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TransportationTransportation PE ReviewPE Review

Horizontal and Vertical Curves

Azimuths and Bearings

But first, a little plane surveying…..

See Page 78-12

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Computation of Bearings

See Page 78-12

Latitudes and Departures

See Page 78-12

N = y = Latitude = L cos B

E = x = Departure = L sin B

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Deflection Angles

See Page 78-13Take the difference between the two bearings to compute the deflection angle.

Horizontal Curve ElementsSee Page 79-2

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Horizontal Curve EquationsSee Page 79-2

Stationing on a Horizontal Curve

See Page 79-2STA PT = STA PC + L 79.11

STA PC = STA PI – T 79.12

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Time to work a problem

Are you ready?

Symmetrical Parabolic Vertical Curves

See Page 79-11

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Equations for Vertical Curves

See Page 79-11

Vertical Curves with Obstructions

See Page 79-12

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Vertical Curve through a turning point

See Page 79-13

Let’s work one more!Yeah!

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Superelevation See Page 79-8

Definitions:

Tangent runout (TR) aka tangent runoff and crown runoff Point out glitch in text!

Superelevation runoff (L)

Superelevation runoff rate aka transition rate

Equations:Required e:

Side friction factor:

See Page 79-7

Superelevation

Equations:Tangent runout and SE runoff distances:

See Page 79-8

For circular curves, the SE runoff should be developed 60 to 90% on the tangent and 40 to 10% on the curve. Most state agencies use a rule of 2/3 on the tangent and 1/3 on the curve.

Read the problem statement carefully to determine how to determine the superelevation!

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Stopping Sight Distance ValuesSee Page 79-10

Horizontal Sight Distance

See Page 79-10

These equations assume that S <= L and level terrain!

Decision sight distance should be added when appropriate.

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Required lengths of Vertical CurvesSee Page 79-13

K-Values What?See Page 79-13

K = L/A

Where A = G2 – G1 G2 – G1 is always positive!

K-values are used to simplify the selection of a stopping sight distance for a crest or sag vertical curve.

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Design Controls: Crest Vertical CurvesSee Page 79-15

Design Controls: Sag Vertical CurvesSee Page 79-16

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SE Design Chart for 8%

SE Design Chart for 10%

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Desirable Length of Spiral Curve Transitions

Minimum Safe Stopping Sight Distances

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Highway Capacity and LOSSee Page 74

Nomenclature:ADT (Average Daily Traffic) vpd

D (Density) pcpmpl

DDHV (Directional Design Hourly Volume) vph (highest demand direction)

DHV (Design Hourly Volume) vph (both directions)

E (Passenger Car Equivalent for Heavy Vehicles)

f (Adjustment factors) [for lane widths, lateral clearances, etc.]

FFS (Free Flow Speed) mph

BFFS (Base Free Flow Speed) mph

K (ratio of DHV to ADT)

PHF (Peak Hour Factor)

V (Volume) pcphpl v (rate of flow during peak 15-min. period)

S (Speed) mph

Highway Capacity and LOS

See Page 74-5

Symbols:T (Trucks and Buses) for basic freeway segments

R (Recreational vehicles)

Equations:PHF = (Actual Hourly Volume)/(Peak rate of flow)

Peak rate of flow = 4(peak 15-minute flow rate)

Heavy Vehicle Factor:

Peak 15-minute passenger-car equivalent flow rate:

See Page 74-8

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Highway Capacity and LOS

See Page 74-8Equations:

v/c ratio (volume capacity ratio) = v/c

FFS (Free Flow Speed):

Adjustment factors (f) are determined from HCM.

Density:See Page 74-7

Adjustment factors to BFFS

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Additional Adjustment factors

Speed-Flow Relationships

See Page 74-8

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LOS Criteria

See Page 74-7