For obvious reasons the length should be an aliquot part of a mile; and the best authorities claim that on the whole a track hav ing four laps to the mile is most preferable. Therefore a design will be made for a one-quarter mile track.
Proportions of the Field.—To determine the relation be tween the length and the breadth of the field of those tracks which may be considered as the best representatives of current practice, Table 65 was computed. A study of these data shows that a track to meet the requirements of current practice should have a field about twice as long as wide, or a width of field about one fifth of the length of the track. A field of these proportions will give a track affording the spectators a good view of all parts of the race.
Form of Curves. The track should gradually change from the straight line to the maximum curvature in order that the rider may experience no lurch in going from the straight to the curved portions. If in Fig. 168 the full lineABCDE represents a portion of the pole line of a track consisting of semicircles con nected by tangents, a racer riding in the direction indicated, upon arrival at B, the point of tangency, will not be able to change in stantly from a straight path with an infinite radius to a curved path with a uniform finite radius, but will involuntarily take a curvi linear course having a uniformly decreasing radius. The dotted line of Fig. 168 shows the path involuntarily taken by the rider.
Similarly in entering a tangent from a curve, the rider will swing out from the pole line of the tangent in a curve of increasing radius. Since the distances are measured on the pole line, and since all ex cess distance ridden adds to the time of the race, there is a decided advantage in having the pole line of the same curvature as that of the path naturally taken by the rider. Further, the greatest ease with which a wheel can be guided around a curve of gradually varying radius also adds to the speed of the race.
Again, the outer edge of the track on curves should be higher than the inside, to neutralize the effect of centrifugal force; and this super-elevation should vary inversely as the radius of curvature. Since it is impossible to change instantly from flat tangents to banked curves, a track consisting of semicircles and tangents will not permit the proper super-elevation of the outer edge, but if the tangent is connected to the circular arc by a curve of uniformly varying curvature, the banking required increases gradually from zero on the tangent to the full amount at the beginning of the circular arc.
This condition is approximated by joining the tangent and the circular curve by circular arcs of decreasing radii, as in the Man hattan track, Fig. 166, page 635; but this condition is fully and more simply met by using the transition spiral (see § 429).
Fig. 169, page 640, shows a one-fourth mile bicycle track each quadrant of which consists of a tangent 30 feet long, a transition spiral 160.18 feet long and a circular arc 139.82 feet long, making a total length of 330 feet for one quadrant or 1,320 feet for the com plete circumference. The circular arcs may be laid out by any of the methods described for Horse-race Tracks in Art. 2, Chapter VII,. pages 278-92. The transition spiral may be laid out in either of two ways, namely: (1) by deflection angles from the initial tangent. and by chords measured along the curves; or (2) by offsets from the tangent prolonged. Table 66 and 67, page 641, give the data for laying out the spiral by the two methods just mentioned.
The field of the track shown in Fig. 169 is 0.59 as wide as long, and is a little nearer round than the mean of the tracks in Table 65, page 637; but if the field were made narrower, the curvature would be sharper, and curves with a large radius are of more importance than a narrower field. The above design meets all the require ments stated in § 992 and also possesses some important features new in bicycle-race track construction.