Geometric Design

ByHarikrishna gaddamAssistant Professor

Department of Civil Engineering

Horizontal Alignment

• Objective: – Geometry of directional transition to ensure:

• Safety• Comfort

• Primary challenge– Transition between two directions– Horizontal curves

• Fundamentals– Circular curves– Superelevation

Δ

Horizontal Alignment

Components of Highway Design

Plan View

Profile View

Horizontal Alignment

Vertical Alignment

Horizontal Alignment

Tangents Curves

Tangents & Curves

Tangent

Curve

Tangent to Circular Curve

Tangent to Spiral Curve toCircular Curve

Layout of a Simple Horizontal CurveR = Radius of Circular CurveBC = Beginning of Curve (or PC = Point of Curvature)EC = End of Curve (or PT = Point of Tangency)PI = Point of IntersectionT = Tangent Length

(T = PI – BC = EC - PI)L = Length of Curvature

(L = EC – BC)M = Middle OrdinateE = External DistanceC = Chord LengthΔ = Deflection Angle

Properties of Circular CurvesDegree of Curvature• Traditionally, the “steepness” of the curvature is defined by either the

radius (R) or the degree of curvature (D)• In highway work we use the ARC definition• Degree of curvature = angle subtended by an arc of length 100 feet

Degree of CurvatureEquation for D

Degree of curvature = angle subtended by an arc of length 100 feet

By simple ratio: D/360 = 100/2*Pi*R

Therefore

R = 5730 / D

(Degree of curvature is not used with metric units because D is defined in terms of feet.)

Length of Curve

By simple ratio: D/ Δ = ?

D/ Δ = 100/L

L = 100 Δ / D

Therefore

L = 100 Δ / DOr (from R = 5730 / D, substitute for D = 5730/R)

L = Δ R / 57.30

(D is not Δ .)

Horizontal Curve Fundamentals

R

T

PC PT

PI

M

E

R

Δ

Δ/2Δ/2

Δ/2

RRD

000,18

180100

2tan

RT

DRL

100

180

L

Horizontal Curve Fundamentals

1

2cos

1RE

2

cos1RM

R

T

PC PT

PI

M

E

R

Δ

Δ/2Δ/2

Δ/2L

Example 1

A horizontal curve is designed with a 1500 ft.

radius. The tangent length is 400 ft. and the PT

station is 20+00. What are the PI and PT

stations?

Centripetal or Centrifugal?

• As a vehicle moves in a circular path

– Centripetal acceleration acts on the vehicle in the direction of the

center of the curve

• The acceleration is sustained by

– Component of the vehicle’s weight related to the roadway

superelevation

– Side friction developed between the vehicle’s tires and the pavement

surface

– Or a combination of the two

Centrifugal Force

• Imaginary force that drivers believe is pushing

them outward while maneuvering a curve

• In fact, the force they feel is the vehicle being

accelerated inward towards the center of the

curve

Centripetal Acceleration

• Is counter-balanced by two factors:

– Superelevation

– Side Friction Factor

• Research has been conducted (dated) that has established

limiting values for superelevation rate (e max) and side

friction demand (f max)

• Applying the limiting values results in the minimum curve

radius for various design speeds

Superelevation

• Limits of the rate superelevation are related to

– Climate

• Ice and snow can slow vehicles. Should not create a situation

where these vehicles slide into the center of the curve when

traveling slowly or standing still.

– Constructability (cost)

– Adjacent land use

– Frequency of slow moving vehicles

Superelevation

• Too much super– When traveling slowly, must steer up the slope or against

the horizontal curve to maintain proper path– Undesirable to have such situations when slow traveling

traffic can occur often (urban areas with congestion)– Considerations for SUV traffic, high center of gravity, can

cause roll-overs on such designs

Superelevation

cpfp FFW

cossincossin22

vvs gR

WV

gR

WVWfW

α

α

Fcp

Fcn

Wp

Wn F f

F f

α

Fc

W 1 fte

≈Rv

Superelevation

cossincossin22

vvs gR

WV

gR

WVWfW

tan1tan2

sv

s fgR

Vf

efgR

Vfe s

vs 1

2

efg

VR

sv

2

Side Friction Factor

• The vehicle’s need for side friction to maintain

path on curve

• Upper limit of side friction is the point at which a

tire would begin to skid, point of impending skid

• We design for safety, so f values substantially

less than this

Side Friction Factor

• How do we choose maximum side friction

factors for use in design?

• We measure the level of centripetal or lateral

acceleration that causes drivers to react

instinctively to choose a lower speed.

• We set this as the maximum side friction factor.

Maximum Rates of Superelevation

• Controlled by four factors:

– Climate conditions (snow/ice regions)

– Terrain conditions (flat, rolling, mountainous)

– Type of area (rural, urban, suburban)

– Frequency of very slow-moving vehicles

• Conclusion: no universal e max can be set

• However, for similar areas, a consistent maximum

superelevation should be selected

Recommended Practice

• 12 percent superelevation should not be

exceeded

• 4 or 6 percent superelevation is applicable for

urban design with little constraints

• Superelevation may be omitted on low-speed

urban streets where severe constraints exist

Minimum Radius

• Controls design speed• Can be determined from the max

superelevation and the max side friction factor• Can be calculated from equation 3.34 or

determined from Table 3.5

Example – Minimum Radius

EX: 70 mph design speed; e = 8%; fs = 0.10,

Determine the minimum radius of curve

(measured to the traveled path).

Example Continued

ftR

R

efg

VR

v

v

s

v

40.1819

)08.010.0(2.32

)467.170(

1002

2