SUPER-ELEVATION TRACK. On the curves the outside of the track should be higher than the inside, to neutralize the effect of centrifugal force. According to the principles of mechanics, the force required to deflect a body from a rectilinear path is w .
Rg • In which w is the weight of the body, v the velocity in feet per second, R the radius of curvature in feet, and g the accelera tion due to. gravity in feet per second. This force acts radially in the plane of the curve; and since the path of a body moving around the track is a curve whose plane is horizontal, the cen trifugal force acts horizontally.
The horse is acted upon by two forces—gravity and centrifugal force. These forces and their resultant are shown in Fig. 80. If the track is level, the effect of the centrifugal force is the same as though the horse were traveling upon a surface inclined at an angle a with the horizontal; but if the outer edge of the track is elevated until the surface is perpendicular to the resultant represented by R in Fig. 80, page 290, the effect upon the horse is the same as though he were traveling upon a perfectly level track.
This formula shows the relation that should exist between the inclination of the track, and the number of minutes required to go 1 mile.
For the mile track shown in Fig. 78, page 286, and a 2 minute speed, a should be 0.15; that is, the inclination of the sur face of the track on the circular curve should be 15 vertical in 100 horizontal. For the same track and a speed of a mile in 2 minutes and 40 seconds, the inclination should be 8 in 100, and for a mile in 3 minutes, 6.7 in 100. For the half-mile track shown in Fig.
79. page 288, the inclination on the circular curve should be prac tically twice that for the mile track above.
The super-elevation should gradually increase from nothing at the beginning of the transition spiral, i. e., at the end of the straight stretch, to the maximum at the beginning of the circular portion. The advantage of the transition spiral (§ 429) is that its radius of curvature decreases as the distance from the tangent point increases. and therefore the super-elevation at every point can be adjusted so as always to exactly neutralize the centrifugal force. When this condition is secured, the effect upon the horse will be the same as though he were traveling upon a level track all the time.
There is a little room for choice as to the speed for which the super-elevation shall be adjusted. If it is desired to build a track upon which the fastest horses can make the fastest time, then the super-elevation should be computed for their fastest speed; but if it is desired to build a track upon which slower horses can make their fastest time, then the super-elevation should correspond to the fastest speed of the slower horses.
It seems to be the practice to give a slope of 1 in 13 (7.7 per 100) on the mile track shown in Fig. 70, page 279, and on the half mile track shown in Fig. 73, page 282, 1 in 12 (8.5 per 100).
Horsemen claim that there is less need of super-elevation since the introduction of the low-wheeled sulky; but the claim is with out foundation, as the proper inclination is independent of the height of the wheel of the racing sulky.