Horse-Race Tracks

3. Engineer's Method. Set a transit at the tangent point (A, Fig. 72), and lay off successively the equal angles etc., as shown in Fig. 72, and measure, also successively, the equal chords A E, E F, F G, etc. The angle a may have any value, pro vided the length of the chord is made to correspond; but for con venience, a should be an aliquot part of Table 27, page 281,, gives several values of a and the corresponding values of the chord and also of the arc.

The outside edge of the track need not be laid out accu rately. It is sufficient to set a flag pole at the center of the semi circle and measure from the inside edge in the line of the radius. The track shown in Fig. 70, i. e., the standard mile track having a home-stretch 65 feet wide and the remainder 40 feet wide, re quires a rectangle of ground 2,240 X 945 feet, or about 48.5 acres, for the track alone.

Track. Fig. 73, page 282, shows the usual half-mile oval, the only variation being in the width of the track. The dotted line represents the pole line, the line upon which the distance is measured, and is always 3 feet outside of the inner edge of the track. The wire is usually 170 feet from the beginning of the curve. The semi-circular ends may be laid off in any of three ways: 1. Amateur's Method. Fasten one end of a wire of a length ' equal to the radius, at the center of the curve, and with the other mark as many points as desired on the inside edge of the track.

2. Surveyor's Method. Establish five points by laying off the lines and distances shown in Fig. 74.

3. Eng ineer'8 Method. Set a transit at the tangent point (A, Fig. 72, page 281), and lay off successively the equal angles a,, etc., and the equal chords A E, E F, F G, etc., as shown in Fig. 72.

The track shown in Fig. 73, i. e., the standard half-mile oval with a home-stretch 65 feet wide and the remainder 40 feet wide, requires a rectangle of ground 1,060 X 525 feet, or a trifle over 13 acres.

Kite Track.

Fig. 75 shows the form of kite track introduced at Independence, Iowa, in 1890. The larger circular end may be laid out with a wire used as a radius, or by the measurement of the lines shown in Fig. 76; but for somewhat ob vious reasons, the method described in the succeeding paragraph is the best.

The curve could be laid out by setting off equal deflection angles and measuring the corresponding chords as was explained in para graphs 3 of § 424 and § 426; but in this case the central angle con tains fractional degrees, and hence the deflection angle would be inconvenient both to compute and to set off on the instrument. Therefore it is better to lay out the curve by the method usually employed for railroad curves, i. e., by successive 100-foot chords with a fractional chord at the end. The degree of the curve is 12° 0' 11", and hence the deflection angle for a 100-foot chord is 6° 0' 5i" or practically 6° 0'. The arc for a 100-foot chord is 100.183 feet, and hence the number of 100-foot chords is 17.4580 (=1,749÷.100.183); in other words, there will be seventeen 100 foot chords and a chord of 45.80 feet at the end.

The dimensions of the small loop are of no importance, as it is used only for starting and slowing up; and no information is available as to the size in this particular case. In some tracks, the small loop is formed by prolonging the two tangents beyond their intersection and connecting them by a circular arc, thus making a track somewhat like a figure 8 with one loop very much smaller than the other. The form shown in Fig. 75 requires a rectangle of ground 2,900X1,060 feet or about 70.5 acres.

The proportions of the kite track are susceptible of consid erable variation. In Fig. 77, let A be the apex, B the starting point, and Z the finish. ThenBDEF Z=5,280 ft.; or BDE= 2,640 ft. Call the distance from the apex to the starting point z, i. e., A B=A Z=x ft. Then which easily becomes R (cot a + 0.01745 a°) = 2,640 + x. . . . (2) This is a perfectly general equation, and shows that x and either R or a may be assumed arbitrarily. Equation (2) may be used

also to deduce to dimensions of the small loop, in which case either R or the length of the curve must be assumed, a being the same as for the large loop, and x=0. • The kite track is two or three seconds faster than an oval of the same length; but it is not satisfactory to the spectators, and consequently is not much used.

Oval Track with Easement Curves.

All of the three pre ceding forms are defective in that the track changes instantly from a straight line to a circle of comparatively short radius. It is impossible for a horse at any considerable speed to change in stantly from a right line to a curve; and if the change is made in a comparatively short space, a severe shock is experienced and a considerable effort is required. The ideal race track should change gradually from the straight to the curved portion. It will be shown presently that on the curves the outer portion of the track should be higher than the inner edge, to facilitate the passage of the horse around the curves. This super-elevation is not re quired on the straight stretches. With the forms described above, it is impossible to secure at all points the proper amount of super elevation. The total super-elevation can not be attained in stantly; and if it begins on the straight portion and reaches the proper amount at the tangent point, it is an obstruction on the straight stretch; and if it begins on the curve and gradually in creases to the proper amount, the first part of the curve does not have the needed super-elevation. Therefore the straight stretch of the track should be joined to the circular portion by a curve of uniformly varying curvature. This easing of the curves is not common in race-track construction; but it is absolutely necessary on railroads, is very important in bicycle racing (see Chapter XX), and would be very beneficial on horse-race tracks.

Various curves for connecting the straight and the circular portions have been proposed. but the best is the transition spiral.* In this curve, the radius varies inversely as the distance along the curve.

Mile Track. Fig. 78 shows one quadrant of the inside curve of a mile oval with a transition spiral between the straight and the circular portions. Except for the easement curve, the track is substantially the same as the standard mile oval shown in Fig. 70, page 279.

Either of two methods may be employed in laying of the spiral—that by deflection angles and chords, or by rectangular co-ordinates. Table 29, page 287, contains the necessary data for the first method, and Table 30 those for the second. The point P.S. (point of spiral) in the tables is the point B in Fig. 78, and the point P.C.C. (point of compound curve) is C in Fig. 78.

The circular CD is most readily laid out by successive chords. The deflection angle for a 100-foot chord is 7° 0' 59" or practically 7° 1'. The arc for a 100-foot chord is 100.249 feet, and hence the number 100-foot chords is 4.3202 ( = 433.09+100.245); that is to say, in the distance CD there will be four 100-foot chords and a chord of 32.02 feet at the end, or in the entire circular arc at one end of the track there will be practically eight 100-foot chords and one chord of 64.04 feet.

Half-mile Track. Fig. 79, page 288, shows one quadrant of the curve of the inside of the track of a half-mile track having a transition spiral, which except for the easement curve is sub stantially the same as the half-mile track shown in Fig. 73, page '282.

Tables 31 and 32, contain the data for the two methods of laying out the transition spiral. The deflection angle for chords is 7° 1' 00". The arc for a 50-foot chord is 50.124 feet; and hence the number of 50-foot chords in half the circular arc is 4.2567, or in the entire circular curve there are 4.2567, or four 50-foot chords and one chord of 12.83 feet.