fig. 10 a one degree forty minute curve, and in Fig. 11 a two degree curve, and this set of curves will meet all the requirements of modern railroad practice.

I claim:

1. An instrument for drafting transition spirals, said instrument having a drawing edge following a spiral of predetermined curvature, and being provided with graduations from zero representing the degree of the spiral, and characters opposite the graduations to indicate the gradual increase in the degree of curve to thereby facilitate the location of the connecting point of the spiral with a circular curve.

2. A drafting instrument comprising a curve, the drawing edge of which is straight in one direction from a zero point, and in the opposite direction from the zero point is curved to follow a transition spiral, there being graduations along the curved portion of the drawing edge, and characters to indicate the gradually increasing degree of curvature in accordance with the distance from such zero mark.

In testimony that I claim the foregoing as my own, I have hereto aflixed my signature in the presence of two witnesses.

JAMES ALFRED MERRITT.

Witnesses S. SCOTT BECK, Tnoims MASSEY.

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