HCM UNSIGNALIZED SAMPLE PROBLEM

Highway Capacity Manual 2000

PART D. EXAMPLE PROBLEMS Problem No. 1 2 3 4 5 6

Description TWSC Unsignalized Intersection TWSC Unsignalized Intersection TWSC Unsignalized Intersection AWSC Unsignalized Intersection AWSC Unsignalized Intersection Roundabout

Application Operational LOS Operational LOS Operational LOS Operational LOS Operational LOS Capacity and v/c ratio

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Chapter 17 - Unsignalized Intersections Example Problems

Highway Capacity Manual 2000

EXAMPLE PROBLEM 1 The Intersection The Question

A TWSC T-intersection with an exclusive westbound left-turn lane. What are the delay and level of service?

The Facts √ Two-lane major street, √ Two-lane minor street, √ Level grade, √ Stop-controlled on minor street approach,

√ 10 percent HV, √ No special intersection geometry, and √ No pedestrians.

Outline to Solution The steps below show the northbound approach calculations only. Calculations for other approaches are shown on the worksheets. Steps 1. Data input.

Worksheets 1 and 2

2.

Site characteristics.

Worksheet 3 - lane designation, grade, rightturn channelization, and arrival type

3.

t c and t f (use Equations 17-1 and 17-2 and Exhibit 17-5 ).

t c,x = tc,base + tc,HV P HV + tc,G G – tc, T – t 3,LT t f,x = tf,base + tf,HV PHV t c,4 = 4.1 + 1.0(0.10) + 0 – 0 – 0 = 4.200 s t f,x = 2.2 + 0.9(0.10) = 2.290 s

4.

Skip Worksheets 5a through 5e.

5.

v2 Movement capacity c m,x accounting for impedance (use Equation 17-4 ). v c,9 = N + 0.5v3 + v14 + v15

No upstream signals within 0.4 km

v c,9 = 250 + 20 + 0 + 0 = 270 veh/h c p,x = v c,x

e

1− e

c p,9 = 270 * c m,9 = cp,9

− v c,x tc,x / 3,600 − v c,x t f,x / 3,600

e −270*6.300/ 3,600

= 750 veh/h 1− e −270*3.390/ 3,600 * P p,9 = 750 (1) = 750 veh/h

P0,i = 1−

vi c m,i

P0,9 = 1−

120 = 0. 840 750

6.

Skip Worksheets 7a and 7b.

No two-stage gap acceptance

7.

Shared-lane capacity (use Equation 17-15).

Worksheet 8 - Movements 7 and 9 share the same lane ∑ vy y

c SH =

∑ y

vy c m,y

c SH(NB) = 8.

Chapter 17 - Unsignalized Intersections Example Problems

Skip Worksheet 9.

40 + 120 = 523 veh/h 40 120 + 274 750

No flared minor-street approach

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Highway Capacity Manual 2000

9.

Control delay and LOS (use Equation 17-38 and Exhibit 17-2).

Worksheet 10 d=

3,600 + 900T[... ] + 5 c m,x

dNB =

3,600 + 900( 0. 25 )[... ] + 5 = 14. 9 s , 523

LOS B 10. Skip Worksheet 11.

No Rank 1 vehicle delay

Example Problem 1 TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET

Worksheet 1 General Information

Site Information

KMN ______________________ CEI ______________________ 5/17/99 ______________________ AM Peak ______________________

Analyst Agency or Company Date Performed Analysis Time Period

Intersection Jurisdiction Analysis Year

Jones/Market ________________________ Latah County ________________________ 1999 ________________________

Geometrics and Movements grade = ______

Street

Jones

v12 v11 v10

STOP

0% grade = ______ v6 v5 v4

v16 v13

S2

Show North

v1 v2 v3

v14

v15

300 150 S5

250 40

v7 v8 v9

40 120

0% grade = ______

STOP

Market Street

0% grade = ______

0.25 h Length of study period = _____

Worksheet 2 Vehicle Volumes and Adjustments Vehicle Volumes and Adjustments Movement

1

2

3

4

5

6

7

8

9

Volume (veh/h)

250

40

150

300

40

120

Peak-hour factor, PHF

1.00

1.00

1.00

1.00

1.00

1.00

Hourly flow rate (veh/h)

250

40

150

300

40

120

Proportion of heavy vehicles, PHV

0.10

0.10

0.10

0.10

0.10

0.10

10

11

12

Pedestrian Volumes and Adjustments Movement Flow, Vx (ped/h)

13

14

15

16

0

0

0

0

Lane width, w (m) Walking speed,1 Sp (m/s) Percent blockage, fp (Equation 17-11) 1. Default walking speed = 1.2 m/s

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Chapter 17 - Unsignalized Intersections Example Problems

Highway Capacity Manual 2000 Example Problem 1 TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET Worksheet 3 General Information

Example Problem 1 Project Description _________________________________________________________________________________ Lane Designation Movements

Lane 1

1, 2, 3

2, 3

4, 5, 6

4

7, 8, 9

7, 9

Lane 2

Lane 3

Grade, G

5

Right Turn Channelized?

0

N

0

N

0

N

10, 11, 12 Flared Minor-Street Approach Movement 9

" Yes

X No "

Storage space, n

________________ (number of vehicles)

Movement 12

" Yes

X No "

Storage space, n

________________ (number of vehicles)

Median Storage* * Includes raised or striped median (RM), or two-way left-turn lane (TWLTL)

Type Movements 7 and 8

" Yes

_____

" X No

Storage space, m

________________ (number of vehicles)

Movements 10 and 11

" Yes

_____

" X No

Storage space, m

________________ (number of vehicles)

Upstream Signals Movements

S2

Distance to Signal, D (m)

Prog Speed, Sprog (km/h)

Cycle Length, C (s)

Green Time, geff (s)

protected LT

Arrival Type

Saturation Flow Progressed Flow, Rate, s (veh/h) Vprog (veh/h)

3

TH S5

protected LT

3

TH Computing Delay to Major-Street Vehicles Data for Computing Effect of Delay to Major-Street Vehicles Shared-lane volume, major-street through vehicles, vi1, blocked by LT Shared-lane volume, major-street right-turn vehicles, vi2, blocked by LT Saturation flow rate, major-street through vehicles, si1 Saturation flow rate, major-street right-turn vehicles, si2 Number of major-street through lanes Length of study period, T (h)

Chapter 17 - Unsignalized Intersections Example Problems

17-52

S2 Approach

S5 Approach

Highway Capacity Manual 2000 Example Problem 1 TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET

Worksheet 4 General Information

Example Problem 1 Project Description _________________________________________________________________________________ Critical Gap and Follow-Up Time tc = tc,base + tc,HV PHV + tc,G G - tc,T - t3,LT Major LT Movement

1

tc,base (Exhibit 17-5) tc,HV PHV (from Worksheet 2) tc,G

-

G (from Worksheet 3) t3,LT

Minor RT 4

9

4.1 1.0 0.10

6.2 1.0 0.10

0 0.0

0.1 0 0.0

Minor TH 12

8

Minor LT 11

7

10

7.1 1.0 0.10 0.1

0.2

0.2

0.2 0 0.7

0.2

tc,T

single stage two stage

0.0

0.0

0.0

tc (Equation 17-1)

single stage two stage

4.200

6.300

6.500

tf = tf,base + tf,HV PHV Major LT Movement tf,base (Exhibit 17-5) tf,HV

1

PHV (from Worksheet 2) tf (Equation 17-2)

Minor RT 4

9

2.2 0.9 0.10 2.290

3.3 0.9 0.10 3.390

Minor TH 12

8

Minor LT 11

7

10

3.5 0.9 0.10 3.590

Worksheet 5a Time to Clear Standing Queue (Computation 1) Movement 2 vT,prog

Movement 5 vL,prot

vT,prog

vL,prot

Effective green, geff (s) Cycle length, C (s) Saturation flow rate, s (veh/h) Arrival type vprog (veh/h) Rp (from Chapter 16) Proportion of vehicles arriving on green, P (Equation 17-17) gq1 (Equation 17-18)

3

3

1.00

1.00

gq2 (Equation 17-19) gq (Equation 17-20)

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Chapter 17 - Unsignalized Intersections Example Problems

Highway Capacity Manual 2000 Example Problem 1 TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET Worksheet 6 General Information Project Description _________________________________________________________________________________ Example Problem 1 Impedance and Capacity Calculation Step 1: RT from Minor Street

v9

Conflicting flows (Exhibit 17-4) Potential capacity (Equation 17-3 or 17-29) Ped impedance factor (Equation 17-12) Movement capacity (Equation 17-4) Prob of queue-free state (Equation 17-5)

v12

vc,9 = 270 cp,9 = 750

vc,12 =

pp,9 = 1.000 cm,9 = cp,9 pp,9 = 750 p0,9 = 0.840

pp,12 =

Step 2: LT from Major Street

cp,12 = cm,12 = cp,12 pp,12 = p0,12 = 1.000 v1

v4

Conflicting flows (Exhibit 17-4)

vc,4 = 290

vc,1 =

Potential capacity (Equation 17-3 or 17-29)

cp,4 = 1227

cp,1 =

Ped impedance factor (Equation 17-12)

pp,4 = 1.000

pp,1 =

Movement capacity (Equation (17-4)

cm,4 = cp,4 pp,4 = 1227

cm,1 = cp,1 pp,1 =

Prob of queue-free state (Equation 17-5)

p0,4 = 0.878

p0,1 = 1.000

Major left shared lane prob of queue-free state (Equation 17-16)

* = p0,4

* = p0,1

Step 3: TH from Minor Street (4-leg intersections only) Conflicting flows (Exhibit 17-4)

v8

v11

vc,8 =

vc,11 =

Potential capacity (Equation 17-3 or 17-29)

cp,8 =

cp,11 =

Ped impedance factor (Equation 17-12)

pp,8 =

pp,11 =

Capacity adjustment factor due to impeding movement (shared lane use p*) (Equation 17-13)

f8 = p0,4 p0,1 pp,8 =

f11 = p0,4 p0,1 pp,11 =

Movement capacity (Equation 17-7)

cm,8 = cp,8 f8 =

cm,11 = cp,11 f11 =

Prob of queue-free state

p0,8 =

Step 4: LT from Minor Street (4-leg intersections only) Conflicting flows (Exhibit 17-4)

p0,11 = v10

v7 vc,7 =

vc,10 =

Potential capacity (Equation 17-3 or 17-29)

cp,7 =

cp,10 =

Ped impedance factor (Equation 17-12)

pp,7 =

pp,10 =

Major left, minor through impedance factor

p''7 = p0,11 f11 =

'' = p f = p10 0,8 8

Major left, minor through adjusted impedance factor (Equation 17-8)

p'7 =

' = p10

Capacity adjustment factor due to impeding movements (Equation 17-14)

f7 = p7' p0,12 pp,7 =

' p p f10 = p10 0,9 p,10 =

Movement capacity (Equation 17-10)

cm,7 = f7 cp,7 =

cm,10 = f10 cp,10 =

Step 5: LT from Minor Street (T-intersections only) Conflicting flows (Exhibit 17-4)

vc,7 = 870 cp,7 = 312

Potential capacity (Equation 17-3 or 17-29) Ped impedance factor (Equation 17-12) Capacity adjustment factor due to impeding movement (shared lane use p*) (Equation 17-13) Movement capacity (Equation 17-7) Notes 1. For 4-leg intersections use Steps 1, 2, 3, and 4. 2. For T-intersections use Steps 1, 2, and 5.

Chapter 17 - Unsignalized Intersections Example Problems

17-54

v10

v7 vc,10 = cp,10 =

pp,7 = 1.000 f7 = p0,4 p0,1 pp,7 = 0.878

pp,10 =

cm,7 = cp,7 f7 = 274

cm,10 = cp,10 f10 =

f10 = p0,4 p0,1 pp,10 =

Highway Capacity Manual 2000 Example Problem 1 TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET Worksheet 8 General Information

Example Problem 1 Project Description _________________________________________________________________________________ Shared-Lane Capacity

cSH =

∑vy y

( )

∑ vy y cm,y

(Equation 17-15)

Movement

v (veh/h)

cm (veh/h)

7

40

274

cSH (veh/h)

8

523

9

120

750

10 11 12

Worksheet 9 Effect of Flared Minor-Street Approaches Movement 7

Movement 8

Movement 9

Movement 10

Movement 11

Movement 12

csep (from Worksheet 6 or 7) Volume (from Worksheet 2) Delay (Equation 17-38) Qsep (Equation 17-34) Qsep + 1 Round (Qsep + 1) nmax (Equation 17-35) cSH csep n cact (Equation 17-36)

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Chapter 17 - Unsignalized Intersections Example Problems

Highway Capacity Manual 2000 Example Problem 1 TWSC - UNSIGNALIZED INTERSECTIONS WORKSHEET

Worksheet 10 General Information

Example Problem 1 Project Description _________________________________________________________________________________ Control Delay, Queue Length, Level of Service Lane

v (veh/h)

1 X7

X8 X9

2 7

8

9

3 7

8

9

cm (veh/h)

160

523

v/c

Queue Length Control Delay LOS (Equation 17-37) (Equation 17-38) (Exhibit 17-2)

0.306