Lec. 13 reverse circular curves

Engineering Surveying Lectures

1. The Thirteenth Lecture
1
.ﻦﻴﻄﻴﺴﺒﻟﺍ ﻦﻴﻳﺮﺋﺍﺪﻟﺍ ﻦﻴﻴﻨﺤﻨﻤﻟﺍ ﺮﺻﺎﻨﻋ ﺏﺎﺴﺣ ﻲﻓﺔﻘﺑﺎﺴﻟﺍ ﻦﻴﻧﺍﻮﻘﻟﺍ ﺲﻔﻧ ﻡﺪﺨﺘﺴﻳ
Surveying Engineering
Reverse Circular Curves:
A reverse curve is made up of two arcs having equal or different radius bending in the
opposite direction with a common tangent at their junction. Reverse curves are used when the
straights are parallel or intersect at a very small angle.
They are commonly used in railway sidings and sometimes on railway tracks and roads meant
for low speeds. They should be avoided as far as possible on main lines and highways where
speeds are necessarily high.
Calculation of Reverse Circular Curve:-
Elements calculate two simple circular curves using the same previous methods…
T = R
tan∆2
L =
?????? ?????? ∆ᵒ180ᵒ
C = 2 R
sin∆2
ﻦﻴﻴﻨﺤﻨﻣ (ﺏﻮﻠﻘﻤﻟﺍ)
ﻥﻮﻜﻳﻭ
ﻒﺼﻧ ,ﺮﺧﻻﺍ
ﻦﻴﻤﻴﻟﺍ )
ﺱﺎﻤﻤﻟﺍ (ﻼﺜﻣ
.(ﻼﺜﻣ ﺭﺎﺴﻴﻟﺍ ﻰﻟﺍ) ﻙﺮﺘﺸﻤﻟﺍ
ﺔﻳﺪﻳﺪﺤﻟﺍ
ﻕﺮﻄﻟﺍ
ﺔﻴﺴﻴﺋﺮﻟﺍ .ﺓﺮﻋﻮﻟﺍ
ﺓﺭﻭﺮﻀﻟﺎﺑ ﺔﻴﻟﺎﻋ ﺕﺎﻋﺮﺴﻟﺍ ﻥﻮﻜﺗ ﺚﻴﺣ ﺔﻌﻳﺮﺴﻟﺍ ﻕﺮﻄﻟﺍﻭ

2. The Thirteenth Lecture
2
ﻲﻨﺤﻨﻤﻟﺍ (P.C)
ﻊﻣ (P.R.C)
ﻁﺎﻘﻨﻟﺍ
.ﻲﻨﺤﻨﻤﻟﺍ
P.R.C.: Point of Reverse Curvature
R₁, ∆₁, T₁, L₁, C₁ & P.I₁: Elements of the first curve.
R₂, ∆₂, T₂, L₂, C₂ & P.I₂: Elements of the second curve.
St. P.C = St. P.I₁ – T ₁
St. P.R.C = St. P.C + L₁
St. P.T = St. P.R.C + L₂
St. P.I₂ = St. P.R.C + T₂
Example: - Compute the main stations of reverse circular horizontal curve, if (C₁=244m, ∆₁=42ᵒ
36′, St. P.R.C=51+42.50, T₂=108m & R₂=325m).
Solution: -
C₁ = 2 R₁ → R₁335.86m
sin∆₁2C₁2 sin∆₁22442 sin21ᵒ 18′
T₁ = R₁130.95m
tan∆₁2×tan21ᵒ 18′
L₁ = = = 249.95m
?????? ??????₁ 180ᵒ3.14156×335.86×21ᵒ 18′180ᵒ
T₂ = R₂→→ =
tan∆₂2 tan∆₂2T₂R₂10832518ᵒ 23′∆₂36ᵒ 46′
L₂ = = = 208.552m
?????? ??????₂ ∆₂ᵒ180ᵒ3.14156×325×36ᵒ 46′180ᵒ
C₂ = 2 R₂ = 2 325 = 204.99m
sin∆₂2 ××sin18ᵒ 23′
St. P.C = St. P.I₁ – T ₁ = (51+42.50) – (2+49.72) = (48+92.78)
St. P.R.C = St. P.C + L₁ = (51+42.50) + (2+08.55) = (53+51.05)
St. P.T = St. P.R.C + L₂ = (48+92.78) + (1+30.95) = (50+23.73)
St. P.I₂ = St. P.R.C + T₂ = (51+42.50) + (1+08) = (52+50.50)
.ﻝﻭﻻﺍ ﻱﺮﺋﺍﺪﻟﺍ ﻲﻨﺤﻨﻤﻟﺍ ﺮﺻﺎﻨﻋ.ﻲﻧﺎﺜﻟﺍ ﻱﺮﺋﺍﺪﻟﺍ ﻲﻨﺤﻨﻤﻟﺍ ﺮﺻﺎﻨﻋ.ﺱﻮﻜﻌﻤﻟﺍ ﺱﻮﻘﺘﻟﺍ ﻭﺍ ﺏﺪﺤﺘﻟﺍ ﺔﻄﻘﻧ