Question 2: Trip Distribution (15 points)

Three zones A, B and C are connected by unidirectional road links as shown below. The travel time (minutes) between the zones are indicated in the figure. Assume that all intra-zonal travel times are equal to 5minutes.

The trip production and attraction are given in the table below.

Further, the friction factor from zone to is defined as a function of travel time as given in the figure below.

a. (10 points) Determine the trip distribution using a gravity model before applying row and column factoring. Include intrazonal trips (provide 2dp)

b. (5 points) Determine the trip distribution matrix after one iteration of column and row factoring (i.e., do one iteration of column factoring and one iteration of row factoring. (provide 2dp)

 (You need not enter the answers in the box provided below)

Question 1: Traffic Flow Theory (20 points)

A survey team collected traffic data between two points of a highway, XX and YY, 450m apart. Observations at XX show that five vehicles passed that location at intervals of 3, 4, 3, and 5 sec, respectively. The speeds of the vehicles at point XX were 84, 72, 63, 56.2, and 52 km/h respectively. Assume that the vehicles maintain these speeds whilst approaching YY.

Please provide the following information (Provide 2dp);

a. (5 points) Fill in the distance values in the schematic below showing the locations of the five vehicles 20 sec after the first vehicle passed location XX. (Note: the distances are not drawn to scale

b. (4 points) Calculate the time mean speed.

c. (4 points) Calculate the space mean speed.

d. (4 points) Calculate the density between XX and YY on the highway using the fundamental traffic equation.

 e. (3 points) Determine the space (time) mean speed using the empirical relationship: v_t=0.966v_s+3.541. Compare your answer with that obtained in part (c) and quantify the differences. Is it significant?

(You need not enter the answers in the box provided below)

Question 2: Trip Distribution (15 points)

Three zones A, B and C are connected by unidirectional road links as shown below. The travel time (minutes) between the zones are indicated in the figure. Assume that all intra-zonal travel times are equal to 5minutes.

The trip production and attraction are given in the table below.

Further, the friction factor from zone to is defined as a function of travel time as given in the figure below.

a. (10 points) Determine the trip distribution using a gravity model before applying row and column factoring. Include intrazonal trips (provide 2dp)

b. (5 points) Determine the trip distribution matrix after one iteration of column and row factoring (i.e., do one iteration of column factoring and one iteration of row factoring. (provide 2dp)

 (You need not enter the answers in the box provided below)

Question 1: Traffic Flow Theory (20 points)

A survey team collected traffic data between two points of a highway, XX and YY, 450m apart. Observations at XX show that five vehicles passed that location at intervals of 3, 4, 3, and 5 sec, respectively. The speeds of the vehicles at point XX were 79, 69, 65, 59, and 47 km/h respectively. Assume that the vehicles maintain these speeds whilst approaching YY.

Please provide the following information (Provide 2dp);

a. (5 points) Fill in the distance values in the schematic below showing the locations of the five vehicles 20 sec after the first vehicle passed location XX. (Note: the distances are not drawn to scale

b. (4 points) Calculate the time mean speed.

c. (4 points) Calculate the space mean speed.

d. (4 points) Calculate the density between XX and YY on the highway using the fundamental traffic equation.

 e. (3 points) Determine the space (time) mean speed using the empirical relationship: v_t=0.966v_s+3.541. Compare your answer with that obtained in part (c) and quantify the differences. Is it significant?

(You need not enter the answers in the box provided below)

Question 2: Trip Distribution (15 points)

Three zones A, B and C are connected by unidirectional road links as shown below. The travel time (minutes) between the zones are indicated in the figure. Assume that all intra-zonal travel times are equal to 5minutes.

The trip production and attraction are given in the table below.

Further, the friction factor from zone to is defined as a function of travel time as given in the figure below.

a. (10 points) Determine the trip distribution using a gravity model before applying row and column factoring. Include intrazonal trips (provide 2dp)

b. (5 points) Determine the trip distribution matrix after one iteration of column and row factoring (i.e., do one iteration of column factoring and one iteration of row factoring. (provide 2dp)

 (You need not enter the answers in the box provided below)

Which of the following situation(s) depict the case of a collision?

Question 5: Vertical Alignment (25 Points)

a. (18 points) A section of a proposed undivided 1-lane bidirectional road has a +4% grade and ends at point A with station 0+122.00. It must be connected to another section of the road, which has a 0% grade, at point B with station 1+322.00. It is determined that the crest and sag curves required to connect the two sections should be connected (i.e the EVC of the crest and the BVC of the sag) with a constant-grade section at -3% grade. Design a vertical alignment to connect between these two points using a 60-km/h design speed.

b. (5 points) Sketch the alignment of the entire road section showing the following elements: the grades; BVC, EVC and lengths of crest and sag curves; elevations of BVC and EVC of both curves and constant-grade section; stations of BVC of crest and EVC of sag. Assume elevation of BVC for crest as 0m

c. (2 points) It is given that the elevations at points A and B are 163m and 150m respectively. Comment on the accuracy of the design proposed in step (a). How the design can be improved?

 (You need not provide answers in the box provided below)

Question 4: Horizontal Alignment (25 Points)

a. (15 points) A horizontal curve has been designed with the following properties:

• Operating speed of 80km/hr
• TC Station: 5+478.400
• PI Station: 5+723.900
• Superelevation of 5% and a normal cross-fall of 3%. 

1. (4 points) Calculate the minimum radius required for the curve. Is a transition curve required for this radius? Give reason.
2. (6 points) Assume that the designer decides to do away with the transition curve. What should be the minimum radius in this case? What is the station value of CT for this radius?
3. (5 points) Sketch the elements of the horizontal curve clearly indicating stations at TC, PI and CT points. Also mark the radius value chosen in step (ii), the central angle (Δ) and the length of the circular curve.

b. (10 points) A spiral curve (transition curve) has been designed for a one-lane two-way highway (each lane is 3.6m wide) with a design speed of 90km/hr. The spiral curve transitions the geometry from a normal crown with a 3% slope to a superelevated slope of 5%. The spiral curve, containing the superelevation runoff, is 110 metres long.

1. Draw cross-sections of only

   the carriageway of the highway at the following locations. Ensure you clearly present the slopes of the cross-section (for both lanes of the highway) and the elevation of the outside edge and inside edge of the carriageway relative to the centreline.

   • TS

   • 40m into the spiral curve from TS

   • 80m into the spiral curve from TS

   • SC

2. Calculate the station for the point 80m into the spiral curve from TS. Assume the radius of circular curve as 360m and the station for TS as 3+500.0

(You need not enter answers in the box given below)

Question 3: Traffic Assignment (15 points)

There are three paths between an origin and destination, each composed of a single link. The link performance functions are given by:

            t_A=10.0+0.4V_A 

            t_B=5.0+0.2V_B

            t_C=4.0+0.4V_C

Where is the travel time given in minutes, and is the flow given in thousands of vehicles per hour on a link . There are 4000 vehicles per hour traveling between the origin and destination. Assuming user equilibrium, determine the flow on each path and the travel time (Provide 2dp).

(You need not enter answers in the box provided below)

Question 2: Trip Distribution (15 points)

Three zones A, B and C are connected by unidirectional road links as shown below. The travel time (minutes) between the zones are indicated in the figure. Assume that all intra-zonal travel times are equal to 5minutes.

The trip production and attraction are given in the table below.

Further, the friction factor from zone to is defined as a function of travel time as given in the figure below.

a. (10 points) Determine the trip distribution using a gravity model before applying row and column factoring. Include intrazonal trips (provide 2dp)

b. (5 points) Determine the trip distribution matrix after one iteration of column and row factoring (i.e., do one iteration of column factoring and one iteration of row factoring. (provide 2dp)

 (You need not enter the answers in the box provided below)