TRANSPORTATION ON LAND BY VEH1CLES:-THE ROADS 41 



"Return" curves built on a slope are very expensive, since it becomes necessary to dig into the slope 

 to the depth of the diameter of the curve; and at this depth rock is almost invariably encountered. The 

 proper place for return curves are flats or terraces, shoulders, "epaulettes," spurs, coves, &c. 



(b) Locomotives and cars. Minimum curvature for a railroad depends on:- 



1. Length of wheelbase of trucks, or rather of locomotive, the base of which is apt to be longer 

 than that of the trucks; 



2. Height of wheels -high wheels being more apt to climb the rail; 



3. Gauge of road -the outer wheel describing, partly sliding, a wider circle than the inner wheel 

 (unless wheels run round the axle, not with the axle). "Conical" tires may make up for this, in part; 



4. Possibility of widening track in curves, depending on width of tire of wheel; 



5. Strength of flange of wheel; 



6. Ratio between tractive force and load. 



In practice, the following maxima of curvature hold good:- 



Standard public carriers 10" 



Standard logging roads 23° 



Narrow-gauge logging roads ... 35". 

 The railroad engineer expresses curvature in degrees of the centerangle (A) spanning a subtended 

 chord 100 feet long. 



r. J- •'^ • i 1 r. J- 100 



Radius = . — r-T^ or approximately Radius = .— r 

 Sin A'^ sin A 



II. Curve -resistance. In the case of railroads, curve -resistance is to be reckoned with. It is much 

 greater per ton per degree for light curves than for heavy curves. The resistance of a 1 -degree curve 

 in a standard -gauge road is, for example, r6 pounds per ton; that of a 20-degree curve approximately 

 10 pounds per ton. As a general rule — since the sharpest curve determines the hauling capacity of an 

 engine -the engineer reckons with a resistance of ','2 pound per ton (equal to 0'025 per cent) per degree 

 of curvature. 



The curve -resistance in a narrow-gauge road is directly proportioned to that of a standard-gauge 

 road at the ratio of the gauges. The frictional- resistance, for instance, on a standard -gauge road in a 

 28-degree curve is about 14 pounds per ton; on a 36-inch gauge road it is about 



14 X c^ ^ 9 pounds per ton 



III. Curve -equations. 



(a) The inside curve replacing the angle B found between two lines, starting from one line at (a) 

 and ending at the other line at (c), with (a) and (c) equidistant from the apex of angle B, has for 

 its radius :— „ 



Radius = 



2 cos B/2 



(b) The center angle A formed between two radii, and subtended over a chord 100 feet long is 



found from the equation: — 



. A 100 



''"2 = 2R 

 IV. Construction of curves. 



(a) Curves are constructed either inside or outside the angles which they replace. A special 

 case of an outside curve is the "loop." 



(b) Methods for construction of curves inside the angle are:- 



1. The radius method; staking out radii from center of curvature; 



2. The quartering method; join the 2 points at which the curve is to begin and to end by a line (a); 

 draw a perpendicular (b) at middle and on (a) making (b) equal to (or smaller than) (a) divided 

 by 2. Join the free end of (b) with both ends of (a) by lines (d) and (d). Erect in the midst 



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