Fremling Field Notes 1993-2000

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Pr/I-A-:--~lt t:hl;i I9,:~.~.. -RrRi~l)f-P4 A.ii ) C).2)-.fFn-~ J f4'4}Nu:::i---.-~sE9.- iI ;c -o-.-~~TIi~-7'KifttI~.~...1....rCi'4iI4;/ IE(.$'"~ ----rK/t~): .i I..jg~riTI-IAjz7LlI:C4Po.L;" ic~~W)T ./bAv~>~Aj~jiIkiOf/p- ~9 r 8~~~andrll$f k~ptn.li~-iI; ::/t~LE ~.~~-. ..~1ir"-Ys~-4i iiKN%J--10>2*ii"4~wi4d. 440o -~1t1q1 ttA 14r7-ig(~-i 6 i~g1>4 (.1 4 -..:ii:~kC-+$'",--- -,--------.--~--~-~-< r'fJ771, ia eA-vv 44 4,L4a49 m4I':.S/g~- l-i^-C';4+<1...a -':;'---~---~~~---~~n ~u~i~i~ ~-~; t~-~-"i,~-:a,, O ~L4i~'~~~~-~-~-:I cW-~P"~rB~~Jirb-~ tc~nI'rd t uJ} t @./"Vlr L.a.+1'2 f--------91j"4-I-- -JP7~( jceI, iT: :IS+)V'~ Yt2M W ยง1(Sk!"IQy 9) ) fJ ~4I;~4E i~~~~~:~~V ~:~.,~c,/d9 7 L7:~()fJw -~~fcl~-.I:.'69),;2 .lI i.,i.'t-'0r"3';,J: ,: '4-I ,, '-k::dialr -n.,L..-\S '1~-Fi-i--i-I.. 1..ii'r ',)1st~ l((,tBf1!,I;1:-c-iLA. I-,.,j':j.-... ltti:!}- .LL-/Siwaq;%;?12)i.f ifI^/rrf"?acsI(Scs(34' 45~f 4rI 'C r SiL; (~~~g(kCi V" :.:t,001bAln~i3t,ik"l~il: r rIS: -iwI1r,,"iA{Irl < I1-,vxINDEX OF CURVE AND REDUCTION TABLES Table TableI-SLOPE STAKE II-STADIA CORRECTION AND HORIZONTAL DISTANCESTable III-TRIGONOMETRIC FORMULAE TableIV-NATURAL TRIGONOMETRICAL FUNCTIONS CURVE FORMULAETable° V-TANGENTS AND EXTERNALS TO A 1 CURVEUSEFUL RELATIONS TableVI-INCHES TO DECIMALS OF A FOOTTable VII-MINUTES IN DECIMALS OF A DEGREE Table VIII-MIDDLE ORDINATES OF RAILS TableIX-SHORT RADIUS CURVESTableX-RODS IN FEET, IOTHS AND 100THS OF FEETTable XI-LINKS IN FEET, 10THS AND 100THS OF FEETTABLE I. SLOPE STAKEDISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING ROADWAY OF ANYWIDTH.SIDESLOPES11/2TO 1.SLOPE STAKESIDE ISTAKEi 1----,,1'SIDE ISTAKE IIi1- L. C.Distance out from Side or Shoulder Stake. 0 .1 1 .1 000 0 151 0.80 1.50 165 1 80 8.00 8.15 8.80 4.50 465 4.80 6.00 6 15 6.80 7 50 7.65 7.80 9 00 9 15 9.80 10.5010 65 10.80 12.00 12 15 12.80 13 50 13.65 18 80 15.00 15 15 15 80 16 50 16 65 16 80 1800 18.153 18.30 19 50 19 65 19.80 21.00 21 15 21.80 22 50 2265 2280 24.00 2415 24 30 25.50 2565 25.80 27.00 27 15 27.30 28650 2865 2880 8000 80 15 30.30 31 50 31 65 31.80 3300 33 15 33 30 3450 8465 84.80 86.00 86 15 36.80 87.5037.65 37 80 3900 39 15 39.80 4050 4065 40 80 42 00 42 15 42.30 48-50 4365 43.80 4500 45 15 45.80 46.5046.65 46.80 4800 48.15 48.30 49.50 49 65 49.80 51 00 51.15 51.30 52 50 52.65 52.80 5400 54.15 54.30 5550 5565 55.80 57.00 57.15 57.30 5850 58.65 58 80 60 00 60.15 60 30.3 .4 1.5I, .9 I8..61 .70.45 0.60 0.75 0.90 1.05 1.20 1.35 1.95 2.10 2.25 2.40 2.55 2.70 2.85 345 3.60 S75 8.90 4.05 4.20 435 4.95 5 10 525 540 5.55 5.70 5.85 6.45 6.60 6 75 6.90 7.05 7.20 7.35 7.95 8.10 8.25 8.40 8.55 8.70 8.85 9.45 9.60 9.75 9.90 10.05 10.20 10.35 10.95 11.10 11.25 11.40 11.55 11 70 11.85 12.45 '12.60 12.75 12.90 13.05 13.20 13.35 18 95 14.10 14.25 14.40 14 55 14.70 14.85 15 45 15.60 15.75 15.90 16.05 16.20 16 35 16.95 17 10 17.25 17.40 17.55 17.70 17.85 18 45 18.60 18 75 18.90 19.05 19.20 1985 19.95 20.10 20.25 2040 20.55 20.70 20.85 21.45 21 60 21.75 21.90 2205 2220 2235 2295 28.25 23.40 23.55 23.70 23.85 2445 24.60 24.75 2490 25 05 25.20 25.85 25 95 23.10 2625 2640 26.55 26.70 26.85 27 45 27.60 27.75 27.90 28.05 2820 28.85 28.9529.10 29.25 29.40 29.55 29.7029.85 30.45 30.60 30.75 30.90 81.05 31.20 31.85 31.95 82 10 3225 32.4032.55 8270 8285 33 45 33.60 3375 33.90 34.05 84.20 34.35 34.95 35.10 85 25 35 40 35.55 35.70 3585 36 45 36.60 36.75 36.9037.05 37.20 37.35 87.9538.10 38.25 38.40 38.55 88.70 38.85 89 45 3960 39.75 39.90 40.05 40.2040.35 40.95 41.10 41.25 41 40 41.55 41.70 41.85 42.45 42.6042 75 42.90 48.05 43.20 48.35 43 95 44.10 4425 4440 44.55 44.70 4485 4545 45.60 45.75 45.90 46.054620 46.85 46 95 47.10 47.25 47.40 47.55 47.70 47.85 4845 48.60 48 75 48.90 49.05 49 20 49.35 49.95 50.10 50.25 50.40 50.55 50.7050.85 51.45 51.60 51.75 51.90 52.05 52.20 52.85 52.95 53.10 53.25 58.40 583.55 53.7058.85 54 45 54.60 54.75 54.90 55.05 55.20 55.85 55.95 56.10 56.25 56.40 56.55 56.7056.85 57 45 57.60 57.75 57.90 58.05 58.20 5835 58.95 59.10 59 25 69.40 5955 59.70 59.85 60 45 6060 60.75 6090 61.05 61 20 61.35 ,,,,TABLE II. STADIA CORRECTION AND HORIZONTAL DISTANCES STADIA REDUCTIONS FOR READING 100 Vertical Angle erticl AngleI20-0a3o-00' 4°-00' 5°-O 6°-00'Horizontal CorrectionDifference in ElevationHorizontal CorrectionVerticalAngleDifference in Elevation0.1 0.3 0.5 0.8 1.13.5 5.3 7.0 8.7 10.418°-30' 19°-00, 19°-30" 20-00' 20°-30'10.1 10.6 11.2 11.7 12.330.1 30.8 31.5 32.1 32.81.5 1.9 2.521-00a 210-30, 22°-00' 22°-30' 23o-00'12.8 13.4 14.0 14.7 15.333.5 34.1 34.7 35.4 36.010°-00'3.010°-30'3.312.1 13.8 15.5 17.10 17.9110-00,3.6 4.0 4.3 4.7 5.118.7 19.5 20.3 21.1 21.923°-30' 24°-00' 24°-30' 25°-00' 25v°-30'15.9 16.5 17.2 17.9 18.636.6 37.2 37.7 38.3 39.05.5 5.9 6.3 6.7 7.222.7 23.4 24.2 25.0 25.826°-00' 26°-30' 27°-00' 27°-30' 28°-00'19.2 19.9 20.6 21.3 22.039.4 39.9 40.5 41.0 42.07.6 8.1 8.5 9.0 9.526.5 27.2 28.0 28.7 29.428°-30' 29°-00' 29°-30' 30°-00'22.8 23.5 24.3 25.041.9 42.4 42.9 43.37°--00'80 -00' 90 -00,110--30, 12°-00' 12-30' 13°-00'13°-30'14°-00' 14°-30' 15°-00' 15o--3a116°-00' 16°-30' 17°-00' 17-30'18-00'Chains to Feet 1 2 3 4 5 6 7 8 9 10........ 66 .......... 132 198 .......... ....... 264 ........ 330 .......... 396 ........ 462 .......... 528 .......... 594 ......... 660Feet to Chains 100 ....1.515....3.030300 ....4.545400 .... 500 .... 600 ....6.060 7.575 9.090200700 .... 10.606 800 .... 12.121 900 .... 13.6361,000 .... 15.151TABLE III. TRIGONOMETRIC FORMULAE B C ABCaCabAB abAb y b 0 Right Triangle Oblique Triangles Solution of Right Triangles a b a b For Angle A. sin, Cos= b, tan ,cot -, sec-,, SbGiven a, batan A =A, B, bsinA = a-=cosB, b== cot B, c =0B, b, aB = 90 -A,GivenRequiredSasin BA, B, ab, c, Csin AA, a A, b A, abaRequired A, B ,o2jCecosecb'a= a(c+a)(o--a) =ob = a cot A, ce= -1--2asin A. sin A. co= A, tan b = a B = 90°--A, B, a, a cos A. B=90°-A, a = csin A, b= ecos A, B, a, b olution of Oblique Triangles a sin (sin Ab sin Aa sin CA, a, bB, e, Csin B=a, b,A, B, aA+B=180*-- C, tan # (A-B)=(a-b)tan I (A-B) a+b a sin C sin AC0A, B, aCa0,C = 180 -(Asin jB=,v 8= a2Areaarea =A.in A=-cb,s=a- 2Area+ B), o =, area =atxc , C=180*-(A+B) (s-a)(a-sb c sin A 22A, B, C,a Areaarea =a sin B sin C 2 sin AREDUCTION TO HORIZONTAL Horizontal distance -=Slope distance multiplied by the cosine of the vertical angle. Thus: slope distance =319.4ft.aso,Vert. angle-5" 10'. From Table. IV. cos 5 10'= 9959. Horizontal distance - 319.4%.. 995 = 31809 ft. Horizontal distance also - Slope distance minus slope distance times (I-cosine of vertical angle). With thesame figures as in the preceding example, the following result is obtained. Cosine 50 10- .959. 1-.9959=.0041. Horizontal distance 319.4X.0041 =1.31. 319.4-1.31= 31809 ft. When the rise is known, the horizontal distance is approximately:-the slope distance less the square of the rise divided by twice the slope distance. Thus: rise=14 ft.. slope distanee=302.6 ft. Horizontal distance=3026-- 14 14 =302.8-0.32302.28 ft. 2 X 302.6TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS AngleSe.Cosec.SinTan.0 .0029 .0058 .0087 .0116 .01450 .0029 .0058 .0087343.8 171.9401161.000185.94.0145 1.0001Cotg.AngleCosin.00Sin.Tn.S.c.Cosec.Cotg.Coin.7.185 7.040 6.900 6.766 6.636 6.5127.115 6.968 6.827 6.691 6.561 6.435.99027 .98986 .98944 .98902 .98858 .9881468.761. .99998 .99996 .99993 .999891392 .1421 .1449 .1478 .1507 .15361.0098 1.0102 1.0107 1.0111 1.0115 1.0120114.6.0175 .0175 0204 .0204 .0233 .0233 .0262 .0262 .0291 .0291 .0320 .03201.0002 1.0002 1.0003 1.0003 1.0004 1.000557.30 49.11 42.98 38.20 34.38 31.26.99985 99979 .99973 .99966 .99958 .99949.1564 .1593 .1622 .1650 .1679 .17081.0125 6.394 6.314 .98769 1.0129 6.277 6.197 .98723 1.0134 6.166 6.084 .98676 1.0139 6.059 5.976 .98629 1.0144 5.955 5.871 .98580 1.0149 5.855 5.769 .98531.0349 .0378 .0407 .0436 .0465 .0494.0349 .0378 .0407 .0437 .04661.0006 1.0007 10008 1.0010 1.0011 1001228.65.99939 .9992924.56 22.93 21.49 20.23.99917 .99905 .99892 .99878.1736 .1765 .1794 .1822 .1851 .18801.0154 1.0160 1.0165 1.0170 1.0176 1.01815.759 5.665 5.575 5.488 5.403 5.320.0523.0524 1.0014 .0553 1.0015 0582 1.0017 .0612 1.0019 .0641 10020 .0670 1.002219.11 18.10 17.20.99863 .99847 .99831 .99813 .99795 99776.1908 .1937 .1965 .1994 .2022 .20511.0187 1.0193 1.0199 1.0205 1 0211 1.02175.2415.145 .98163.2079 .2108 .2136 .2164 .2193 .22211.0223 1.0230 1.0236 1.0243 1.0249 102564.810 4.745 4.682 4.620.0552 0581 .
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