Laserfiche WebLink
Table VI. -Corrections for Tangents and Externals. <br />These corrections are to be added to the approximate values, found by dividing <br />the tangent, or external, for a 10 curve (Table IV) by the degree of curve, in order <br />to obtain the true tangents, or externals. Intermediate values may be obtained by <br />interpolation. <br />FOR TANGENTS ADD <br />Central <br />DECREE OF CURVE <br />Angle <br />24 <br />22 <br />20 <br />32 <br />30 <br />28 <br />26 <br />24 <br />22 <br />D <br />10 <br />20 <br />30 <br />5° <br />10° <br />15° <br />20° <br />25° <br />1 30° 35° 40° <br />45° <br />50° <br />SSo <br />60- <br />fro <br />70- <br />100 <br />.03 <br />.O6 <br />.09 <br />.13 <br />.16 <br />.19 <br />.22 <br />.25 <br />.28 <br />.31 <br />.34 <br />299.97 <br />399.92 499.85 <br />6 <br />150 <br />.04 <br />.10 <br />.14' <br />19 <br />.24 <br />.29 <br />.34 <br />.39 <br />.45 <br />.51 <br />.53 <br />,38 <br />.58 <br />.42 <br />.45 <br />200 <br />.06 <br />.13 <br />.19 <br />.26 <br />.32 <br />.39 <br />.45 <br />.51 <br />.58 <br />,.65 <br />.72 <br />.79 <br />.63 <br />.84 <br />.68 <br />250 <br />.08 <br />.16 <br />.24 <br />.33 <br />.40 <br />.49 <br />.58 <br />.67 <br />.75 <br />.83 <br />.90 <br />.99 <br />1.06 <br />.90 <br />1.14 <br />300 <br />.10 <br />.19 <br />.29 <br />.39 <br />.49 <br />.59 <br />.69 <br />.79 <br />.89 <br />' .99 <br />1.09 <br />1.20 <br />3.29 <br />1.39 <br />35° <br />400.13 <br />.11 <br />.22 <br />.34 <br />.47 <br />.58 <br />.69 <br />.70 <br />.81 <br />.92 <br />1.04 <br />1.29 <br />1.42 <br />1.54 <br />1.66 <br />450 <br />.05 <br />.06 <br />.26 <br />.40 <br />.53 <br />.67 <br />.80 <br />.93 <br />1.06 <br />1.20 <br />1.34 <br />1.49 <br />1.64 <br />1.79 <br />1.94 <br />23 <br />.15 <br />.30 <br />.44 <br />.60 <br />.76 <br />.91 <br />1.06 <br />1.21 <br />1.37 <br />1.52 <br />1.70 <br />1.87 <br />2.04 <br />2.21 <br />500 <br />.17 <br />.34 <br />.51 <br />.68 <br />.85 <br />1.02 <br />1.19 <br />1.36' <br />1.54 <br />1.72 <br />1.91 <br />2.10 <br />2.29 <br />2.48 <br />550 <br />.19 <br />.38 <br />.57 <br />.76 <br />.95 <br />1.14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 <br />2.14 <br />2.35 <br />2.56 <br />2.77 <br />600 <br />.21 <br />.42 <br />.63 <br />.84 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 <br />2.38 <br />2.60 <br />2.83 <br />3.07 <br />650 <br />.23 <br />.46 <br />.69 <br />.93 <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.38 <br />2.63 <br />2.88 <br />3.13 <br />3.39 <br />700 <br />.25 <br />.51 <br />.76 <br />102 <br />1.28 <br />1.54 <br />1.80 <br />2.06 <br />2.33 <br />2.60 <br />2.88 <br />3.16 <br />3.44 <br />3.72 <br />750 <br />.27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98 <br />2.27 <br />2.57 <br />2.87 <br />3.16 <br />3.47 <br />3.78 <br />4.09 <br />800 <br />.30.61 <br />.257 <br />.91 <br />L 22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 <br />3.44 <br />3.78 <br />4.12 <br />4.46 <br />850 <br />.33 <br />.66 <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.36 <br />2.70 <br />3.05 <br />3.40 <br />3.77 <br />4.14 <br />4.55 <br />4.89 <br />90° <br />.36 <br />.72 <br />1.09 1.45 <br />.62 <br />1.83 <br />2.20 <br />2.57 <br />2.94 <br />3.32 <br />3.70 <br />4.10 <br />4.50 <br />4.91 <br />5.32 <br />95° <br />..39 <br />.79 <br />1.19 <br />1.55 <br />2.00 <br />2.40 <br />2.80 <br />3.20 <br />3.61 <br />4.02 <br />4.40 <br />4.98 <br />5.38 <br />5.83 <br />100° <br />.43 <br />.86 <br />1.30 <br />1.74 <br />2.18 <br />2.62 <br />3.06 <br />3.50 <br />3.95 <br />4.40 <br />4.88 <br />5.37 <br />5.85 <br />6.34 <br />110°' <br />.51 <br />1.03 <br />1.56 2.08 <br />.85 <br />2.61 <br />3.14 <br />3.67 <br />4.21 <br />4.76 <br />5.31 <br />5.8616 <br />-4317 <br />-DI <br />, <br />120° <br />.62 <br />1.25 <br />1.93 2.52 <br />.94 <br />3.16 <br />3.81 <br />4.45 <br />5.11 <br />5.77 <br />6:44 <br />7.12 <br />7.60 <br />8.50 <br />17.:6-0 <br />922 <br />FOR EXTERNALS ADD <br />Central <br />DEGREE OF CURVE <br />Angle <br />1.02 <br />1.05 <br />.98 <br />.78 <br />.46 <br />2.74 <br />X44 <br />191.26 <br />265.$1 <br />317.12 340.73 <br />48 <br />.27 <br />.52 <br />.75 <br />1.00 <br />50 <br />100 <br />15° <br />200 <br />250 300 <br />2.99 <br />35° <br />40° 1 <br />45° <br />50° <br />55° <br />60° <br />650 <br />700 <br />100 <br />.001 <br />.003 <br />.004 <br />.006 <br />.007 .008 <br />3.24 <br />.009 <br />.011 <br />.012 <br />298.03 305.99 <br />52 <br />.96 <br />150 <br />200 <br />003 <br />.007 <br />.010 <br />.014 <br />.018 .023 <br />3.52 <br />.027 <br />.029 <br />.032 <br />.014 <br />.035 <br />.015 <br />.039 <br />.017 <br />.043 <br />.018 <br />.047 <br />.020 <br />.051 <br />250 <br />.006 <br />.011 <br />.017 <br />.022 <br />.028 .034 <br />3.80 <br />.038 <br />.045 <br />.051 <br />.057 <br />.063 <br />.070 <br />.076 <br />.083 <br />1.38 <br />.009 <br />.018 <br />.027 <br />.036 <br />.046 .056 <br />4.09 <br />.065 <br />.074 <br />.063 <br />.093'.106 <br />58 <br />.120 <br />.127 <br />.135 <br />30° <br />.013 <br />.025 <br />.038 <br />.051 <br />.065 .078 <br />4.40 <br />.090 <br />.103 <br />.116 <br />:129 <br />60 <br />.44 <br />.47 <br />.91 <br />1.29 <br />351 <br />.018 <br />.035 <br />.054 <br />.072 <br />.086 .109 <br />4.72 <br />.131 <br />'.153 <br />.175 <br />244.51 212.92 <br />.149 <br />.170 <br />.179 <br />.188 <br />40° <br />45° <br />.023 <br />.046 <br />.070 <br />.093 <br />.117 .141 <br />.172 <br />.203 <br />.234 <br />.197 <br />.265 <br />.213 <br />.277 <br />.230 <br />.290 <br />.247 <br />.315 <br />,.264 <br />.341 <br />.030 <br />.060 <br />.093 <br />.119 <br />.153 .184 <br />.216 <br />.254 <br />.289 <br />.325 <br />.351 <br />.378 <br />.411 <br />:445 <br />50° <br />.037 <br />.075 <br />.116 <br />.151 <br />.189 .227 <br />.266 <br />.305 <br />.345 <br />;508 <br />55° <br />60° <br />.046 <br />.093 <br />.142 <br />.188 <br />.236 .283 <br />.332 <br />.381 <br />.420 <br />.384 <br />.479 <br />.425 <br />'530 <br />.467 <br />.582 <br />.641 <br />.550 <br />.700 <br />651 <br />.056 <br />.112 <br />.168 <br />.225 <br />.283 .340 <br />.398 <br />.457 <br />.516 <br />.575 <br />.636 <br />.697 <br />.774 <br />.851 <br />.067 <br />.135 <br />.204 <br />.273 <br />.343 .412 <br />.483 <br />.554 <br />.625 <br />.697 <br />.711 <br />.845 <br />.922 <br />1.01 <br />700 <br />750 <br />.080 <br />.159 <br />.240 <br />.321 <br />.403 .485 <br />.568 <br />.652 <br />.735 <br />.819 <br />.906 <br />.9941.08- <br />1.17 <br />800' <br />.095 <br />.182 <br />.286 <br />.383 <br />.480 .578 <br />.678 <br />.777 <br />.877 <br />.977 <br />1.07 <br />1.18 <br />1.29 <br />1.39 <br />850 <br />.110 <br />.128 <br />.220 <br />.259 <br />.332 <br />.391 <br />.445 <br />.524 <br />.558 .671 <br />.657 .790 <br />.787 <br />.926 <br />.903 <br />1.06 <br />1.02 <br />1.20 <br />1.13 <br />1.34 <br />1.25 <br />1.47 <br />1.38 <br />1.62 <br />1.50 <br />1.76 <br />1.62 <br />1.91 <br />900 <br />950 <br />.149 <br />.299 <br />.450 <br />.603 <br />.756 .910 <br />1.07 <br />1.22 <br />1.38 <br />1.54 <br />1.70 <br />1.87 <br />2.03 <br />2.20 <br />1000 <br />.174 <br />.350 <br />.522 <br />.706 <br />.985 1.06 <br />1.25 <br />1.43 <br />1.62 <br />1.80 <br />1.99 <br />2.18 <br />2.38 <br />2.53 <br />1100 <br />.200 <br />.268 <br />.401 <br />.536 <br />.604 <br />.806 <br />.809 <br />1.08 <br />1.01 1.22 <br />1.35 1.63 <br />1.43 <br />1.91 <br />1.64 <br />2.20 <br />1:85 <br />2.48 <br />2.06 <br />2.76 <br />2.28 <br />3.05 <br />2.50 <br />3.35 <br />2.73 <br />3.66 <br />2.96 <br />3.96 <br />1200 <br />.360 <br />.721 <br />1.08 <br />1.45 <br />1.82 2.19 <br />2.57 <br />2.95 <br />3.33 <br />3.72 <br />4.11 <br />4.50 <br />4.91 <br />5.32 <br />A& - <br />Table VII. -Corrections for Sub -Chords <br />and Long Chords. <br />FOR SUR -CHORDS ADD <br />Excess <br />of are <br />LONG CHORDS <br />LENGTH OF RAILS <br />3230 <br />28 <br />26 <br />24 <br />22 <br />20 <br />32 <br />30 <br />28 <br />26 <br />24 <br />22 <br />D <br />10 <br />20 <br />30 <br />40 150 <br />.013 <br />60 <br />70 <br />80 <br />90 <br />100 er ft. <br />D <br />200 <br />300 <br />400 500 <br />4° <br />.139 <br />2 <br />.022 <br />.01 <br />.01 <br />.01 <br />.01 <br />.00 <br />.02 <br />1 <br />199.99 <br />299.97 <br />399.92 499.85 <br />6 <br />.00 <br />.00 <br />.01.O1 <br />.01 <br />.01 <br />.02 <br />.02 <br />.02 <br />.02 <br />.01 <br />.01 <br />.05 <br />2 <br />199.97 <br />299.88 <br />399.70 499.39 <br />8 <br />.00 <br />.190 <br />.156 <br />4 <br />.03 <br />.03 <br />-.03 <br />.02 <br />.01 <br />.08 <br />3 <br />199.93 <br />299.73 <br />399.32 498.63 <br />10 <br />.01 <br />.01 <br />.02 <br />.02 <br />.02 <br />.03 <br />.03 <br />.04 <br />.05 <br />.05 <br />.05 <br />.04 <br />.02 <br />.13 <br />4 <br />199.88 <br />299.51 <br />398.78 497.57 <br />12 <br />.02 <br />.04.05 <br />.250 <br />.06 <br />.07 <br />.07 <br />.07 <br />.05 <br />.03 <br />.19 <br />5 <br />199.81 <br />299.24 <br />398.10 496.20 <br />14 <br />.410 <br />.357 <br />.309 <br />.262 <br />.09 <br />.10 <br />.09 <br />.07 <br />.04 <br />.25 <br />6 <br />199.73 <br />298.90 <br />397.26 494.53 <br />16 <br />.02 <br />.03 <br />.05 <br />.06 <br />.07 <br />.08 <br />.11 <br />.12 <br />.12 <br />.12 <br />.09 <br />.05 <br />.33 <br />7 <br />199.63 <br />298.51 <br />396.28 492.57 <br />18.04 <br />23 <br />.509 <br />.09 <br />.14 <br />.15 <br />.16 <br />.15 <br />.12 <br />.07 <br />.41 <br />8 <br />199.51 <br />298.05 <br />395.14 490.31 <br />20 <br />.05 <br />.08 <br />.10 <br />.11 <br />'.14 <br />.17 <br />.19 <br />.20 <br />.18 <br />.15 <br />.09 <br />.51 <br />9 <br />199.38 <br />297.54 <br />393.86 487.75 <br />22 <br />.106 <br />.087 <br />:.17 <br />.21 <br />.23 <br />.24 <br />.22 <br />.18 <br />.10 <br />.62 <br />10 <br />199.24 <br />296.96 <br />392.42 484.90 <br />24 <br />.06 <br />.12 <br />.096 <br />.25 <br />.28 <br />.28 <br />.26.21 <br />.382 <br />.12 <br />.74 <br />12 <br />198.90 <br />295.63 <br />389.12 478.34 <br />26 <br />.07 <br />.14 <br />.17 <br />.20 <br />.29 <br />.32 <br />.33 <br />.31 <br />.25 <br />.15 <br />.86 <br />14 <br />198.51 <br />294.06 <br />385.22 470.65 <br />28 <br />.09 <br />.19 <br />.24 <br />.34 <br />.37 <br />.38 <br />.36 <br />.29 <br />.17 <br />1.00 <br />16 <br />198.05 <br />292.25 <br />380.76 461.86 <br />30 <br />.10 <br />Al. <br />22 <br />.27 <br />.31 <br />.39 <br />.43 <br />.44 <br />.41 <br />.33 <br />.19 <br />1.15 <br />1.6 <br />197.54 <br />290.21 <br />375.74 452.02 <br />32 <br />.312 <br />.334 <br />.25 <br />.257 <br />.44 <br />.49 <br />.50 <br />.47 <br />.38 <br />.22 <br />1.31 <br />20 <br />196.90 <br />287.94 <br />370.17 441.15 <br />34 <br />.13 <br />.28 <br />.36 <br />.40 <br />.50 <br />:55 <br />.57 <br />.53 <br />.43 <br />.25 <br />1.48 <br />22 <br />196.32 <br />295.44 <br />364.06 429.30 <br />36 <br />.15 <br />.32 <br />.45 <br />.56 <br />.62 <br />.64 <br />.59 <br />.48 <br />.28 <br />1.66 <br />24 <br />195.63 <br />282.71 <br />357.43 416.53 <br />38 <br />.17 <br />.36 <br />.51 <br />.62 <br />.70 <br />.71 <br />.66 <br />.53 <br />.31 <br />1.86 <br />26 <br />194.87 <br />279.76 <br />350.30 402.89 <br />40 <br />.18 <br />.21 <br />'40 <br />.56 <br />.69 <br />.77 <br />.79 <br />.73 <br />.59 <br />.35 <br />2.06 <br />28 <br />194.06 <br />276.59 <br />342.69 388.42 <br />42 <br />.62 <br />.76 <br />.85 <br />.87 <br />.81 <br />.65 <br />.38 <br />2.28 <br />30 <br />193.18 <br />273.20 <br />334.61 373.20 <br />44 <br />.23 <br />.44 <br />.48 <br />'.68 <br />.84 <br />.94 <br />.96 <br />.89 <br />.72 <br />.42 <br />2.503`� <br />192.25 <br />269.61 <br />326.08 357.28 <br />46 <br />.25 <br />.92 <br />1.02 <br />1.05 <br />.98 <br />.78 <br />.46 <br />2.74 <br />X44 <br />191.26 <br />265.$1 <br />317.12 340.73 <br />48 <br />.27 <br />.52 <br />.75 <br />1.00 <br />1.12 <br />1.14 <br />1.06 <br />.86 <br />.50 <br />2.99 <br />36 <br />190.21 <br />261.80 <br />307.77 323.61 <br />50 <br />.30 <br />.32 <br />.57 <br />.62 <br />.81 <br />.89 <br />1.09 <br />1.21 <br />1.24 <br />1.15 <br />.93 <br />.55 <br />3.24 <br />38 <br />189.10 <br />257.60 <br />298.03 305.99 <br />52 <br />.96 <br />1.18 <br />1.31 <br />1.35 <br />1.25 <br />1.01 <br />.59 <br />3.52 <br />40 <br />187.94 <br />253.21 <br />287.94 287.94 <br />54 <br />.35 <br />.67 <br />1.04 <br />1.28 <br />1.42 <br />1.46 <br />1.35 <br />1.09 <br />.64 <br />3.80 <br />42 <br />186.72 <br />248.63 <br />277.51 269.54 <br />56 <br />.38 <br />.73 <br />.78 <br />1.12 <br />1.38 <br />1.53 <br />1.57 <br />1.46 <br />1.17 <br />.69 <br />4.09 <br />44 <br />185.44 <br />243.87 <br />266.78 250.85 <br />58 <br />.41 <br />.84 <br />1.20 <br />1.48 <br />1.65 <br />1.69 <br />1.57 <br />1.20 <br />.74 <br />4.40 <br />46 <br />184.10 <br />239.93 <br />255.78 231.95 <br />60 <br />.44 <br />.47 <br />.91 <br />1.29 <br />1.59 <br />1.76 <br />1.81 <br />1.68 <br />1.35 <br />.80 <br />4.72 <br />48 <br />182.71 <br />233.83 <br />244.51 212.92 <br />NoTF:.-When a chord of less than 100 it. is used the corrections given in the above <br />table should be added to the nominal length of chord to get the length which should <br />be used in order that the 100 ft. points will check with those obtained by using the <br />standard loo ft. chord. Thus in locating a 140 curve by 23 ft. chords measure 251.06 <br />for each chord. Long chords are useful in passing obstacle's. <br />Table VIII. -Middle Ordinates for Rails in Feet. <br />Deg. <br />of <br />Curve <br />LENGTH OF RAILS <br />Ueg <br />of <br />Curve <br />LENGTH OF RAILS <br />3230 <br />28 <br />26 <br />24 <br />22 <br />20 <br />32 <br />30 <br />28 <br />26 <br />24 <br />22 <br />20 <br />10 <br />.020.016 <br />.013 <br />.011 <br />:009 <br />.008 <br />160 <br />.356 <br />.313 <br />.273 <br />.236 <br />.200 <br />.170 <br />.139 <br />2 <br />.022 <br />.034 <br />.029 <br />.025 <br />.021 <br />.017 <br />17 <br />.378 <br />.333 <br />.290 <br />.252 <br />.213 <br />.180 <br />.148 <br />3 <br />.045 <br />.038 <br />.058 <br />.051 <br />.044 <br />.037 <br />.031 <br />.026 <br />18 <br />.400 <br />.351 <br />.306 <br />.265 <br />.225 <br />.190 <br />.156 <br />4 <br />.067 <br />.079 <br />.069 <br />.060 <br />.050 <br />.042 <br />.035 <br />19 <br />AM <br />.371 <br />.324 <br />.280 <br />.238 <br />.201 <br />.165 <br />.089 <br />.099 <br />.086 <br />.074 <br />.063 <br />.053 <br />.044 <br />20 <br />.445 <br />.392 <br />.341 <br />.296 <br />.250 <br />.212 <br />.174 <br />.6 <br />6 <br />.112 <br />.117 <br />.102 <br />.088 <br />.076 <br />.064 <br />.052 <br />21 <br />.466 <br />.410 <br />.357 <br />.309 <br />.262 <br />.222 <br />.182 <br />7 <br />.134 <br />.137 <br />.120 <br />:104 <br />.088 <br />.074 <br />.061 <br />22 <br />.487 <br />.430 <br />.375 <br />.325 <br />.275 <br />.233 <br />.191 <br />8 <br />.156 <br />.158 <br />.137 <br />.119 <br />.100 <br />.085 <br />.070 <br />23 <br />.509 <br />.450 <br />.390 <br />.338 <br />.287 <br />.243 <br />.199 <br />9 <br />.179 <br />.153 <br />.133 <br />.112 <br />.095 <br />.078 <br />24 <br />.531 <br />.469 <br />.408 <br />.354 <br />.299 <br />.253 <br />.208 <br />10 <br />.201 <br />.175 <br />.171 <br />'.148 <br />.125 <br />.106 <br />.087 <br />25 <br />.552 <br />.486 <br />.424 <br />.367 <br />.311 <br />.263 <br />.216 <br />11 <br />.223 <br />.196 <br />.216 <br />.188 <br />.163 <br />.139 <br />.117 <br />.096 <br />26 <br />.573 <br />.506 <br />.441 <br />.382 <br />.323 <br />.274 <br />.225 <br />12 <br />.245 <br />.236 <br />.206 <br />.179 <br />.151 <br />.128.105 <br />27 <br />.594 <br />.524 <br />.457 <br />.396 <br />.335 <br />.284 <br />.233 <br />13 <br />.268 <br />.222 <br />.192 <br />.163 <br />.138 <br />.113 <br />28 <br />.618 <br />.545 <br />.475 <br />.411 <br />.348 <br />.294 <br />.242 <br />14 <br />.290 <br />.254 <br />.239 <br />.207 <br />.175 <br />.148122 <br />29 <br />.638 <br />.564 <br />.491 <br />.424 <br />.361 <br />.303 <br />.250 <br />15 <br />.312 <br />.334 <br />.275 <br />.295 <br />.257 <br />.223 <br />.1881.1591:131 <br />30 <br />.660 <br />.583 <br />.508 <br />.438 <br />.374 <br />.313 <br />1 .259 <br />9 <br />