Speed studiesSpeed studiesincludes data analysis,

spot speed, average speed, & measuring sight distancemeasuring sight distance

February 2009February 2009

1

Speed, Travel Time, and Delay Studies

• Spot Speed: speed of vehicles measured at a particular point along the road

• Average travel speed: speed including all delays and travel time

2

Average SpeedTotal time to traverse link = 140 secTotal time to traverse link 140 sec

Distance = 2192 feet

Average speed = _2192 feet = 15.6 ft/sec (23.0 mph)

30.0

140 sec

20.0

25.0

c)

10 0

15.0

Spee

d (ft

/sec

5.0

10.0

2192 feet

3

0.00 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140

Seconds

2192 feet

Travel Time and DelayTravel Time and Delay

• Studies to estimate the average runningStudies to estimate the average running times (and delays) of vehicle through a road sectionroad section

• Determine operating efficiency of a route• Identify problem delay locationsIdentify problem delay locations• Evaluate user benefits of road improvements• Collect link-node times for network planning

models

4

Travel-Time Study Uses and C ll tiCollection

Uses:Uses:identify problem locations

• Specifically looks at delay• Specifically looks at delay• Measure arterial LOS• Input to traffic assignment modelsInput to traffic assignment models• Economic analysis of reduced travel time• Measure of congestionMeasure of congestion• Before and after studies to assess

improvements

5• Input to air quality models

Study ProcedureStudy Procedure

• Test Vehicle:Test Vehicle:• Floating Car• Average CarAverage Car• Moving Car

• No Test Vehicles:• License plate studies• Interviews

6

• Floating Car: measure the time toFloating Car: measure the time to traverse a test section while overtaking and being overtaken by an equal numberand being overtaken by an equal number of vehicles– Pass as many cars as pass the test carPass as many cars as pass the test car– record travel time and distance to calculate average

speedl d t d d l t l– can also record stopped delay separately

7

• Average Car: measure the time toAverage Car: measure the time to traverse a test section traveling at the average speed of the traffic stream (highlyaverage speed of the traffic stream (highly subjective)– Driver mimic average road conditionsg– Easier than floating car but driver interprets average conditions– record travel time and distance to calculate average speed– can also record stopped delay separatelypp y p y

8

• License Plate Method: it provides ce se ate et od p o desinformation about travel time and delay. It also provide information about circulation ppatterns. It relies on vehicle matching from observations at two synchronized ylocations. Often done using video cameras.

9

Spot Speed StudiesSpot Speed Studies

• Speed Limit Effectiveness StudiesSpeed Limit Effectiveness Studies• Establish Trends• Design Impacts (SSD)Design Impacts (SSD)• Traffic Control Placement and timing• Collision Study with Speed Cause• Collision Study with Speed Cause• Investigate speed complaints

10

Collection of spot speedsCollection of spot speeds

• Collect during time period representative of desired goutcome

• Usually cannot collect all vehicles• Random sample

11

Location & TimeLocation & Time

• Depends on purposeDepends on purpose• Time:

D d– Depends on purpose– Free-flow: off-peak– Time period corresponding to complaint

12

Study LayoutStudy Layout

VerticalReference Point

End Timing

VerticalReference Point

Study LengthStudy LengthApproaching Vehicle

ObserverX

Start Timing

13

Recommended Study LengthsRecommended Study Lengths

Traffic Stream Average Recommended StudyTraffic Stream Average Speed

Recommended Study Length (feet)

Below 25 mph 88

25-40 mph 176

Above 40 mph 264

14

Vehicle Speed CalculationVehicle Speed Calculation

DV= spot speed (mph) t

DV471

V spot speed (mph) t47.1D= length (ft)

t = elapsed time (sec.)

1 47= constant that converts feet per second to15

1.47= constant that converts feet per second to miles per hour

Data AnalysisData Analysis

• Transportation studies often require analysis ofTransportation studies often require analysis of data

• Large datasetsg• Only collecting a sample of a larger population• Use of statistics to ensure:Use of statistics to ensure:

– Results are accurate and meaningful– Correct sample sizep– Accurate use of statistical tests– Confidence in interpretation of results

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Random Variables

• Sampling populationSampling population• Too large to measure all

S l ll b t t• Sample smaller number to represent• Population should be sampled randomly to

prevent bias– Biased sampling: sampling all red sports cars

in a spot speed study– Random sampling: sampling every 5th vehicle

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Other StatisticsOther Statistics

• Generally assume spot speeds areGenerally assume spot speeds are normally distributed

• Assume sufficient samples are collected• Assume sufficient samples are collected• Should be able to calculate mean,

t d d d i ti t b dstandard deviation, etc. based on assumption of normality

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Population Vs SamplePopulation Vs. Sample63 mph

57 mph

55 mph43 mph

62 mph 51 mph 59 mph

43 mph

57 mph

50 mph

22 mph 55 mph47 h

63 mph53 mph

62 mph51mph

56 mph47 mph

47 mph55 mph 42 mph

36 mph42 mph

51 mph39 mph 41 mph

49 mph

65 mph70 mph

53 mph

1961 mph Population

Sample

Collection of spot speedsp p

• Systematic Errors and Solutions– Error – looking for “fastest” vehicleg

• Solution – Sample every nth vehicle– Error – too many heavy vehicle measurements

• Solution – same as above – sample every nth vehicle

E I l i f hi l f ll i l t– Error – Inclusion of vehicle following platoon leader• Solution Don’t include vehicles following too

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• Solution – Don t include vehicles following too closely (200’ if < 40 mph, and 350’ otherwise)

Frequency Distribution Table for Actual Data Versus Expected Normal Distribution

35%

Data Versus Expected Normal Distribution

25%

30% NormalData

15%

20%

eque

ncy

10%

15%Fre

0%

5%

27 5 32 5 37 5 42 5 47 5 52 5 57 5 62 5 67 5

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27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5

Speed (mph)

Normal DistributionNormal Distribution

Bell shaped

Symmetric about µ (mean)

X ~ N(µ σ2)

Image source: http://library.thinkquest.org/10030/7ndndpnd.htm

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X ~ N(µ,σ2)

Completely described by mean and variance

DispersionDispersion

• Same meanSame mean– Speeds 15 mph and 75 mph

(15 + 75)/2 = 45 mph(15 75)/2 45 mph

– Speeds 44 and 46 mph(44 + 46)/2 = 45 mph( ) p

• But very different ranges of values• Variance and standard deviation• Variance and standard deviation

– Magnitude of variation around mean

23

STDSTD

Standard deviation is square root of variance

24Equation from Roess et al

Standard deviationStandard deviation

s2 = 599.7 = 85.7s 599.7 85.7(7-1)

s = 85.70.5 = 9.25 mph

25Mean is 24.6 mph with std of 9.25 mph

Confidence Intervals (normal dist)Confidence Intervals (normal dist)• How confident are we in our estimate of a statistic? (i.e. mean)• Resampling a population would give us a slightly different mean• Standard error of the mean (E)

µ = X ± E with 68 3% confidenceµ = X ± E, with 68.3% confidence

µ = X ± 1.96E, with 95% confidence

µ = X ± 3.0E, with 99.7% confidence

26Equation from Roess et al

Confidence Intervals (normal dist)

Example: Mean = 45.5 mph, standard deviation = 4.5, what is the 95% confidence interval, N = 67

E = _σ_ =___4.5___ = 0.55N0 5 (67)0 5N0.5 (67)0.5

•

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Sample SizeSample Size

• Selection of sample size depends on desired confidence leveldesired confidence level

N = minimum sample size at selected confidence levelconfidence level

Z = number of standard deviation for confidence level (1.64 for 90%, see tableconfidence level (1.64 for 90%, see table 4.1 page 88 of text)

σ = standard deviation (mph)

28d = limit of acceptable error in average speed estimate

Example: Sample SizeExample: Sample Size

• An engineer wishes to determine whether vehicles are traveling at the posted speed limit for a school zone

• Desired standard deviation is ± 7 mph• Desired standard deviation is ± 7 mph• Limit of acceptable error = ± 1.5 mph• Desired confidence level is 90%• How many samples need to be collected?

N (Z )2 (1 64*7)2 58 57 hi l 58 hi lN = (Zσ)2 = (1.64*7)2 = 58.57 vehicles = 58 vehicles( d )2 ( 1.5 )

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Example: Sample SizeExample: Sample Size

• What if a confidence level of 99% is desired?

N = (Zσ)2 = (2.58*7)2 = 144.96 = 145 vehicles( d )2 ( 1.5 )

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Spot Speed Study MetricsSpot Speed Study Metrics

• Mean: averageMean: average• Mode: value that appears the most

P 10 il i t i hi h th• Pace: 10 mile increment in which the highest percentage of drivers is observed– 45 to 55 mph

• 85th Percentile speed• 15th percentile speed

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Mean (Average Speed)Mean (Average Speed)

• Larger sample size = greater probabilityLarger sample size = greater probability that calculated mean is not significantly different from true meandifferent from true mean

32

MeanMean

• Speeds = 22, 15, 11, 25, 31, 41, 27 (mph)

Mean = 22 + 15 + 11 + 25 + 31 + 41 + 2777

= 24.6 mph

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Other MetricsOther Metrics

• Range: highest and lowest valueRange: highest and lowest value observed

Minimum: 5 mph– Minimum: 5 mph– Maximum: 65 mph

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Spot Speed Study of 100 Vehiclesp p y

Raw Data for 16 vehicles Data for 185 Vehicles by 5

35

mph range

Modal: Value that occurs the most frequently in a sample of spot speeds

Mode is 53 mph

36

Pace: range in which most vehicles are found (i.e. 10 mph hour range)

47

92

104

37

DistributionDistribution

10 vehicles from data collection

38

10 vehicles from data collection were traveling from 25 to < 30 mph

F ti i 25 t < 30 bi # f hi l iFraction in 25 to < 30 bin = # of vehicles in bin/total # of vehicles (80) = __10__ = 0.13 (13%)

80

39

80

This should = 1.0 (100%)

40

0.30

0.20

0.25

0.15

0.10

0.05

0.0022.5 27.5 32.5 37.5 42.5 47.5 52.5

Shows fraction of vehicles in each speed bin –

41

pfrequency distribution

About 12% in speed bin 27.5

Group 15 to < 35 has 0 +0.06 + 0.13 + 0.19 = 0.38 or

42

p38% of vehicles are found in those 4 bins or 38% of vehicles were traveling between 15 and < 35 mph

ith percentile spot speedi percentile spot speed

• Spot speed below which i% of vehicles areSpot speed below which i% of vehicles are traveling

• 50th percentile: 50% of vehicles are50 percentile: 50% of vehicles are traveling at or below that speed (this is also the median speed)p )

• 85th Percentile: 85% of vehicles traveling at or below that speed; 15% traveling over p gthat speed

43

frequencyCumulative Frequency Distribution

0.9

1

0.6

0.7

0.8

100% of vehicles are below 55 mph

0.4

0.5

0 1

0.2

0.3

0

0.1

15 to < 20 20 to < 25 25 to < 30 30 to < 35 35 to < 40 40 to < 45 45 to < 50 50 to < 55

44

frequency

0.9

1

0.6

0.7

0.8

0.4

0.5

0 1

0.2

0.3

0

0.1

15 to < 20 20 to < 25 25 to < 30 30 to < 35 35 to < 40 40 to < 45 45 to < 50 50 to < 55

What is the 85th percentile speed?

45

p p

Would have been easier if we had used smaller speed bins