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Chapter_3_Equations

# Chapter_3_Equations - VERTICAL ALIGNMENT y = ax2 bx c dy dx...

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VERTICAL ALIGNMENT y = ax 2 + bx + c dy / dx = 2ax + b = slope (rise / run) dy/dx = b = G1 (initial slope when x=0) d 2 y/dx 2 = 2a d 2 y/dx 2 = (G 2 - G 1 ) / L a = (G 2 - G 1 ) / 2L a = coefficient in the parabolic curve equation L = KA x hl = KG 1 (x is the high/low point) Y = offset at distance, x, from PVC (ft) Y m = midcurve offset (ft) Y f = offset at end of vertical curve (ft) A = absolute value of difference in grades (| G1 - G2 |) (%) SSD = V 1 2 + V 1 *t r 2g[(a/g) ± G] SSD = stopping sight distance (ft) V 1 = initial vehicle speed (ft/sec) g = gravitational constant (32.2 ft/sec2) a = deceleration rate (ft/s 2 ) Equation 3.1 Equation 3.2 Equation 3.3 Equation 3.4 Equation 3.5 Equation 3.6 b = coefficient in the parabolic curve equation c = elevation of PVC Equation 3.7 Equation 3.8 Equation 3.9 Equation 3.10 Equation 3.11 L = length of vertical curve (ft) x = distance from the PVC (ft) K = horizontal distance (ft) to affect a 1% change in slope. x hl = distance from PVC to high/low point (ft) Equation 3.12 G = roadway grade (+ for uphill and - for downhill) in percent/100 t r = perception reaction time 200 AL Y f = 2 200 x L A Y = 800 AL Y m =

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