SPIRAL CURVES Yo = distance along time tangent Terms: from +.5 . to S. C . Sc = spiral angle @ s. c. RS : Radius of Spiral curve i = deflection angle a any point Re : Radius of circular curve Ls = Length of spiral CN T. S. = tangent to spiral Le: length of curve S.C. : Spiral to curve c.s : curve to Spiral 1 Spiral angle @ any point of s. t . : Spiral to tangent spiral : Is = tangent distance 180 S ? To = tangent distance for the curve 2 RC LS I = angle of intersection of Spiral easement curve 2) Spiral angle @ s. C. Ic = angle of intersection of LS 180 So simple curve 2 RC bc : Degree of simple curve LT : Long tensent 3) Spiral angle @ s.c . using ST = short tangent Degree of curve ( ARC BASIS ONLY) Es= External distance of the DC LS spiral curve 40 L. C. = Long chord Of spiral SC torunsition 4) off set distance from tanscht to * = offset from tangent ase 4 2 to Starling3) Offact distance from tangents ") Deflection angle wartestes denied any point of the spiral: the square of the lengths counts * - to L2 0 4 3 ic Le 2 @ pistance along tangent line @ 1) central Angle offor spiral any point of spiral I = Ic + 2 5 0 LS 40 RC 2 Lg 2 12) Tangent Distance for Spiral: Is Distance along tangent line at 2 y NOO . O 2 SO LS 13 ) External Distance 40 Re 2 3 Deflection angle @ cing point O of spiral : 14) Length of throw @ T.S. . PC d - or = Ty @ Deflection angle @ so () Length of throw a any point of spiraly And any trodd (if to = 3 * c L2 4 24RXproperty f UNSYMMETRICAL DA RANDOLIE CURVES Maximum offset ( # ) H = = ( 5 2 - 91 ) 4L Maximum offset ( #) H = ( 8 1 - 92 ) Likz 2 (LI TLE ) where " 2 H L2 2 : Length of curve LI = ( 91 - 92) 62 - 2 H SYMMETRICAL PARABOLIC CURVE From the PT! - made us of single vertical coundition! : parabolic curve when 491 40 2 Locating the highest ( or lowest) 82 12 2 5 2 points on the curve 2 41 From the Po! From the PC when LIS1 2 4 2 SIL 1 1 - 92 S=OIL 2 2 4 From the PT 12 62 L so Highest ( or lowest ) point 52 - 92 -51 StarluryCompound Curve V . For Metric (Arc and Chord Basis) A 0 - 112 B 1. A compound curve is to be used to 38" connect two highways and two T. PCC 12 railways. Both roadways have the following data: I, = 30', 12 = 38, D, = PC PT 3', D2 = 6'. If the stationing of the vertex is 1+234.567, a. What is the stationing of PC. 12 = 38' PCC, and PT of the two R, highways? 1, = 30" b. What is the stationing of the PC, PCC, and PT of the two railways? 0 = 180 - 30 - 380 = 1120T1 R,tan NIVERTICAL PARABOLIC CURVE PROPERTY pt BACKWARD 91 4 TAUGENT TANG FUT Lenight of parablic curve is PC PT L . PC KOV= BACKWARD TANGENT stationing (length of station ) RT to PT : FORWARD TANGENT English - 10off tangents = grades Metric - 20 m PROPERTY 3 BT = 91 4 = S2 - 91 = (sag) lute: when no I is given FT * 92 ( summit ) 52 Property 4 Cc Lo. of stations or both side summit sag must be cqual ( on symeffical) property 7 Date of Charge of shape 92 - 9 1 4/2 where PROPERTY Y * 2 ( 7 2 ) 2 n: number of station SterlingTom Joseph Rivera 12 3 4 5 6 7 89 60 ROUTE SURVEYING NOTES ARC BASIS ( metrio ) CHORD BASIS (english D . 11 45 . 916 (50 /80 R D = 2 sind 11 45. 916 704 0 50 39 mont I D R = SIA where : R : radios D = angle or degree metric = meter ( m )john english - feet ( ft ) M . ARC BASIS ( english ) 5729. 578 Stationing sobim of guzoo R 1+ 600 - 00 = 1 kilometer 5729 . 578 /V2) 1 + 00. 00 men10 ft R = Baseline station pool : 3 . CHORD BASIS ( metric ) D + 000. 00 : Metric/umyoff (M ) - used For railway - . . too. con go= English . D = 2 sin + ( -2 ) Elements of simple curve 10 . PC - Point of curvature Sin (2 ) . PT - Point of Fanscacy . PI = Point of Inter section . V : verter Still Edit More EU U U W . R = Radios . For subtangent (T ) . I : D - Degree of curve (# ) (NOT 2121 4 09A T = Rtan- CentralozAngle = A . T = subtangent = distance from PC HOOP1 . For Lingo chord ( c ) . E = external pistance 6 = 2 R sin. I = distance From PI to cojbor . 29 . just middle of curve sivtom . M : Middlex ordinate tor . For External Distance (E ) distance from middle of the 1 2/24 394 E =R curve to middle of initiate Cos 2 chores 00. 000 + 1 OF . LI= Length Cof curve! Kre . P& ra = intercepted arc. . C = Long chordle .go//202 Formulas for simpleoccurve ( virtom ) 21249 Q30# J . For Length of Aro . CL )O . For Hidden ordinate ( M) RT RI M = R () cos 2 OF ponbent 20 tojoy - 790 S = 19.COMPOUND CURVES . two or mor simple curve Formulas theappt romeos with different radii w/ Parallel Long Chord and Point of compund curvature ( P.C.C) common tansense - common tangent where the tho curves meet point triangle A PC-PJ - PI common tangent ( Ic ) ( 2 = (T , + a ) 2 + +2 + b ) 2 - 2 ( Tita ) (+ 2+ b ) ros 180 - J+) - line VI - PCC - U2 - TC : TI + +2 Sine Law ! a b C Ind vertex ( v , , V2 ) sin At sinB sinc Radius sublangent (t , at2 ) C Ti ta tatb to centrale ( ! , , I2 ) Sin ( 180 - It sin I2 ) sin (I tho chords ( C , , 6 2) cos the Law: Long Chord (C ) - PC to PJ (2 = a2+62 - zab coso * C, + C 2 vertex triangle Chord trianglelength of Spiral your nottostill upfor not must gangtest tooth e ( V) keph ) Re J tensaid 47 Super - elevation e Soper -elevation considering 79% ?!) OF V to winter act super clevation 0 . 0 0 4 V 2 2 e a ( ) begree of curve varies directly. with the length from T.S : D tulag was team noitalysa 3 DS MIN 20 Long tangent of Spiral LT = YC - h (2 1) short tung end of / spiral ST Stan SU