ROUTE SURVEYING
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1
$Simple\ Curve$
Deflection and Central Angle of a
Certain Point along the Curve
Deflection and Central Angle of a
Certain Point along the Curve
$\alpha\ =\ \frac{\theta}{2}$
2
$Simple\ Curve$
Perpendicular Offset from
the tangent of the Curve
Perpendicular Offset from
the tangent of the Curve
$\ tan\ \alpha\ =\ \frac{x}{b}$
3
$Simple\ Curve$
$\left(Radius\ of\ Curve\right)$
$(R)$
$\left(Radius\ of\ Curve\right)$
$(R)$
$20\ m\ =\ \frac{\pi\ R\ D}{180°}$
$100\ ft\ =\ \frac{\pi\ R\ D}{180°}$
$100\ ft\ =\ \frac{\pi\ R\ D}{180°}$
4
$Simple\ Curve$
$\left(Curve\ Length\right)$
$(L_c)$
$\left(Curve\ Length\right)$
$(L_c)$
$L_c=\frac{\pi\ R\ I}{180}\ \ \ =\frac{20\ I}{D}$
5
$Simple\ Curve$
$\left(Tangent\ Distance\right)$
$(T)$
$\left(Tangent\ Distance\right)$
$(T)$
$Distance\ of\ PI\ \Longleftrightarrow PC$
$Distance\ of\ PI\ \Longleftrightarrow PT$
$Distance\ of\ PI\ \Longleftrightarrow PT$
6
$Simple\ Curve$
$\left(Length\ of\ Long\ Chord\right)$
$(L)$
$\left(Length\ of\ Long\ Chord\right)$
$(L)$
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$Simple\ Curve$
$\left(External\ Distance\right)$
$(E)$
$\left(External\ Distance\right)$
$(E)$
8
$Simple\ Curve$
$\left(Middle\ Ordinate\right)$
$(M)$
$\left(Middle\ Ordinate\right)$
$(M)$
9
$Minimum\ Radius$
$(R_{min})$
$(R_{min})$
$R_{min\ }=\ \frac{v^2}{g\ \left(e+\mu\right)}$
10
$kph\ \Rightarrow\ \ \ \ m/s$
$kph\ \ \ \ \ \Rightarrow\ \ \ \ \frac{kph}{3.6}\ \ \ \ \ \Rightarrow\ m/s$
11
$Impact\ Factor$
$(I.F.)$
$(I.F.)$
$I.F.\ =\ e+\ \mu\ =\ \frac{v^2}{g\ R}$
12
CONCEPT
COMPOUND CURVE
COMPOUND CURVE
13
CONCEPT
DETERMINING STATIONS in all
HORIZONTAL CURVES
DETERMINING STATIONS in all
HORIZONTAL CURVES
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$Compound\ Curve$
Common Tangent
$(CT)$
Common Tangent
$(CT)$
$CT=\ T_1+T_2$
15
$Reverse\ Curve$
Common Tangent
$(CT) $
Common Tangent
$(CT) $
$CT=\ T_1+T_2$
16
Spiral Curve Concept
17
SPIRAL CURVE
Distance along
tangent to any point
on the Spiral
Distance along
tangent to any point
on the Spiral
$Y\ =\ L-\ \frac{{\ L}^5}{40\ R^2\ {L_s}^2}$
18
SPIRAL CURVE
Offset Distance from
Tangent to any point
in the Spiral
Offset Distance from
Tangent to any point
in the Spiral
$x\ =\ \frac{L^3}{6\ R\ L_s\ }$
19
SPIRAL CURVE
Spiral angle from Tangent
to any point on the Spiral
Spiral angle from Tangent
to any point on the Spiral
$\theta\ =\ \frac{L^2}{2\ R\ L_s\ }$
20
SPIRAL CURVE
Deflection Angle from
TS to any point
on the spiral
(i)
Deflection Angle from
TS to any point
on the spiral
(i)
$i\ =\ \frac{\theta}{3\ }$
21
SPIRAL CURVE
Ratio of
$i\ and\ i_s$
Ratio of
$i\ and\ i_s$
$\frac{i}{{L\ }^2}=\frac{i_s}{{L_s}^2\ }$
22
SPIRAL CURVE
Tangent Distance (TS to PI)
${(T}_s)$
Tangent Distance (TS to PI)
${(T}_s)$
$T_s=\ \frac{L_s}{2}+\ \left(R+P\right)\ tan\left(\frac{I}{2}\right)$
23
SPIRAL CURVE
Length of Throw
(P)
Length of Throw
(P)
$P=\frac{X_c}{4\ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P=\ \frac{{L_s}^2}{24\ R}$
24
IN VERTICAL CURVES ALWAYS CREATE FIGURE THOROUGHLY
and REFER TO IT FOR THE SIGN CONVENTION
and REFER TO IT FOR THE SIGN CONVENTION
IN VERTICAL CURVES ALWAYS CREATE FIGURE THOROUGHLY
and REFER TO IT FOR THE SIGN CONVENTION
and REFER TO IT FOR THE SIGN CONVENTION
25
SPIRAL CURVE
External Distance
$(E_s)$
SPIRAL CURVE
External Distance
$(E_s)$
$E_s=\frac{R+P}{cos\ \left(\frac{I}{2}\right)}-P $
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Degree of Spiral Curve
at any point
at any point
$\frac{D}{D_C}=\ \frac{L}{L_S}$
27
Desirable Length of Spiral
$L_S=\ \frac{0.036\ v_{\left(kph\right)}^3}{\ R}$
28
Super Elevation Rate
$e\ =\ tan\ (\theta)$
$tan\ (\theta)\ =\ \frac{v_{\left(m/s\right)}^2}{g\ R_{(m)}}$
$tan\ (\theta)\ =\ \frac{v_{\left(m/s\right)}^2}{g\ R_{(m)}}$
29
Maximum Velocity
in a road with super-elevation
in a road with super-elevation
$e+\ \mu\ =\ \frac{{v_{max}}^2}{g\ R}$
30
Minimum Velocity
in a road with super-elevation
in a road with super-elevation
$e-\ \mu\ =\ \frac{{v_{min}}^2}{g\ R}$
31
Rate of Change in
Centripetal Acceleration
Centripetal Acceleration
$q_{(m/s^2)}=\ \frac{v_{\left(m/s\right)}^3}{\left(R\ L_S\right)_{(m)}} $
32
Symmetrical Vertical Curve
CONCEPT
CONCEPT
33
Symmetrical Vertical Curve
Elevation of PI relative
to the Curve (Road)
Elevation of PI relative
to the Curve (Road)
$H=\ \frac{L}{8}\left(\ \left|g_1\right|+\left|g_2\right|\ \right)$
34
Unsymmetrical Vertical Curve
Elevation of PI relative
to the Curve (Road)
Elevation of PI relative
to the Curve (Road)
$H=\ \frac{\left(\left|g_1\right|+\left|g_2\right|\right)\ L_1\ L_2}{{2\ L}_T}$
$H=\ \frac{\ L_1\ }{2}\ \left(\left|g_1\right|+\left|g_3\right|\right)$
$H=\ \frac{\ L_1\ }{2}\ \left(\left|g_1\right|+\left|g_3\right|\right)$
35
Unsymmetrical Vertical Curve
Elevation of own PI relative
to the Curve (Road)
Elevation of own PI relative
to the Curve (Road)
$h_1=h_2=\ \frac{\ H\ }{4}$
36
Unsymmetrical Vertical Curve
Slope of Common Tangent;
g3
Slope of Common Tangent;
g3
$g_3=g_1-\ \frac{\ 2H\ }{L_1}$
$g_3=\ \frac{\ g_1\ L_1\ +\ g_2\ L_2\ }{L_T}$
$g_3=\ \frac{\ g_1\ L_1\ +\ g_2\ L_2\ }{L_T}$
37
Unsymmetrical Vertical Curve
Locating the summit/ trough
$If\ \ \ \left(g_1\ L_{1\ }\right)\ >\ 2H,\ \ therefore\ ...$
Locating the summit/ trough
$If\ \ \ \left(g_1\ L_{1\ }\right)\ >\ 2H,\ \ therefore\ ...$
$S_2=\ \frac{\ g_2\ \left(L_2\right)^2\ }{2H}$
$S_1=L_T-{\ S}_2$
$S_1=L_T-{\ S}_2$
38
Unsymmetrical Vertical Curve
Locating the summit/ trough
$If\ \ \ \left(g_1\ L_{1\ }\right)\ <\ 2H,\ \ therefore\ ...$
Locating the summit/ trough
$If\ \ \ \left(g_1\ L_{1\ }\right)\ <\ 2H,\ \ therefore\ ...$
$S_1=\ \frac{\ g_1\ \left(L_1\right)^2\ }{2H}$
$S_2=L_T-{\ S}_1$
$S_2=L_T-{\ S}_1$
39
Earthworks
Cross Sectional Cut
Cross Sectional Cut
40
Earthworks
Cross Sectional Fill
Cross Sectional Fill
41
Earthworks
Cross Sectional Cut and Fill
Cross Sectional Cut and Fill
42
Earthworks
Volume by End-Area Method
$({\ V}_e)
Volume by End-Area Method
$({\ V}_e)
${\ V}_e\ =\ \frac{L}{2}\left({\ A}_1+{\ A}_2\right)\ $
43
Earthworks
Volume by Prismoid Formula
$({\ V}_p)$
Volume by Prismoid Formula
$({\ V}_p)$
${\ V}_p\ =\ \frac{L}{6}\left({\ A}_1+{\ 4A}_m+{\ A}_2\right)\ $
44
Earthworks
Prismoid Correction
$({\ C}_p)$
Prismoid Correction
$({\ C}_p)$
${\ {{\ C}_p=\ V}_e\ -V}_p$
$C_p=\ \frac{L}{12}\ \left(c_1-c_2\right)\left(d_1-d_2\right)$
$C_p=\ \frac{L}{12}\ \left(c_1-c_2\right)\left(d_1-d_2\right)$
45
Earthworks
Volume by Truncated Prism
Volume by Truncated Prism
$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]\ $