Traffic And Highway Engineering
Traffic And Highway Engineering
5th Edition
ISBN: 9781133605157
Author: Garber, Nicholas J., Hoel, Lester A.
Publisher: Cengage Learning,
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Chapter 6, Problem 1P
To determine

(a)

Time mean speed.

Expert Solution
Check Mark

Answer to Problem 1P

The time mean speed is ut¯ = 47.19mileshour.

Explanation of Solution

Given:

Observers stationed at two sections XX and YY, 500 ft apart on a highway, recording the time of vehicles on their arrival as shown in the accompanying tableTraffic And Highway Engineering, Chapter 6, Problem 1P , additional homework tip  1

The total time of observation at XX was 15 sec.

In order to calculate time mean speed, we need to figure out traveling time of each vehicle which is the difference of time taken by a vehicle in travelling from XX to YY section between the two sections.

Calculation:

VehiclesSection XXSection YYTravelling time of vehicle,
  ti
A  T0  T0+7.85sec  (7.850)=7.85
  Sec
B  T0+3sec  T0+9.18sec  (9.183.00)=6.18
  Sec
C  T0+6sec  T0+12.36sec  (12.366.0)=6.36
  Sec
D  T0+12sec  T0+21.74sec  (21.7412.0)=9.74
  Sec

We have the following formula for the time mean speed:

  ut¯ = 1ni = 1nui

Where, ui is the speed of the ith vehicle.

n is the number of the vehicles passing.

Now, the speed of the individual vehicles is as follows:

Speed of vehicle A:

  u1=uA=LtAu1=uA=500ft7.58secu1=uA=65.963ftsec.

Speed of vehicle B:

  u2=uB=LtBu2=uB=500ft6.18secu2=uB=80.91ftsec.

Speed of vehicle C:

  u3=uC=LtCu3=uC=500ft7.58secu3=uC=78.62ftsec.

Speed of vehicle D:

  u4=uD=LtDu4=uD=500ft9.74secu4=uD=51.335ftsec.

Now, the time mean speed can be calculated by substituting the values in the following formula:

  ut¯ = 1ni = 1nuiut¯ = 14[u1+u2+u3+u4]ut¯ = 14[65.963ftsec+80.91ftsec+78.62ftsec+51.335ftsec]ut¯ = 14[276.828ftsec]ut¯ = 69.207ftsecut¯ = 69.207ftsec×0.000189394miles60×60hour×secft1ft = 0.000189394milesut¯ = 69.207×0.000189394×3600mileshourut¯ = 69.207×0.681818mileshourut¯ = 47.19mileshour.

Conclusion:

Therefore, the time mean speed is ut¯ = 47.19mileshour.

To determine

(b)

Space mean speed.

Expert Solution
Check Mark

Answer to Problem 1P

The time mean speed is ut¯ = 45.668mileshour.

Explanation of Solution

Given:

Observers stationed at two sections XX and YY, 500 ft apart on a highway, recording the time of vehicles on their arrivalas shown in the accompanying table.

Traffic And Highway Engineering, Chapter 6, Problem 1P , additional homework tip  2

The total time of observation at XX was 15 sec.

Calculation:

We have the following formula for finding out the space mean speed.

  uS¯ = L×ni = 1nti

Where, ti is the time that ithvehicle takes to travel from XX to YY at the speed of ui.

Substitute the values, we have:

  uS¯ = L×n i = 1 n t i .uS¯ = 500 ft×4 i = 1 4 t i .uS¯ = 500 ft×4[7.58sec+6.18sec+ 6.36sec+9.74sec].uS¯ = 500 ft×4[29.86sec].uS¯ = 66.98 ftsec.uS¯ = 66.98 ftsec×0.000189394miles60×60hour×secft.[1ft = 0.000189394miles]uS¯= 66.98×0.000189394×3600mileshour.uS¯ =  66.98×0.681818mileshour.ut¯ = 45.668mileshour.

Conclusion:

Therefore, the time mean speed is ut¯ = 45.668mileshour.

To determine

(c)

Flow at section XX.

Expert Solution
Check Mark

Answer to Problem 1P

The flow at section XX is as follows 960Vehicleshour.

Explanation of Solution

Given:

Observers stationed at two sections XX and YY, 500 ft apart on a highway, recording the time of vehicles on their arrival as shown in the accompanying table.

Traffic And Highway Engineering, Chapter 6, Problem 1P , additional homework tip  3

The total time of observation at XX was 15 sec.

Calculation:

We have the following formula for finding out the flow at XX section.

  qxxnTxx

Where, Txx is the total time of observation at XXsection.

Substitute the values, we have:

  qxx4Vehicles15sec×3600sechourqxx4Vehicles×360015hourqxx14400Vehicles15hourqxx960Vehicleshour

Conclusion:

Therefore, the flow at section XX is as follows 960Vehicleshour.

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ISBN:9781305156241
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