spiral - 1 2 ) ( ) ( y y x x c-+-= (bet. two pts) 5. Throw,...

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SPIRAL QUANTITIES Ls = spiral length Rc = curve radius s = spiral angle PI = alignment delta Ts c = circular curve delta lat.shift LC = long chord orig PC T c = subchord sh. PC LT = long tangent ST = short tangent SPI s s SPI P = throw of the spiral K = x position of throw Xs = x component of spiral K Ys = y component of spiral x,y = x,y of intermed. pt at l throw, P l = position from TS (or ST) P.T. δ = defl. to tang.@ inter. pt. s c s Lc =length circular curve Ts = spiraled cur. tang. length l.s .= lateral shift of PC T = orig. unspiraled cur.tang. 1. Radius : l L R r s c = , l L R r s c = 2. Spiral Angle : s c L R l 2 2 = δ , c s s R L 2 = 3. Rectangular Components : + - + - = ... ! 4 9 ! 2 5 1 4 2 s s s s L X + - + - = ... ! 5 11 ! 3 7 3 5 3 s s s s s L Y (Whole) Spiral) 4. Layout Intermediate Point + - + - = ... ! 4 9 ! 2 5 1 4 2 s s l x + - + - = ... ! 5 11 ! 3 7 3 5 3 s s s l y (Intermediate Point) 2 2 y x c + = (Subchord from TS/ST) x y a 1 tan - = (deflection angle) 2 1 2 2
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Unformatted text preview: 1 2 ) ( ) ( y y x x c-+-= (bet. two pts) 5. Throw, LT/ST : s s Y ST = sin s s s Y X LT -= tan s c s R X K -= sin c s s c R Y R P-+ = cos 6. Stationing s c - = 2 K shift lat T T s + + = . 2 tan . = P shift lat c c c R L = s T I StaP S StaT-= . . . . s L S StaT C StaS + = . . . c L C StaS S StaC + = . . . . s L S StaC T StaS + = . . . . S.T. Station Equation: ( 29 o x shift lat L T I StaP + + +-. . . AHEAD = BACK ( 29 s c s s L L L T I StaP + + +-. . 7. Cartesians : ( 29 180 cos + + = AzIn T N N s PI TS AzIn LT N N TS SPI cos + = ( 29 s SPI SC AzIn ST N N -+ + = / cos ) cos( + + = AzIn T N N s PI ST 8. Jerk of a Spiral : Ls = V^3/(C*Rc) S.C. C.S. T.S. S.T. P.C ....
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This note was uploaded on 10/19/2011 for the course SUR 4201 taught by Professor Gibson during the Fall '09 term at University of Florida.

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