If R = 1r, use half the tabular distance; if R = 3 r, use twice the tabular distance; if R = 4 r, use three times the tabular distance, and so on. 12. TABLE SHOWING THE DISTANCE, d, IN FEET, AT WHICH CURVES OF CONTRARY FLEXURE MUST BE PLACED ASUNDER IN ORDER THAT THE CONNECTING TANGENT, T, MAY BE 300 FEET LONG. 14404AWN DEGREE OF CURVE. 3.9 5.24 5.92 7.84 9.43 ::::: d. 6° 7° 7.08 7.18 12.80 13.06 6.29 6.35 6.68 6.86 7.00 22.76 24.01 25.07 25.97 25.20 26.70 28.00 29.13 38.56 10. Examples. A 7° and 4° should be 19.9 feet asunder; a 5° and 9° should be 25.07 feet asunder. As approximations, for a connecting tangent 400 feet long, take twice the tabular distance: for a connecting tangent 200 feet long, take half the tabular distance. It is thought by some that the parabola is an ideal curve for railroads, and should be adopted; by others, that a spiral or parabolic" easement,” so called, is sufficient by way of transitional flexure from straight line to circular curve; by others, that a circular curve compounded with similar terminal curves of larger radii is to be preferred; by others, that the circular curve alone serves all conditions best. The writer holds with the last party up to curves of about 4°, and for sharper ones, in the absence of proof to the contrary, believes with the third party that circular terminal curves, not less than 200 feet long, having half the degree of the main curve, are likeliest to meet, in a fair measure, the requirements of actual service. Meanwhile the old circular curve continues to do good work. On well-regulated lines a curve is usually indicated to the traveller by the inclination of the car only; there is no jar. Some years ago one of the most intelligent, experienced, and enterprising railroad managements in this country caused a thorough practical test to be made of the second device above mentioned, with a view to fits adoption if found advisable. The engineers and superintendents who made the test reported adversely, on experimental grounds. The proposed improvement was not adopted. PROBLEMS IN FIELD LOCATION. XXVI. HOW TO PROCEED WHEN THE P. C. IS INACCESSIBLE. 1. Suppose, for example, a pro jected 5° curve, beginning at stake E 24.20, or B in the diagram. FIRST METHOD.--At any point B A, which we will assume to be stake 23.40, set up the transit. Let it be judged that stake 27, marked D in the diagram, must fall on accessible ground. Then the distance B D, around the curve is 280 feet, corresponding to an angle EBD of 7° at the circumference, or an angle of 14° at the centre. The chord of a 1° curve consuming this angle, by Table XVI., is 1,396.6 feet; that of a 5° curve, BD in the figure, is one-fifth of this, or 279.3 feet. In the triangle A B D are thus known the sides A B, BD, and the sum of the angles at A and D, which sum is equal to the angle EBD. Hence, by trigonometry, A As the sum of the sides given=359.3 A C So is tan. sum of angles at base To tan. their difference = = 199.3. =3° 30' Adding half the difference to half the sum, the larger angle, A, is found to be 5° 26'; subtracting half the difference from half the sum, the smaller angle, D, is found to be 1° 334. The 93 |