. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . .4ns. 7^1=; 7^2 = ] b. A line crosses a valley by a compound curve which is firsta 6° curve for 46° 30 and then a 9° 30 curve for 84° 16. It isafterward decided that the last tangent should be 6 feet fartherup the hill. What are the required changes? [Note. Thesecond tangent is evidently moved outward. The solution cor-responds to that in the first part of § 69, c. The ismoved forward feet.
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . .4ns. 7^1=; 7^2 = ] b. A line crosses a valley by a compound curve which is firsta 6° curve for 46° 30 and then a 9° 30 curve for 84° 16. It isafterward decided that the last tangent should be 6 feet fartherup the hill. What are the required changes? [Note. Thesecond tangent is evidently moved outward. The solution cor-responds to that in the first part of § 69, c. The ismoved forward feet. If it is desired to know how far is moved in the direction of the tangent (, the projectionof BB, Fig. 33, on F5), it may be found by observing that itis equal to nn = (7?2—7?i)(sin J^—sin J/). In this case it foot, which is very small because J^ is nearly 90°. Thevalue of ^2 (46° 30) is not used, since the solution is independentof the value of Jg- The student should, learn to recognize 82 KAILROAD CONSTRUCTION. §71. which quantities are mutually related and therefore essentialto a solution, and which are independent and TRANSITION CURVES. 71. Superelevation of the outer rair on curves. When a massis moved in a circular path it requires a centripetal force to keepit moving in that path. By the principles of mechanics weknow that this force equals Gv^-^gR, in which G is the weight,V the velocity in feet per second, g the acceleration of gravity infeet per second in a second, and R the radius of the two rails of a curved track were laid on a level (trans-versely), this centripetal force could only be furnished by thepressure of the wheel-flanges against the rails. As this is veryobjectionable; the outer rail is elevated so that the reaction ofthe rails against the wheels shallcontain a horizontal componentequal to the required centripetalforce. In Fig. 35, if oh representsthe reaction, oc will represent theweight
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