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CE 4640: Transportation Design. Prof. Tapan Datta, Ph.D., P.E. Fall 2002. Speed Measures. Time Mean Speed Space Mean Speed 85 th Percentile Speed. Sample Calculation of TMS and SMS. A. B. d = 2 miles. Run #1: t 1 = 2 min, d/t 1 = 60 miles/hour

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Ce 4640 transportation design l.jpg
CE 4640: Transportation Design

Prof. Tapan Datta, Ph.D., P.E.

Fall 2002


Speed measures l.jpg
Speed Measures

  • Time Mean Speed

  • Space Mean Speed

  • 85th Percentile Speed


Sample calculation of tms and sms l.jpg
Sample Calculation of TMS and SMS

A

B

d = 2 miles

Run #1: t1 = 2 min, d/t1 = 60 miles/hour

Run #2: t2 = 2.5 min, d/t2 = 48 miles/hour

Run #3: t3 = 3 min, d/t3 = 40 miles/hour

(d/ti) = 60+48+40 = 148 miles/hour

TMS = (d/ti)/n = 148/3 = 49.33 miles/hour


Calculation of tms and sms l.jpg
Calculation of TMS and SMS

(ti) = t1+t2+t3 = 2+2.5+3 = 7.5 min

(ti/n) = 7.5/3 = 2.5 min

SMS =

= 48 miles/hour

2 miles x 60 min/hour

2.5 min


Spot speed studies l.jpg
Spot Speed Studies

  • Where to take the studies:

  • Trend locations

  • Problem locations for specific purposes

  • Representative locations for basic data surveys

  • Locations where before-and-after studies are being conducted

  • The specific location for the speed study should be selected to reduce the influence of the observer and the measuring equipment as much as possible


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Factors Affecting Spot Speeds

  • Driver

  • Vehicle

  • Roadway

  • Traffic

  • Environment


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Time and Length of Study

  • Peak Hour

    • Morning Peak

    • Afternoon Peak

  • Off Peak Hour


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Speed Study: Ways to Measure Speed

Two ways:

  • Using a stop watch and measuring the time it takes to travel over a specified distance

time2

time1

Speed = d/(time1 -time2)


Speed study ways to measure speed9 l.jpg
Speed Study: Ways to Measure Speed

  • Using a Radar Gun


Radar gun l.jpg
Radar Gun

Operates on Doppler Principle that the speed of a moving target is proportional to the change in frequency between the radio beam transmitted to the target and the reflected radio beam.


Time mean speed tms l.jpg
Time Mean Speed (TMS)

Average speed of all vehicles passing a point on a highway over a specified time period

TMS = (ft/sec or miles/hour)

where d = distance traversed (ft or mile)

ti = travel time of ith vehicle

(sec or hour)

n = number of travel times observed

(d/ti)

n


Space mean speed sms l.jpg
Space Mean Speed (SMS)

Speed corresponding to the average travel time over a given distance

SMS = (ft/sec or miles/hour)

where d = distance traversed (ft or mile)

ti = travel time of ith vehicle (sec or hour)

n = number of travel times observed

d

(ti)/n


Relationship between tms and sms l.jpg
Relationship between TMS and SMS

Assume:

There are “n” number of streams with flow rates q1,…..,qn

and velocities u1, ……,un

Then, the total flow =

Average time interval between vehicles = 1/qi

Distance traveled in time (1/qi) = ui/qi = 1/ki

Density, K = ki

n

qi

i=1

n

i=1


Relationship between tms and sms14 l.jpg

Note:  =

n

i=1

Relationship between TMS and SMS

u = q/k, ku = q

Time Mean Speed (TMS),

Ut =  =  =

Space Mean Speed (SMS),

Us =  =  = Q/K,Q = K Us

Ut = = = where fi = ki/K

qiui

qiui

qi

kiui

ki

Q

qi

kiui

ki

ki

Kfiui2

qiui

kiui2

Q

Q

Q


Relationship between tms and sms15 l.jpg
Relationship between TMS and SMS

SinceQ = K Us

Ut =

Kfiui2

KUs

fiui2

=fi[Us+(ui-Us)]2

=

Us

Us

fi[Us2+(ui-Us)2+2Us(ui-Us)]

=

Us

[fiUs2+fi (ui-Us)2+2fiUs(ui-Us)]

=

Us


Relationship between tms and sms16 l.jpg
Relationship between TMS and SMS

Since, fi (ui-Us)  0,

Ut = +

where =

Therefore, Ut = Us +

s2

Us2

Us

Us

[ki(ui-Us)2]

f(u - X)2

s2

s =

n - 1

K

s2

Us


Speed data measured using radar gun l.jpg
Speed Data Measured Using Radar Gun


Percentile speed calculations l.jpg

n

x = 

Percentile Speed Calculations

 =

 =


Statistical calculations l.jpg
Statistical Calculations

f(u - X)2

s =

Standard Deviation,

= 22442/299 = 8.66 mph

n - 1

s2 = 8.662 = 75.06 mph

Variance,


Statistical calculations20 l.jpg
Statistical Calculations

Median = L + (n/2 – fL)C/fm

where

L = Lower bound of the group in which

the median lies

n = Number of observations

fL = Cumulative number of observations upto the lower

bound of the group where the median lies

fm = Number of observations in the group in which

the median lies

C = Speed interval


Statistical calculations21 l.jpg
Statistical Calculations

  • For the example, the median lies between 36-40 mph.

  • Median = 36 + (300/2 – 103) 5 / 63 = 39.73 mph

    Mode is the area which occurs most frequently.

    In the example, mode is 42.5 mph in 41-45 mph range.

    Pace is the max. number of vehicles within a 10mph speed range.


85 th percentile speed l.jpg
85th Percentile Speed

The speed below which 85% of all traffic units travel, and above which 15% travel.

Speed limits are determined based on 85th percentile speeds.


Graph showing percentile speeds l.jpg
Graph Showing Percentile Speeds

% Cum. Frequency

47.5 mph

Speed


Design vehicles l.jpg
Design Vehicles

  • Standard dimensions of design vehicles given in AASHTO Green Book

  • Minimum turning radius

    • For passenger cars (designated as P): 24 ft

    • For large semi-trailer or full-trailer combination (designated as WB-50 & WB-60): 45 ft

  • Acceleration and Deceleration of vehicles vary depending on their size

    • For cars 6 – 9 ft/sec2

    • For trucks 3 – 5 ft/sec2



The hill area study grosse pointe farms l.jpg
The Hill Area Study,Grosse Pointe Farms


Example grosse pointe farms alley entrance l.jpg
Example: Grosse Pointe Farms Alley Entrance

Turning Template for a Semi-Trailer Truck (AASHTO WB-12 design vehicle) at the Alley Entrance


Example grosse pointe farms alley entrance28 l.jpg
Example: Grosse Pointe Farms Alley Entrance

Turning Template for a Semi-Trailer Truck (AASHTO WB-15 design vehicle) at the Alley Entrance


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Turning Radius Templates

(Source: A Policy on Geometric Design of Highways and Streets 1994, American Association of American State Highway Transportation Officials)


Example grosse pointe farms alley exit l.jpg
Example: Grosse Pointe Farms Alley Exit

Turning Template for a Semi-Trailer Truck (AASHTO WB-12 design vehicle) at the Alley Exit


Example grosse pointe farms alley exit31 l.jpg
Example: Grosse Pointe Farms Alley Exit

Turning Template for a Semi-Trailer Truck (AASHTO WB-15 design vehicle) at the Alley Exit


Intersection design l.jpg
Intersection Design

Should do the following:

  • Reduce number ofconflict points

  • Control relative speeds of intersecting roads

  • Coordinate design with traffic control

  • Consider alternative geometry

  • Separate conflict points

    • Spatially

    • Temporally

  • Reduce area of conflict