Geometric Design

Homework

• Ch 3 # 1,3,7,8,9

Geometric Design• Roadway is designed using v, R, e– Need to know the required Stopping Sight

Distance for the roadway– D = 1.47vt +v2/(30(f+g)

• v is in mph (1.47, 30 are conversion factors)• SSD – distance required to make a full stop• Decision Sight Distance – adds in a maneuver time (3.5 –

4.5s) to the reaction time based on AASHTO guidelines– D = 1.47v(tr+tm) +v2/(30(f+g)

• Gives Decision Sight Distance

Alignment

• 2 types of alignment– Vertical– Horizontal

Vertical Curves

• 2 types of curves– Crest– Sag

• Different criteria for SSD– crest - 6” object over hill– sag headlights

Vertical Curves

• Grade controls – Trucks and f control– Max grade Interstate = 9%– Max grade local street = 15%– min grade = 0.5% - drainage– Fig 3.15– length of grade is important as well– Also look at length of curve and change in grade• Don’t want cars grabbing air

Vertical Curves

• Truck performance• Note crawl speed• Fig 3.16, 3.17, 3.18

Vertical Curves

Vertical Curve Design

• Vertical Curves are Parabolas• A = G2 - G1 –algebraic diff in grades (in %)

• E = AL/8– L is in stations (ft/100)– gives E in ft

• y = [(G2-G1)/2L]*x^2 + G1x+ Y0– Gives y in ft– x is in stations, G1, G2 in %

Vertical Curve Design

• Hi/Lo point occurs at dy/dx = 0– x = -LG1/(G2-G1)

– Not in middle of L– All calcs in stations

Vertical Curve Design• SSD for Crest curves (dead cat distance)– 2 equations - L>=SSD,

– L=(!G2-G1!*(SSD^2))/(200*(h1^0.5+h2^0.5)^2– L<=SSD

– L=2*SSD - (200*(h1^0.5+h2^0.5)^2/(!G2-G1!)– These provide minimum values– only one is true– eye height h1 = 3.5 ft– object height h2 = 0.5 ft– 200*(h1^0.5+h2^0.5)^2 = 1329 (not what is in the

book)

• Given a design speed of 45 mph, approach grade of +3% and a departure grade of -4% meeting at VPI Station = 100+50, VPI Elevation = 347.85. – What is the PVC & PVT stations and elevations– Where is the high point located and what is

elevation

Vertical Curve Design

• L for Sag curves– L>SSD• L=(!G2-G1!*(SSD^2))/(200*(h+SSD*tan)

– L<SSD• L=2*SSD - (200 *(h+SSD*tan) /(!G2-G1!)

– 200 *(h+SSD*tan) = 400+3.5SSD– only one is true– headlight height h = 2 ft– beam angle = 1 degree (dispersion)

• Given a design speed of 45 mph, approach grade of -4% and a departure grade of -1% meeting at VPI Station = 100+50, VPI Elevation = 347.85. – What is the PVC & PVT stations and elevations– Where is the high point located and what is

elevation

Horizontal Alignment

Horizontal Alignment

• 3 parts to alignment– tangents - straight sections– curves– transitions between curves and tangents

Curves

• L=2R/360 • D - degree of curve• D different for RR • and highways

Curves

• External Distance PI -> LE = R(sec(I/2)-1)• Middle Ordinate L->LC M = R(1-cos(I/2)• Tangent PC->PI T = Rtan(I/2)• Curve Length PC->PT L = 100(I/D)• Chord Length PC-> PT LC = 2Rsin(I/2)• Degree of curve D = 5729.58/R– How many degrees to create an arc of 100’ for a

given radius

Horizontal Distance

• Need to maintain SSD around curve• Look at M and L to determine safe speed– L = SSD– I changes to I=L*D/100– M = R(1- cos (I/2))– If M > available M then NO GOOD

Example

• Given the following info for a horizontal curve, determine if a speed limit of 60 mph is safe.– I = 45 degrees, R =1500 ft, 2-12 foot lanes, 6 foot

shoulder, e = 0.04, f=0.12, barn located 14 feet off centerline of inside lane.

Design Vehicles

• Fig 2.4 • Gives tightest turn radius for a low speed turn

by a vehicle• 10 specific types of vehicles used– determine speeds, curb radius, pavement width

Delineation of Vehicle Paths

• Flow Control• pavement markings, medians, islands• Channelization provide improved flow

through an intersection

Channelization

Channelization

Lab

• Develop an Excel Spreadsheet which will solve horizontal and vertical curve problems