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FHWA Home / Safety / HSIP / Railroad-Highway Grade Crossing Handbook

Railroad-Highway Grade Crossing Handbook - Appendix F: New Hampshire Hazard Index, NCHRP Report 50 Accident Prediction Formula, Peabody-Dimmick Accident Prediction Formula

Railroad-Highway Grade Crossing Handbook - Revised Second Edition August 2007
Appendix F: New Hampshire Hazard Index, NCHRP Report 50 Accident Prediction Formula, Peabody-Dimmick Accident Prediction Formula Table of Contents | Previous | Next

APPENDIX

F

New Hampshire Hazard Index,

NCHRP Report 50 Accident Prediction Formula, Peabody-Dimmick Accident Prediction Formula

The New Hampshire Index is as follows:

HI = (V) (T) (Pf)                                                         (1)

where:

HI = hazard index

V = annual average daily traffic

T = average daily train traffic

Pf = protection factor

= 0.1 for automatic gates

= 0.6 for flashing lights

= 1.0 for signs only

Several modifications of the New Hampshire Index are in use. Some states use various other values for Pf as follows:

•    0.13 or 0.10 for automatic gates.

•    0.33, 0.20, or 0.60 for flashing lights.

•    0.67 for wigwags .

•    0.50 for traffic signal preemption.

•    1.00 for crossbucks.

One state adds 1 to average daily train traffic (T). Several states use a hazard index that basically incorporates the New Hampshire Index but also includes other factors:

•    Train speed.

•    Highway speed.

•    Sight distance.

•    Crossing angle.

•    Crossing width.

•    Type of tracks.

•    Surface type.

•    Population.

•    Number of buses.

•    Number of school buses.

•    Number of tracks.

•    Surface condition.

•    Nearby intersection.

•    Functional class of highway.

•    Vertical alignment.

•    Horizontal alignment.

•    Number of hazardous material trucks.

•    Number of passengers.

•    Number of accidents.

Some of these hazard indices are shown in the following table:

Series of equations related to hazard indices

A5

=

Number of accidents in five years

SBP

=

Number of school bus passengers

P

=

Factor for population

Aa

=

Number of accidents per year

P

=

Protection factor

Af

=

Accident factor

SD

=

Factor for sight distance

AL

=

Factor for highway alignment

T

=

Average number of trains per day

AN

=

Factor for approach angle

RF

=

Factor for rideability

FC

=

Factor for functional class

Tf

=

Number of fast trains

G

=

Factor for approach grades

T

=

Number of slow trains

HI

=

Hazard Index

T

=

Train factor

HM

=

Factor for hazardous materials vehicles

TN

=

Factor for number of night trains

TR

=

Factor for number and type of tracks

HS

=

Factor for highway speed

TS

=

Factor for train speeds

L

=

Factor for number of lanes

TT

=

Factor for type of train movements

LI

=

Factor for local interference

TTR

=

Factor for type of tracks

LP

=

Factor for local priority

V

=

Annual average daily traffic

S

=

Factor for surface type

V

=

Factor for annual average daily traffic

SB

=

Number of school buses

VSD

=

Factor for vertical sight distance

NTR

=

Factor for number of tracks

W

=

Factor for crossing width

Source: Railroad-Highway Grade Crossing Handbook, Second Edition. Washington, DC: U.S. Department of Transportation, Federal Highway Administration, 1986.

National Cooperative Highway Research Program Report 50 Accident Prediction Formula

The hazard index presented in National Cooperative Highway Research Program (NCHRP) Report 50 can be expressed as a complex formula or reduced to a more simple equation of coefficients that are taken from a few tables and graphs. The simple formula for calculating the expected number of accidents per year is:

Expected Accident Frequency = A x B x Current Trains per Day

EXAMPLE ASSUME

Vehicles Per Day (10 yr. ADT) A Factor

250-------------------.000347

500-------------------.000694

1000-------------------.001377

2000-------------------.002627

3000-------------------.003981

4000-------------------.005208

5000-------------------.006516

6000-------------------.007720

7000-------------------.009005

8000-------------------.010278

9000-------------------.011435

10000-------------------.012674

12000-------------------.015012

14000-------------------.017315

16000-------------------.019549

18000-------------------.021736

20000-------------------.023877

25000-------------------.029051

30000-------------------.034757

Urban area

Crossbucks

5000 vehicles per day

5 trains per day

EXPECTED ACCIDENT FREQUENCY

EAF = .006516 x 3.06 x 5

EAF = 0.10

EAF = 1 accident every ten years

Accident frequency is greater than 0.02. This would indicate need for higher type device

Try flashing lights B = .23

EAF = .006516 x .23 x 5 EAF = 0.01

THEREFORE FLASHING LIGHTS ARE WARRANTED

‘B' FACTOR COMPONENTS (‘B' FACTOR BASIC VALUE ADJUSTMENTS) BASIC VALUES FOR EXISTING DEVICES

A Crossbucks, highway volume less than 500 per day 3.89

B Crossbucks, urban 3.06

C Crossbucks, rural 3.08

D Stop signs, highways volume less than 500 per day 4.51

E Stop signs 1.15

F Wigwags 0.61

G Flashing lights, urban 0.23

H Flashing lights, rural 0.93

I Gates, urban 0.08

J Gates, rural 0.19

Source: Railroad-Highway Grade Crossing Handbook, Second Edition. Washington, DC: U.S. Department of Transportation, Federal Highway Administration, 1986.

NCHRP 50 also provides formulae for estimating the number of non-train-involved accidents per year as follows:

Automatic gates:

Equation (2)

All other traffic control devices:

Equation (3)

100 where:

X = probability of coincidental vehicle and train arrival scaled by 10-3 ADT = average daily traffic EA = expected number of accidents per year

Modifications of the hazard index exist. State's formula is:

Equation 4

The Site Evaluation factor is based on the following:

•    Most restrictive sight distance of all quadrants.

•    Distance from crossing to business or crossroad.

•    Crossing angle.

•    Distraction from traffic control devices.

•    People factor.

Each factor is rated from 1 (best) through 5 (worst), and the average of the 5 factors is used in the formula.

Peabody-Dimmick Accident Prediction Formula

The Peabody-Dimmick Formula, published in 1941, was based on five years of accident data from 3,563 rural crossings in 29 states. It is sometimes referred to as the Bureau of Public Roads formula. The formula used to determine the expected number of accidents in five years is:

Equation 5

where:

A5 = expected number of accidents in five years V = annual average daily traffic T = average daily train traffic P = protection coefficient K = additional parameter

Several states, such as Florida, have developed their own formulae.

A5 can be determined from a set of curves as shown below:

Line graph plotting Highway Traffic in Vehicles per Day by Accident Factor. The line rises from about 2.5 at 0 Vehicles per day to just over 5 at 14,000 Vehicles per day.

Source: Railroad-Highway Grade Crossing Handbook, Second Edition. Washington, DC: U.S. Department of Transportation, Federal Highway Administration, 1986.

Figure 13a. Relation Between Highway Traffic and Accident Factor, Va

Figure 13a. Relation Between Highway Traffic and Accident Factor, V. This horizontal bar chart has the following statistics: Signs -- 1.65 (Accident Factor), Bells -- 1.78, Wigwag -- 1.99, Wigwag and Bells -- 2.03, Flashing  Lights -- 2.15, Flashing Lights and Bells -- 2.25, Wigwag and Flashing Lights -- 2.27, Wigwag, Flashing Lights and Bells -- 2.35, Watchman, 6 Hours -- 2.27, Watchman 16 Hours -- 2.43, Watchman 24 Hours -- 2.52, Gates 24 Hours -- 2.56, Gates Automatic -- 2.70.

Figure 13b. Relation Between Railroad Traffic and Accident Factor, T

Figure 13b. Relation Between Railroad Traffic and Accident Factor, T. This line graph shows Accident Factor compared to Railroad Traffic -- Trains per Day. This line begins at just higher than 1.0 rises then flattens out until it reaches just higher than 2.0.

Figure 13c. Relation Between Warning Device and Accident Factor, Pc

Figure 13c. Relation Between Warning Device and Accident Factor, Pc. This line graph shows the relationship between Factor K and Unbalanced Accident Factor. The line begins at about -0.5, and first moves down toward zero, then gently rises up to 6.5 at the highest.

The basic form of the equation for use with these curves is:

Basic form of the equation for use with these curves

EXAMPLE: Assume a crossing has an AADT of 3,442 vehicles, an average train traffic of 22 trains per day, and is equipped with wigwags. From Figure 13a, the factor due to highway traffic of 3,442 vehicles per day is found to be 3,99. From Figure 13b, the factor due to train traffic of 22 trains per day is found to be 1.59, and from Figure 13c, the factor for wigwags is found to be 1,99. Substituting these factors into the equation, it is found that the hazard index is equal to:

Substituting these factors into the equation, it is found that the hazard index is equatl to this equation

From Figure 13d, K is determined to be + 2.58 for a value of lu of 4.08 and, with this value for the parameter, the expected number of accidents in 5 years is 6.66.

Florida Department of Transportation Accident Prediction Model

The Florida State University developed an accident prediction model for the Florida Department of Transportation. The model was developed using stepwise regression analysis, transformation of data, dummy variables, and transformation of the accident prediction model to its original scale. The resulting model is:

Equation (6)

where:

A = vehicles per day or annual average daily

traffic L = number of lanes

ln = logarithm to the base e

MASD = actual minimum stopping sight distance along highway

MCSD = clear sight distance (ability to see approaching train along the highway, recorded for the four quadrants established by the intersection of the railroad tracks and road) RSSD = required stopping sight distance on wet pavement

St = maximum speed of train

T = yearly average of the number of trains per day

ta = ln of predicted number of accidents in four-year period at crossings with active traffic control devices

tp= ln of predicted number of accidents in four-year period at crossing with passive traffic control devices

VV = posted vehicle speed limit unless geometrics dictate a lower speed

y = predicted number of accidents per year at crossing

* This variable is omitted if crossing is flagged or the circulation is less than zero.

** This variable is omitted if sight restriction is due to parallel road. *** This variable is omitted when gates are present.

The predicted number of accidents per year, y, is adjusted for accident history as follows:

Equation (7)

where:

Y = accident prediction adjusted for accident history

y = accident prediction based on the regression model

H = number of accidents for six-year history or since year of last improvement

P = number of years of the accident history period

A simple method of rating each crossing from zero to 90 was derived based mathematically on the accident prediction. This method, entitled Safety (Hazard) Index, is used to rank each crossing. A Safety Index of 70 is considered safe (no further improvement necessary). A Safety Index of 60, or one accident every nine years, would be considered marginal. The Safety Index is calculated as follows:

Equation (8)

where:

R = safety index

Y = adjusted accident prediction value

X = 90 when less than 10 school buses per day traverse the crossing = 85 when 10 or more school buses per day and active traffic control devices exist without gates = 80 when 10 or more school buses per day and passive traffic control devices exist


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Page last modified on October 15, 2014.
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