ROUTE SURVEYING

Question 1

$Simple\ Curve$ Deflection and Central Angle of a Certain Point along the Curve

Accepted Answer

$\alpha\ =\ \frac{	heta}{2}$

Question 2

$Simple\ Curve$ Perpendicular Offset from the tangent of the Curve

Accepted Answer

$\ tan\ \alpha\ =\ \frac{x}{b}$

Question 3

$Simple\ Curve$ $\left(Radius\ of\ Curve\right)$ $(R)$

Accepted Answer

$20\ m\ =\ \frac{\pi\ R\ D}{180°}$ $100\ ft\ =\ \frac{\pi\ R\ D}{180°}$

Question 4

$Simple\ Curve$ $\left(Curve\ Length\right)$ $(L_c)$

Accepted Answer

$L_c=\frac{\pi\ R\ I}{180}\ \ \ =\frac{20\ I}{D}$

Question 5

$Simple\ Curve$ $\left(Tangent\ Distance\right)$ $(T)$

Accepted Answer

$Distance\ of\ PI\ \Longleftrightarrow PC$ $Distance\ of\ PI\ \Longleftrightarrow PT$

Question 6

$Minimum\ Radius$ $(R_{min})$

Accepted Answer

$R_{min\ }=\ \frac{v^2}{g\ \left(e+\mu\right)}$

Question 7

$kph\ \Rightarrow\ \ \ \ m/s$

Accepted Answer

$kph\ \ \ \ \ \Rightarrow\ \ \ \ \frac{kph}{3.6}\ \ \ \ \ \Rightarrow\ m/s$

Question 8

$Impact\ Factor$ $(I.F.)$

Accepted Answer

$I.F.\ =\ e+\ \mu\ =\ \frac{v^2}{g\ R}$

Question 9

$Compound\ Curve$ Common Tangent $(CT)$

Accepted Answer

$CT=\ T_1+T_2$

Question 10

$Reverse\ Curve$ Common Tangent $(CT) $

Accepted Answer

$CT=\ T_1+T_2$

Question 11

SPIRAL CURVE Distance along tangent to any point on the Spiral

Accepted Answer

$Y\ =\ L-\ \frac{{\ L}^5}{40\ R^2\ {L_s}^2}$

Question 12

SPIRAL CURVE Offset Distance from Tangent to any point in the Spiral

Accepted Answer

$x\ =\ \frac{L^3}{6\ R\ L_s\ }$

Question 13

SPIRAL CURVE Spiral angle from Tangent to any point on the Spiral

Accepted Answer

$	heta\ =\ \frac{L^2}{2\ R\ L_s\ }$

Question 14

SPIRAL CURVE Deflection Angle from TS to any point on the spiral (i)

Accepted Answer

$i\ =\ \frac{	heta}{3\ }$

Question 15

SPIRAL CURVE Ratio of $i\ and\ i_s$

Accepted Answer

$\frac{i}{{L\ }^2}=\frac{i_s}{{L_s}^2\ }$

Question 16

SPIRAL CURVE Tangent Distance (TS to PI) ${(T}_s)$

Accepted Answer

$T_s=\ \frac{L_s}{2}+\ \left(R+P\right)\ tan\left(\frac{I}{2}\right)$

Question 17

SPIRAL CURVE Length of Throw (P)

Accepted Answer

$P=\frac{X_c}{4\ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P=\ \frac{{L_s}^2}{24\ R}$

Question 18

IN VERTICAL CURVES ALWAYS CREATE FIGURE THOROUGHLY and REFER TO IT FOR THE SIGN CONVENTION

Accepted Answer

IN VERTICAL CURVES ALWAYS CREATE FIGURE THOROUGHLY and REFER TO IT FOR THE SIGN CONVENTION

Question 19

SPIRAL CURVE External Distance $(E_s)$

Accepted Answer

$E_s=\frac{R+P}{cos\ \left(\frac{I}{2}\right)}-P $

Question 20

Degree of Spiral Curve at any point

Accepted Answer

$\frac{D}{D_C}=\ \frac{L}{L_S}$

Question 21

Desirable Length of Spiral

Accepted Answer

$L_S=\ \frac{0.036\ v_{\left(kph\right)}^3}{\ R}$

Question 22

Super Elevation Rate

Accepted Answer

$e\ =\ tan\ (	heta)$ $tan\ (	heta)\ =\ \frac{v_{\left(m/sight)}^2}{g\ R_{(m)}}$

Question 23

Maximum Velocity in a road with super-elevation

Accepted Answer

$e+\ \mu\ =\ \frac{{v_{max}}^2}{g\ R}$

Question 24

Minimum Velocity in a road with super-elevation

Accepted Answer

$e-\ \mu\ =\ \frac{{v_{min}}^2}{g\ R}$

Question 25

Rate of Change in Centripetal Acceleration

Accepted Answer

$q_{(m/s^2)}=\ \frac{v_{\left(m/s\right)}^3}{\left(R\ L_S\right)_{(m)}} $

Question 26

Symmetrical Vertical Curve Elevation of PI relative to the Curve (Road)

Accepted Answer

$H=\ \frac{L}{8}\left(\ \left|g_1\right|+\left|g_2\right|\ \right)$

Question 27

Unsymmetrical Vertical Curve Elevation of PI relative to the Curve (Road)

Accepted Answer

$H=\ \frac{\left(\left|g_1\right|+\left|g_2\right|\right)\ L_1\ L_2}{{2\ L}_T}$ $H=\ \frac{\ L_1\ }{2}\ \left(\left|g_1\right|+\left|g_3\right|\right)$

Question 28

Unsymmetrical Vertical Curve Elevation of own PI relative to the Curve (Road)

Accepted Answer

$h_1=h_2=\ \frac{\ H\ }{4}$

Question 29

Unsymmetrical Vertical Curve Slope of Common Tangent; g3

Accepted Answer

$g_3=g_1-\ \frac{\ 2H\ }{L_1}$ $g_3=\ \frac{\ g_1\ L_1\ +\ g_2\ L_2\ }{L_T}$

Question 30

Unsymmetrical Vertical Curve Locating the summit/ trough $If\ \ \ \left(g_1\ L_{1\ }\right)\ >\ 2H,\ \ therefore\ ...$

Accepted Answer

$S_2=\ \frac{\ g_2\ \left(L_2\right)^2\ }{2H}$ $S_1=L_T-{\ S}_2$

Question 31

Unsymmetrical Vertical Curve Locating the summit/ trough $If\ \ \ \left(g_1\ L_{1\ }\right)\ <\ 2H,\ \ therefore\ ...$

Accepted Answer

$S_1=\ \frac{\ g_1\ \left(L_1\right)^2\ }{2H}$ $S_2=L_T-{\ S}_1$

Question 32

Earthworks Volume by End-Area Method $({\ V}_e)

Accepted Answer

${\ V}_e\ =\ \frac{L}{2}\left({\ A}_1+{\ A}_2\right)\ $

Question 33

Earthworks Volume by Prismoid Formula $({\ V}_p)$

Accepted Answer

${\ V}_p\ =\ \frac{L}{6}\left({\ A}_1+{\ 4A}_m+{\ A}_2\right)\ $

Question 34

Earthworks Prismoid Correction $({\ C}_p)$

Accepted Answer

${\ {{\ C}_p=\ V}_e\ -V}_p$ $C_p=\ \frac{L}{12}\ \left(c_1-c_2\right)\left(d_1-d_2\right)$

Question 35

Earthworks Volume by Truncated Prism

Accepted Answer

$V\ =\ A\left[\frac{1\ \left(\sum{\ h}_1\right)+\ 2\ \left(\sum{\ h}_2\right)+3\ \left(\sum{\ h}_3\right)\ +4\ \left(\sum{\ h}_4\right)}{4}\ \right]\ $

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