GEOMETRIC DESIGN: HORIZONTAL ALIGNMENT

GEOMETRIC DESIGN:HORIZONTAL ALIGNMENT CE331 Transportation Engineering

Objectives • Describe components of horizontal alignment • Determine design parameters for circular curve • Understand the impact of superelevation and stopping sight distance on the design of horizontal curve

General Concepts • Components • Tangents • Curves (circular) • Design values • Function of design speed and superelevation • Stopping sight distance at any point • Length measured along centerline of the curve

πR Δ/180 Arc L = Δ Cord C = 2R sin(Δ/2) R tan(Δ/2) Tangent T = M Δ/2 C R R Δ Horizontal Curves PI T M = R [1 – cos (Δ/2)] PT PC Sta PC = Sta PI – T Sta PT = Sta PC +L

30o 1257.3 Example Given: R = 1800 ft, Δ = 30 o, Sta PI Find: L, Sta PC, Sta PT? Sta 12+57.3 T L Sta 17+17.5 Sta 7+75 Sta PC = Sta PI - T Sta PT = Sta PC + L PT PC L = π R Δ/180 = π(1800)(30)/180 = 942.5 ft T = R tan(Δ/2) = 1800 tan(30/2) = 482.3 ft

Example A highway has a design speed of 70mph and a superelevation rate of 0.01. If fs = 0.15, What should be the radius of the curve? R = V2/[15(fs+e)] = 702/[15*(0.15+0.01)] = 2042 (ft)

Example (cont’d) If the curve is fitted through two tangents with central angle Δ = 25°, How long should the curve be? L = πRΔ/180 = π*2042*25/180 = 891 (ft)

SSD C C L L M’ R R’ Sight Distance on Horizontal Curves • Clearance from roadside obstruction • M’ measured from the CL of the inside lane • M’ = R’ {1 – cos[90SSD/(πR’)]}

M’ C L 60 mph 0.00 11.2 2 1000-12/2 Example Min. distance to wall from centerline to ensure SSD? Given: R=1000 ft; tr= 2 sec; V=60mph; a=11.2ft/sec2; G=0%; lane width (W) = 12ft SSD = 1.47Vtr + V2/[30(a/32.2+G)] = 521.4 (ft) M’ = R’ {1 – cos[90SSD/(π R’)]} = 34.0 (ft)  Clearance from centerline of the road = 34.0 + 12/2 = 40 ft

M’ C L Example (cont’d) What if the clearance from the centerline is 35 ft? Change V. M’ = 35 – 12/2 = 29 ft Find SSD associated with M’: M’ = R’ {1 – cos[90SSD/(π R’)]}  SSD = πR’ cos-1(1- M’/R’)/90 = 481.4 (ft) SSD = 1.47Vtr + V2/[30(a/32.2+G)] • V = 57.1 (mph) • Speed limit = 55 mph

Deflection Angles • Used in laying out curves • Incremental central angle δi = 180 xi/(Rπ) • Subtended angles θi = δi/2=180 xi/(2Rπ) • Deflection angles • Cumulative of subtended angles • Chords for laying out curve • Ci = 2R sin(δi/2) = 2R sin(θi)

30o Example(1/4) R = 600 m Deflection angles, cords? Sta 1+556.91 Sta 1+396.14 Sta 1+710.30 PT PC

30o θ2 θ1 1+500.00 1+400.00 1+396.14 1+450.00 θ3 Laying Out a Curve(2/4) PC

Example(3/4) • 1st Station • 1400-1396.14 = 3.86 m • θ1 = 180 (3.86)/[2 (600) π] = 0.18o • C1 = 2 (600)sin(0.18) = 3.86 m • 2nd Station • 1450-1400 = 50.00 m • θ2 = 180 (50)/[2 (600) π] = 2.39o • C2 = 2 (600)sin(2.39) = 49.99 m

Curve Layout Data(4/4)

Used to help surveyors stakeout curve Arc -> Roadways Chord -> Railroads

Superelevation • Pavement cross slope to keep vehicles on road • e + fs = V2/(15R) • e = tan(α), superelevation rate • fs: coefficient of side friction • V: design speed, mph • R: radius ofthe curve, ft

Superelevation Issues • emax – Lower in Maine than in Florida – Why? • fs is a function of driver comfort and safety • ranges from 0.17 for 20mph to 0.08 at 80mph • Max superelevation sets Min radius • Practice: AASHTO Green Book tables

0% 2% e% 0% Superelevation Transition To From • Tangent Runout • Superelevation Runoff • Pavement rotation rate 1:200 • L = 200 W e

0% 2% e% Superelevation Transition PC Example W = 3.30 m TR = 200(3.3)(0.02)=13.2 m SR = 200(3.3)(0.08)=52.8 m A-PC = SR(2/3) = 35.2 m A

Where do we rotate the roadway? • Rotate pavement about the centerline • most common for undivided roadways • Others mainly for drainage or terrain • Rotate pavement about the inner edge • Rotate pavement about the outside edge • Rotate about the center of the median

Super-elevation Transition

Superelevation Road Section View Road Plan View CL 2% 2%

Superelevation Road Section View Road Plan View CL 1.5% 2%

Superelevation Road Section View Road Plan View CL -0.0% 2%

Superelevation Road Section View Road Plan View CL -1% 2%

Superelevation Road Section View Road Plan View CL -1.5% 2% 2%

How do we transition into a super-elevated curve? • No Spiral • Spiral

GEOMETRIC DESIGN: HORIZONTAL ALIGNMENT