Fundamentals of Transportation/Design

Grade

$G=\frac{F_t-F_a-F_r}{W}f$

$F=W\left(\sin \left(\gamma \right)-f\cos \left(\gamma \right)\right)$

$a=g\left(\sin \left(\gamma \right)-f\cos \left(\gamma \right)\right)$

$\begin{array}{c}{F}_t=ma+F_a+F_r+F_g\\ F_r=\left(0.015\right)W:passengercars\\ F_r=\left(0.010\right)W:commercialtrucks\\ F_a=\frac{\rho }{2}A{C}_D{\nu }^2\\ F_g=GW\\ P=\frac{F_t\nu }{1000}\end{array}$

%$\mathrm{\%}d=\frac{v_i^2-v_e^2}{-2a}\mathrm{\%}$

%$\mathrm{\%}{d}_{stopping}=\frac{v_i^2-v_e^2}{2g\left(f\cos \left(\gamma \right)\pm \sin \left(\gamma \right)\right)}\mathrm{\%}$

$d_{stopping}=\frac{v_i^2-v_e^2}{2g\left(f\pm G\right)}$

$d_{perceptionreaction}=\frac{1000}{3600}t{v}_i$

$SSD=d_{perceptionreaction}+d_{stopping}$

$R_c=0.5*\frac{{\left(\frac{1000}{3600}v\right)}^{2}m}{R}$

$F_c=\frac{W{a}_c}{g}$

$\frac{m{v}^2}{R}=\frac{W{v}^2}{gR}=W\sin \alpha +W{f}_s\cos \alpha$

$R=\frac{v^2}{g\left(e+f_s\right)}$

%$\mathrm{\%}\begin{array}{c}\mathrm{\%}\frac{\partial x{\mathrm{\backslash limits}}^{\bullet }}{\partial t}=a\\ \mathrm{\%}x{\mathrm{\backslash limits}}^{\bullet }=at+C_1\\ \mathrm{\%}x=0.5a{t}^2+C_{1}t+C_2\\ \mathrm{\%}\end{array}\mathrm{\%}$

%$\mathrm{\%}\frac{\partial u_t}{\partial t}=\alpha -\beta u_t\mathrm{\%}$

Horizontal curves

Radius of Curve

$R=\frac{v^2}{g\left(e+f_s\right)}$

$S<L:m=R\left(1-\cos \frac{28.65S}{R}\right)$

$S>L:m=R\left(1-\cos \frac{28.65L}{R}\right)+\left(\frac{S-L}{2}\right)\sin \left(\frac{28.65L}{R}\right)$

%$\mathrm{\%}R=\frac{1746}{D_a}\mathrm{\%}$

$T=R\tan \left(\frac{\mathrm{\Delta }}{2}\right)$

$C=2R\sin \left(\frac{\mathrm{\Delta }}{2}\right)$

$E=R\left(\frac{1}{\cos \left(\frac{\mathrm{\Delta }}{2}\right)}-1\right)$

$M=R\left(1-\cos \left(\frac{\mathrm{\Delta }}{2}\right)\right)$

$L=\frac{R\mathrm{\Delta }\pi }{180}$

Crest vertical curves

$Y=y_{PVC}+G1*x+\frac{(G2-G1)x^2}{2L}$

%where: %$y_{pvc}$: elevation of the PVC % %$G1$: Initial Roadway Grade (m/m) % %$G2$: Final Roadway Grade (m/m) % %$L$: Length of Curve (m)

$S>L:L=2S-\frac{200{\left(\sqrt{h_1}+\sqrt{h_2}\right)}^2}{A}$

$S<L:L=\frac{A{S}^2}{200{\left(\sqrt{h_1}+\sqrt{h_2}\right)}^2}$

Sag Vertical curves

$S>L:L=2S-\frac{200\left(H+S\tan \beta \right)}{A}$

$S<L:L=\frac{A{S}^2}{200\left(H+S\tan \beta \right)}$

%$\mathrm{\%}L=\frac{A{\left(u\right)}^2}{390}\mathrm{\%}$ % %$$L=30.48A$$

Pavement design

%$$SN = a_1D_1 + a_2D_2M_2 + a_3D_3M_3 $$

%$$G_T = ((1+r)^Y-1)/r$$