Traffic Analysis & Safety

D. Traffic analysis

Volume, Speed & Delay Studies

Expand short counts to AADT with daily/monthly/axle factors, read the 85th-percentile speed from a spot-speed study, and quantify travel time and delay from runs.

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E. Traffic safety analysis

Crash Rates & Collision Analysis

Normalize crashes by exposure (MEV at intersections, HMVM on segments), weight by severity with EPDO, and screen high-crash locations against a critical rate.

Safety questions almost never ask 'how many crashes?' — they ask 'how many crashes ·per unit of exposure·?', because a busy interchange with twenty crashes a year can be far safer than a sleepy rural curve with three. Converting a raw count into a rate, weighting that rate by how badly people were hurt, and then comparing the site against its peers is the core skill the PE tests in the safety area. The NCEES PE Civil Reference Handbook (§5.1.4 Accident Analysis) names accident rates and collision diagrams but supplies almost no method, so the working procedure here is drawn from the AASHTO Highway Safety Manual (HSM-1) — cite the HSM, not a handbook page, for everything in this concept.

Two exposure denominators: MEV and HMVM

Exposure is measured differently for a point and for a length. An intersection is a ·spot· — exposure is the number of vehicles that arrive, so the denominator is million entering vehicles (

\text{MEV}

), built from the total approach volume. A segment is a ·length· — exposure is vehicle travel, so the denominator is hundred million vehicle-miles (

\text{HMVM}

), built from

\text{AADT}\times L

. Picking the wrong denominator (rating an intersection per HMVM, or a segment per MEV) is the single most common setup error on these problems, so first decide: point or length?

R_{\text{MEV}} = \dfrac{C \times 10^{6}}{365\,T\,V}, \qquad R_{\text{HMVM}} = \dfrac{C \times 10^{8}}{365\,T\,(\text{AADT})\,L}

Building the intersection rate

For an intersection,

V

is the total entering volume in vehicles per day summed over all approaches,

T

is the study period in years, and

C

is the crash count over that same period. Total exposure in

\text{MEV}

is

365\,T\,V/10^{6}

, and the rate is simply

C

divided by that exposure. Keep the

10^{6}

honest: a rate 'per million entering vehicles' means you divide the count by exposure expressed ·in millions·, so a typical urban signal lands around

0.3

to

1

crash per

\text{MEV}

. If your answer is in the hundreds, you forgot the

10^{6}

.

Building the segment rate

For a roadway segment the exposure is vehicle-miles of travel:

\text{VMT} = 365\,T\,(\text{AADT})\,L

with

L

in miles. The HSM and most state DOTs report segment rates per ·hundred· million vehicle-miles, hence the

10^{8}

in the numerator. A useful sanity anchor: a two-lane rural road runs on the order of

50

to a few hundred crashes per

\text{HMVM}

, while a modern freeway is far lower per mile of travel because the exposure denominator is enormous.

Severity weighting with EPDO

Two sites with identical crash rates are not equally dangerous if one has fatalities and the other only fender-benders. The equivalent-property-damage-only (

\text{EPDO}

) index collapses severity onto a single scale by weighting each crash by an agency-specific factor — typically derived from comprehensive crash costs — relative to a property-damage-only (

\text{PDO}

) crash of weight

1

. Fatal/serious-injury weights are large (often hundreds when based on cost), so a single severe crash can dominate the index. Always use the agency's published weights; the numbers below are illustrative only.

\text{EPDO} = w_F\,N_F + w_I\,N_I + w_{P}\,N_{P}

The collision diagram

Before any screening, the collision diagram turns a crash list into a picture: each collision is drawn at its location and approach with a standardized arrow symbol (rear-end, right-angle, sideswipe, head-on, pedestrian, fixed-object), annotated with date, time, severity, and condition (wet, dark). Patterns the table hides jump out — a cluster of wet-night run-off-road crashes points to friction or drainage; a stack of left-turn right-angle crashes points to sight distance or signal phasing. The diagram is qualitative but it drives the countermeasure, so the PE may ask you to read one and name the likely contributing factor.

High-crash-location screening with a critical rate

A site is flagged for investigation when its observed rate exceeds a ·critical rate· built from the average rate of similar facilities plus a statistical allowance for random variation. The critical-rate method adds a confidence term (with

K=1.645

for the

95\%

level) that shrinks as exposure

M

grows, so low-volume sites need a much higher rate before they are flagged — this protects against over-reacting to a couple of crashes at a quiet location. If

R_{\text{site}} > R_c

, the site is a candidate for a road-safety audit.

R_c = R_a + K\sqrt{\dfrac{R_a}{M}} + \dfrac{1}{2M}

Exam strategy

Decide point-vs-length first, then write the matching rate formula with its power of ten (

10^{6}

for

\text{MEV}

,

10^{8}

for

\text{HMVM}

) before plugging numbers. Watch the period

T

: multiply

365\,T

in the denominator, and use the ·same·

T

-year count

C

in the numerator. For EPDO, read the weights from the problem and do not assume

\text{PDO}=1

implies the others are small. For screening, compute exposure

M

in

\text{MEV}

once and reuse it in both the rate and the critical-rate confidence term — a mismatch there is the classic trap.

Key equations

Intersection crash rate (per MEV)

R_{\text{MEV}} = \dfrac{C \times 10^{6}}{365\,T\,V}

$C$ = crashes in study period, $T$ = years, $V$ = total entering AADT (vpd). Result in crashes per million entering vehicles.

Segment crash rate (per HMVM)

R_{\text{HMVM}} = \dfrac{C \times 10^{8}}{365\,T\,(\text{AADT})\,L}

$L$ = segment length (mi). Result in crashes per hundred million vehicle-miles of travel.

Exposure — intersection (MEV)

M = \dfrac{365\,T\,V}{10^{6}}

Million entering vehicles over the period; reused in the critical-rate term.

Exposure — segment (VMT)

\text{VMT} = 365\,T\,(\text{AADT})\,L

Vehicle-miles of travel over the period; divide by $10^{8}$ for HMVM.

Equivalent property-damage-only index

\text{EPDO} = w_F N_F + w_I N_I + w_P N_P

$N$ = counts by severity (fatal/injury/PDO), $w$ = agency severity weights relative to PDO $=1$ .

Critical crash rate

R_c = R_a + K\sqrt{\dfrac{R_a}{M}} + \dfrac{1}{2M}

$R_a$ = average rate of similar sites, $M$ = site exposure (MEV or HMVM), $K=1.645$ at 95%. Flag if $R_{\text{site}}>R_c$ .

Crash frequency

f = \dfrac{C}{T}

Crashes per year — raw, un-normalized; use only to compare identical-exposure sites.

Severity index

SI = \dfrac{\text{EPDO}}{C}

Average equivalent-PDO weight per crash; higher means more severe crash mix.

Worked examples

Intersection rate per million entering vehicles

Problem. A signalized intersection carries a total entering volume of $25{,}000\ \text{vpd}$ . Over a $3$ -year study it experienced $18$ reported crashes. Compute the crash rate per MEV.

Solution. Exposure:

M = \dfrac{365(3)(25{,}000)}{10^{6}} = \dfrac{27{,}375{,}000}{10^{6}} = 27.375\ \text{MEV}

. Rate:

R_{\text{MEV}} = \dfrac{18}{27.375} = 0.6575\ \text{crashes/MEV}

. **Answer:

0.658

crashes per MEV.** Sanity check: a value under

1

is typical for an urban signal; if the

10^{6}

had been dropped the answer would be a meaningless

6.6\times10^{-7}

, confirming the units are handled correctly.

R_{\text{MEV}} = \dfrac{18 \times 10^{6}}{365(3)(25{,}000)} = 0.658

Segment rate per HMVM with EPDO

Problem. A $2.4\text{-mi}$ rural two-lane segment ( $\text{AADT}=14{,}500\ \text{vpd}$ ) had $32$ crashes over $5$ years: $1$ fatal, $6$ injury, $25$ PDO. Using agency weights $w_F=12$ , $w_I=3$ , $w_P=1$ , find the crash rate per HMVM and the EPDO index.

Solution. Exposure:

\text{VMT}=365(5)(14{,}500)(2.4)=6.351\times10^{7}\ \text{veh-mi}

. Rate:

R_{\text{HMVM}} = \dfrac{32\times10^{8}}{6.351\times10^{7}} = 50.4\ \text{crashes/HMVM}

. EPDO:

12(1)+3(6)+1(25) = 12+18+25 = 55

. **Answer:

50.4

crashes/HMVM; EPDO

=55

.** Sanity check: rate is in the expected tens-to-hundreds band for a rural two-lane; severity index

SI = 55/32 = 1.72

, reasonably above

1

given the fatal and injury crashes.

R_{\text{HMVM}} = \dfrac{32 \times 10^{8}}{365(5)(14{,}500)(2.4)} = 50.4

Critical-rate screening

Problem. Similar signals in the region average $R_a = 0.45$ crashes/MEV. For the intersection of Example 1 ( $M = 27.375\ \text{MEV}$ , observed rate $0.658$ ), apply the critical-rate method at the $95\%$ confidence level ( $K=1.645$ ). Is it a high-crash location?

Solution. Confidence term:

K\sqrt{R_a/M} = 1.645\sqrt{0.45/27.375} = 1.645(0.1282) = 0.2109

. Probability term:

\dfrac{1}{2M} = \dfrac{1}{54.75} = 0.0183

.

R_c = 0.45 + 0.2109 + 0.0183 = 0.679\ \text{crashes/MEV}

. Compare:

R_{\text{site}} = 0.658 < R_c = 0.679

. **Answer: NOT flagged** — the observed rate is below the critical rate, so the excess over the average is within expected random variation. Sanity check: the confidence allowance (

0.21

) is large relative to the excess over average (

0.658-0.45=0.21

), which is exactly why a borderline site like this does not screen positive.

R_c = 0.45 + 1.645\sqrt{\tfrac{0.45}{27.375}} + \tfrac{1}{2(27.375)} = 0.679

Common pitfalls

•Citing the NCEES handbook for the crash-rate or critical-rate ·method· — it lists accident analysis (§5.1.4) but does not give these formulas. The governing source is the AASHTO HSM; cite it.
•Mismatching the denominator: intersections are rated per MEV (entering vehicles), segments per HMVM (vehicle-miles). Using AADT×L for an intersection, or entering volume for a segment, is the most common setup error.
•Dropping the power of ten: $10^{6}$ for MEV and $10^{8}$ for HMVM. The number is meaningless without it; if your rate is microscopic or in the millions, the exponent is wrong.
•Forgetting $365\,T$ in the denominator — using a one-year exposure with a multi-year crash count (or vice versa) is a factor-of- $T$ blunder. Count and exposure must span the same period.
•Assuming EPDO weights are small. Cost-based fatal/serious-injury weights are often in the hundreds; a single severe crash can dominate the index, so always read the agency's published weights.
•Computing the critical rate with a different exposure than the site rate. Compute $M$ once and reuse it in both $R_{\text{site}}=C/M$ and the $K\sqrt{R_a/M}$ and $1/(2M)$ terms.
•Confusing crash frequency (crashes per year) with crash rate (per unit exposure). Frequency only compares sites with identical exposure; ranking by frequency alone over-flags high-volume locations.

References

AASHTO Highway Safety Manual, 1st Edition (HSM-1) — Part B, network screening and crash-rate/critical-rate methods
NCEES PE Civil Reference Handbook — §5.1.4 Accident Analysis (names accident rates and collision diagrams)
FHWA, Highway Safety Improvement Program (HSIP) Manual — site screening and EPDO weighting

F. Nonmotorized facilities analysis

Nonmotorized (Pedestrian & Bicycle) Facilities

Quantify walkway flow and pedestrian space for LOS, size pedestrian clearance times, and select bicycle facilities and assess shared-use-path level of service.

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G. Traffic forecasts and monitoring

Traffic Forecasting & Growth

Project volumes to a design year with linear and compound growth, accumulate traffic with a growth factor, and convert AADT to the design-hour volume via K and D.

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H. Highway safety analysis

HSM Predictive Method & Crash Modification Factors

Predict crashes from a safety performance function, adjust for site features with crash modification factors and a calibration factor, then refine with the empirical-Bayes method.

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D. Traffic analysis

Volume, Speed & Delay Studies

Trip Generation & Modal Split

E. Traffic safety analysis

Crash Rates & Collision Analysis

Two exposure denominators: MEV and HMVM

Building the intersection rate

Building the segment rate

Severity weighting with EPDO

The collision diagram

High-crash-location screening with a critical rate

Exam strategy

Key equations

Worked examples

Common pitfalls

References

F. Nonmotorized facilities analysis

Nonmotorized (Pedestrian & Bicycle) Facilities

G. Traffic forecasts and monitoring

Traffic Forecasting & Growth

H. Highway safety analysis

HSM Predictive Method & Crash Modification Factors

D. Traffic analysis

Volume, Speed & Delay Studies

Trip Generation & Modal Split

E. Traffic safety analysis

Crash Rates & Collision Analysis

Two exposure denominators: MEV and HMVM

Building the intersection rate

Building the segment rate

Severity weighting with EPDO

The collision diagram

High-crash-location screening with a critical rate

Exam strategy

Key equations

Worked examples

Common pitfalls

References

F. Nonmotorized facilities analysis

Nonmotorized (Pedestrian & Bicycle) Facilities

G. Traffic forecasts and monitoring

Traffic Forecasting & Growth

H. Highway safety analysis

HSM Predictive Method & Crash Modification Factors