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6. AMFs for Highway Segments

The procedures for determining the values of the AMFs for highway segments (AMF₁ through AMF₉) are described in this section. The geometric and traffic control data needed to evaluate these AMFs are described in Highway Segment Geometric and Traffic Control Data. The AMFs for highway segments include all of the variables in the highway segment base model (with the exception of vertical curvature) plus additional variables. Report No. FHWA-RD-99-207, Prediction of the Expected Safety Performance of Rural Two-Lane Highways, provides a more detailed description of the base models for highway segments.

6.1 Lane Width (AMF₁)

The value of the AMF for lane width (AMF_ra) is determined as shown in Table 2., Values of AMF for Lane Width of Highway Segments (AMF_ra). If the lane width is less than or equal to 9 ft, the AMF for 9 ft shown in the table is used. If the lane width is greater than or equal to 12 ft, the AMF for 12 ft is used. If the lane width is equal to 9, 10, 11, or 12 ft, the value of the AMF is shown or is computed with the formulas provided in the table. If the lane width falls between the integer values listed, the value of AMF_ra is determined by interpolation between the values for those integer values of lane width.

Table 2.: Values of AMF for Lane Width of Highway Segments (AMF_ra)
Lane width (ft)	ADT < = 400	ADT = 401 to 1999 ^a	ADT >= 2000
9	1.05	1.50 - 0.000281*(2000 - ADT)	1.50
10	1.02	1.30 - 0.000175*(2000 - ADT)	1.30
11	1.01	1.05 - 0.000025*(2000 - ADT)	1.05
12	1.00	1.00	1.00

^a This column presents mathematical expressions used to evaluate AMF_ra as a function of ADT.

The value of AMF_ra determined from Table 2., Values of AMF for Lane Width of Highway Segments (AMF_ra) is modified as follows to convert it from related accidents to total accidents:

AMF₁ = (AMF_ra - 1.0) P_ra + 1.0 (A-1)

where:

AMF₁ = accident modification factor for total accidents
AMF_ra = accident modification factor for related accidents (i.e., single-vehicle run-of-road and multiple-vehicle
opposite-direction accidents), such as the accident modification factor for lane width shown in Table 2., Values of AMF for Lane Width of Highway Segments (AMF_ra)
P_ra = proportion of total accidents constituted by related accidents

The proportion of related accidents (P_ra) should be set equal to the sum of four values from Table 14., Default Percentage Distributions for Crash Type and Manner of Collision on Rural Two-Lane Highways expressed as a proportion rather than as a percentage. These four values are:

Percentage of single vehicle run-off-road accidents
Percentage of multiple-vehicle head-on collisions
Percentage of multiple-vehicle opposite-direction sideswipe collisions
Percentage of multiple-vehicle same-direction sideswipe collisions

Based on the values in Table 14., Default Percentage Distributions for Crash Type and Manner of Collision on Rural Two-Lane Highways, the value of P_ra is 0.35. If the default values are replaced with data from the accident records of a specific highway agency, those replacement values are used in determining P_ra.

If the lane width differs between the two directions of travel for any highway segment, AMF₁ is computed separately for each direction of travel and the results averaged.

6.2 Shoulder Width and Type (AMF₂)

For each side of the highway shoulder, Effective Width is defined as 8 ft if the width of the shoulder on that side of the highway is greater or equal to 8 ft and is the actual shoulder width if it is less than 8 ft wide.

The AMF for shoulder width (AMF_wra) is determined as shown in Table 3., Values of AMF for Shoulder Width of Highway Segments (AMF_wra)., Values of AMF for Shoulder Width of Highway Segments (AMF_wra). If the shoulder effective width is equal to 0, 2, 4, 6, or 8 ft, the value of AMF_wra is shown or is computed with the formulas provided in the table. If the shoulder effective width falls between these values, the value of AMF_wra is determined by interpolation.

If there is only one type of shoulder on the same side of the highway, the AMF for shoulder type (AMF_tra) for that side of the highway is determined from Table 4., Accident Modification Factors for Shoulder Effective Width (SEW) and Shoulder Type on Two-Lane Highways (AMF_tra), Accident Modification Factors for Shoulder Width (SW) and Shoulder Type on Two-Lane Highways (AMF_tra) using interpolation, as needed, between the shoulder width values shown in the table. If there are more than one type of shoulder on the same side of the highway, only the shoulder types within the effective width of the shoulder would be considered in the calculation of the AMF for shoulder type (AMF_tra) for that side of the highway. In this case, AMF_tra for each type of shoulder within the effective width is determined from Table 4., Accident Modification Factors for Shoulder Effective Width (SEW) and Shoulder Type on Two-Lane Highways (AMF_tra),using the full effective width to determine AMF_tra for each shoulder type. Then, a weighted average of the calculated AMF_tras is taken, with the actual width of each type divided by the effective width as the weight for each type.

The AMF for shoulder width and type combined is determined as follows:

AMF₂ = (AMF_wra AMF_tra - 1.0 ) P_ra + 1.0 (A-2)

where:

AMF_wra = accident modification factor for related accidents based on shoulder width (from Table 3., Values of AMF for Shoulder Width of Highway Segments (AMF_wra), Table 4., Values of AMF for Shoulder Width of Highway Segments (AMF_wra) )
AMF_tra = accident modification factor for related accidents based on shoulder type (from Table 4., Accident Modification Factors for Shoulder Effective Width (SEW) and Shoulder Type on Two-Lane Highways (AMF_tra), Accident Modification Factors for Shoulder Width (SW) and Shoulder Type on Two-Lane Highways (AMF_tra))

Table 3.: Values of AMF for Shoulder Width of Highway Segments (AMF_wra)
Shoulder effective width (ft)	ADT <=400	ADT = 401 to 1999 ^a	ADT >=2000
0	1.10	1.50 - 0.000250*(2000 - ADT)	1.50
2	1.07	1.30 - 0.000144*(2000 - ADT)	1.30
4	1.02	1.15 - 0.0000813*(2000 - ADT)	1.15
6	1.00	1.00	1.00
8	0.98	0.87 + 0.0000688*(2000 - ADT)	0.87

^a This column presents mathematical expressions used to evaluate AMF_wra as a function of ADT.

Table 4.: Accident Modification Factors for Shoulder Effective Width (SEW) and Shoulder Type on Two-Lane Highways (AMF_tra)
Shoulder type	SW=0 ft	SW=1 ft	SW=2 ft	SW=3 ft	SW=4 ft	SW=6 ft	SW=8 ft
Paved	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Gravel	1.00	1.00	1.01	1.01	1.01	1.02	1.02
Turf	1.00	1.01	1.03	1.04	1.05	1.08	1.11

The proportion of related accidents (P_ra) used in Equation (A-2) should be the same as that used in Equation (A-1).

If the shoulder effective width and/or shoulder types differ between the two directions of travel for any highway segment, AMF₂ is computed separately for each direction of travel and the results averaged.

6.3 Horizontal Curve Length, Radius, and Presence or Absence of Spiral Transition (AMF₃)

If a highway segment is located on a tangent highway or on a spiral transition curve (i.e., not on a circular horizontal curve), then the value of AMF₃ is 1.00.

If a highway segment is located on a horizontal curve, then the value of AMF₃ is determined as follows:

AMF₃ = ( 1.55 L_c + 80.2 / R - 0.012 S ) / 1.55 L_c (A-3)

where:

L_c = length of horizontal curve (mi)
R = radius of curvature (ft)
S = 1 if spiral transition curve is present
0 if spiral transition curve is not present
0.5 if spiral transition curve is present on one end of circular curve

Some homogeneous highway segments may be shorter than the horizontal curve being analyzed; L_c represents the total length of the horizontal curve which may be greater than the length of the highway segment. Where spiral transitions are present, L_c represents the length of the circular curve plus the lengths of spiral transitions.

In applying Equation (A-3), if the radius of curvature is less than 100 ft, the radius is set equal to 100 ft. If the length of the horizontal curve is less than 100 ft, the length of the horizontal curve is set equal to 100 ft.

AMFs are computed for each curve in a compound curve set. The length of the horizontal curve (L_c) used in Equation (A-3) is the total length for the compound curve set and the radius of curvature (R) is the radius for the individual curve in the compound curve set that is being analyzed.

If the computed value of AMF₃ for a horizontal curve is less than 1.00, AMF₃ is set equal to 1.00. This AMF applies to total highway segment accidents.

6.4 Superelevation (AMF₄)

The AMF for the superelevation of a horizontal curve is based on the superelevation deficiency defined as the difference between the actual superelevation of the horizontal curve (e_act) and the design superelevation (e_design) specified in the 1994 AASHTO Green Book. Superelevation deficiency (SD) is computed as:

SD = 0.00 if e_act > e_design (A-4)
SD = e_design - e_act if e_act < e_design (A-5)

The value of e_act for each horizontal curve is that input by the user as part of the highway geometric data. In applying Equation (A-6), negative values of e_act are permitted; such negative values are associated with superelevation with the opposite cross slope to that intended, which may well be associated with a superelevation deficiency. The value of e_design is determined from interpolation in Design Superelevation tables (see Table 5 to Table 9). Use of the Design Superelevation tables requires the horizontal curve radius, the horizontal curve design speed, and the value of the maximum superelevation rate (e_max) used by a highway agency. Interpolation of values of e_design between the radii shown in the Design Superelevation tables for a given value of e_max is performed. Interpolation between design speeds will be necessary for design speeds in US customary units between those shown in the table and for design speeds converted from metric units. If e_design exceeds 0.120, e_design is set equal to 0.120.

The value of the AMF for superelevation (AMF₄) is determined as:

AMF₄ = 1.00 for SD < 0.01 (A-6)
AMF₄ = 1.00 + 6 (SD-0.01) for 0.01 < SD < 0.02 (A-7)
AMF₄ = 1.06 + 3 (SD-0.03) for 0.02 < SD (A-8)

6.5 Grades (AMF₅)

The AMF for percent grade (AMF₅) is determined as:

AMF₅ = (1.016) ^|PG| (A-9)

where:

PG = percent grade for the highway segment

If the percent grade exceeds 12 percent, PG is set equal to 12 percent. Grades are determined from Vertical Point of Intersection (VPI) to Vertical Point of Intersection. Vertical curves are not considered.

Table 5.: Design Superelevation (e_design) as a Function of Maximum Superelevation Rate, Curve Radius (e_max=0.04) and Design Speed (V mi/h)
e_max	Radius(ft)	V=30	V=40	V=50	V=60	V=70
0.04	22918	0.000	0.000	0.000	0.000	0.000
0.04	11459	0.000	0.000	0.000	0.000	0.000
0.04	7639	0.000	0.000	0.000	0.000	0.000
0.04	5730	0.000	0.000	0.000	0.025	0.025
0.04	3820	0.000	0.000	0.024	0.029	0.029
0.04	2865	0.000	0.022	0.027	0.033	0.033
0.04	2292	0.000	0.025	0.030	0.036	0.036
0.04	1910	0.020	0.027	0.033	0.039	0.039
0.04	1637	0.022	0.028	0.035	0.040	0.040
0.04	1432	0.024	0.030	0.037	0.040	0.040
0.04	1146	0.026	0.033	0.039	0.040	0.040
0.04	955	0.028	0.036	0.040	0.040	0.040
0.04	819	0.030	0.037	0.040	0.040	0.040
0.04	716	0.031	0.039	0.040	0.040	0.040
0.04	637	0.033	0.040	0.040	0.040	0.040
0.04	573	0.034	0.040	0.040	0.040	0.040
0.04	521	0.035	0.040	0.040	0.040	0.040
0.04	477	0.036	0.040	0.040	0.040	0.040
0.04	441	0.037	0.040	0.040	0.040	0.040
0.04	409	0.038	0.040	0.040	0.040	0.040
0.04	358	0.039	0.040	0.040	0.040	0.040
0.04	318	0.040	0.040	0.040	0.040	0.040
0.04	286	0.040	0.040	0.040	0.040	0.040
0.04	260	0.040	0.040	0.040	0.040	0.040
0.04	239	0.040	0.040	0.040	0.040	0.040
0.04	220	0.040	0.040	0.040	0.040	0.040

Table 6.: Design Superelevation (e_design) as a Function of Maximum Superelevation Rate, Curve Radius (e_max=0.06) and Design Speed (V mi/h)
e_max	Radius(ft)	V=30	V=40	V=50	V=60	V=70
0.06	22918	0.000	0.000	0.000	0.000	0.000
0.06	11459	0.000	0.000	0.000	0.000	0.000
0.06	7639	0.000	0.000	0.000	0.021	0.026
0.06	5730	0.000	0.000	0.020	0.027	0.033
0.06	3820	0.000	0.020	0.025	0.037	0.046
0.06	2865	0.000	0.025	0.030	0.045	0.055
0.06	2292	0.020	0.030	0.034	0.051	0.059
0.06	1910	0.023	0.034	0.038	0.055	0.060
0.06	1637	0.026	0.038	0.041	0.058	0.060
0.06	1432	0.029	0.041	0.046	0.060	0.060
0.06	1146	0.034	0.046	0.050	0.060	0.060
0.06	955	0.038	0.050	0.053	0.060	0.060
0.06	819	0.041	0.053	0.056	0.060	0.060
0.06	716	0.043	0.056	0.058	0.060	0.060
0.06	637	0.046	0.058	0.059	0.060	0.060
0.06	573	0.048	0.059	0.060	0.060	0.060
0.06	521	0.050	0.060	0.060	0.060	0.060
0.06	477	0.052	0.060	0.060	0.060	0.060
0.06	441	0.054	0.060	0.060	0.060	0.060
0.06	409	0.055	0.060	0.060	0.060	0.060
0.06	358	0.058	0.060	0.060	0.060	0.060
0.06	318	0.059	0.060	0.060	0.060	0.060
0.06	286	0.060	0.060	0.060	0.060	0.060
0.06	260	0.060	0.060	0.060	0.060	0.060
0.06	239	0.060	0.060	0.060	0.060	0.060
0.06	220	0.060	0.060	0.060	0.060	0.060

Table 7.: Design Superelevation (e_design) as a Function of Maximum Superelevation Rate, Curve Radius (e_max=0.08) and Design Speed (V mi/h)
e_max	Radius(ft)	V=30	V=40	V=50	V=60	V=70
0.08	22918	0.000	0.000	0.000	0.000	0.000
0.08	11459	0.000	0.000	0.000	0.000	0.000
0.08	7639	0.000	0.000	0.000	0.022	0.028
0.08	5730	0.000	0.000	0.021	0.029	0.036
0.08	3820	0.000	0.021	0.030	0.041	0.051
0.08	2865	0.000	0.027	0.038	0.051	0.065
0.08	2292	0.021	0.033	0.046	0.061	0.075
0.08	1910	0.025	0.038	0.053	0.068	0.080
0.08	1637	0.028	0.043	0.058	0.074	0.080
0.08	1432	0.031	0.047	0.063	0.078	0.080
0.08	1146	0.038	0.055	0.071	0.080	0.080
0.08	955	0.043	0.062	0.077	0.080	0.080
0.08	819	0.048	0.067	0.080	0.080	0.080
0.08	716	0.053	0.071	0.080	0.080	0.080
0.08	637	0.056	0.075	0.080	0.080	0.080
0.08	573	0.060	0.078	0.080	0.080	0.080
0.08	521	0.063	0.079	0.080	0.080	0.080
0.08	477	0.065	0.080	0.080	0.080	0.080
0.08	441	0.068	0.080	0.080	0.080	0.080
0.08	409	0.070	0.080	0.080	0.080	0.080
0.08	358	0.074	0.080	0.080	0.080	0.080
0.08	318	0.077	0.080	0.080	0.080	0.080
0.08	286	0.079	0.080	0.080	0.080	0.080
0.08	260	0.080	0.080	0.080	0.080	0.080
0.08	239	0.080	0.080	0.080	0.080	0.080
0.08	220	0.080	0.080	0.080	0.080	0.080

Table 8.: Design Superelevation (e_design) as a Function of Maximum Superelevation Rate, Curve Radius (e_max=0.10) and Design Speed (V mi/h)
e_max	Radius(ft)	V=30	V=40	V=50	V=60	V=70
0.10	22918	0.000	0.000	0.000	0.000	0.000
0.10	11459	0.000	0.000	0.000	0.000	0.000
0.10	7639	0.000	0.000	0.000	0.023	0.028
0.10	5730	0.000	0.000	0.021	0.030	0.037
0.10	3820	0.000	0.021	0.031	0.043	0.054
0.10	2865	0.000	0.028	0.040	0.055	0.070
0.10	2292	0.021	0.034	0.049	0.067	0.085
0.10	1910	0.025	0.040	0.057	0.077	0.096
0.10	1637	0.029	0.046	0.065	0.086	0.100
0.10	1432	0.033	0.051	0.072	0.093	0.100
0.10	1146	0.040	0.061	0.083	0.098	0.100
0.10	955	0.046	0.070	0.092	0.100	0.100
0.10	819	0.053	0.078	0.098	0.100	0.100
0.10	716	0.058	0.084	0.100	0.100	0.100
0.10	637	0.063	0.089	0.100	0.100	0.100
0.10	573	0.068	0.094	0.100	0.100	0.100
0.10	521	0.072	0.097	0.100	0.100	0.100
0.10	477	0.076	0.099	0.100	0.100	0.100
0.10	441	0.080	0.100	0.100	0.100	0.100
0.10	409	0.083	0.100	0.100	0.100	0.100
0.10	358	0.089	0.100	0.100	0.100	0.100
0.10	318	0.093	0.100	0.100	0.100	0.100
0.10	286	0.097	0.100	0.100	0.100	0.100
0.10	260	0.099	0.100	0.100	0.100	0.100
0.10	239	0.100	0.100	0.100	0.100	0.100

Table 9.: Design Superelevation (e_design) as a Function of Maximum Superelevation Rate, Curve Radius (e_max=0.12) and Design Speed (V mi/h)
e_max	Radius(ft)	V=30	V=40	V=50	V=60	V=70
0.12	22918	0.000	0.000	0.000	0.000	0.000
0.12	11459	0.000	0.000	0.000	0.000	0.000
0.12	7639	0.000	0.000	0.000	0.023	0.029
0.12	5730	0.000	0.000	0.022	0.030	0.038
0.12	3820	0.000	0.022	0.032	0.044	0.056
0.12	2865	0.000	0.029	0.042	0.058	0.073
0.12	2292	0.022	0.035	0.051	0.070	0.090
0.12	1910	0.026	0.042	0.060	0.082	0.106
0.12	1637	0.030	0.048	0.069	0.094	0.118
0.12	1432	0.034	0.054	0.077	0.104	0.120
0.12	1146	0.041	0.065	0.092	0.117	0.120
0.12	955	0.049	0.075	0.104	0.120	0.120
0.12	819	0.055	0.085	0.113	0.120	0.120
0.12	716	0.068	0.094	0.119	0.120	0.120
0.12	637	0.068	0.101	0.120	0.120	0.120
0.12	573	0.074	0.107	0.120	0.120	0.120
0.12	521	0.079	0.112	0.120	0.120	0.120
0.12	477	0.084	0.116	0.120	0.120	0.120
0.12	441	0.089	0.119	0.120	0.120	0.120
0.12	409	0.093	0.120	0.120	0.120	0.120
0.12	358	0.101	0.120	0.120	0.120	0.120
0.12	318	0.108	0.120	0.120	0.120	0.120
0.12	286	0.113	0.120	0.120	0.120	0.120
0.12	260	0.116	0.120	0.120	0.120	0.120
0.12	239	0.119	0.120	0.120	0.120	0.120
0.12	220	0.120	0.120	0.120	0.120	0.120

6.6 Driveway Density (AMF₆)

The AMF for driveway density (AMF₆) is determined as:

AMF₆ = ( 0.3218 + [0.05 - 0.005 ln ADT_y] DD ) / ( 0.3218 + [0.05 - 0.005 ln ADT_y] (5) ) (A-10)

where:

ADT_y = annual average daily traffic volume of the highway being evaluated (veh/day)
DD = driveway density for both sides of the road combined (driveways/mile)

6.7 Passing Lanes and Short Four-Lane Sections (AMF₇)

If no passing lane is present on a highway segment, then the value of AMF₇ is 1.00.

If a passing lane is present in one direction of travel (i.e., two lanes in one direction and one lane in the other direction of travel), then the value of AMF₇ is 0.75.

If a short four-lane section is provided on a two-lane highway, then the value of AMF₇ is 0.65. The value of 0.65 should be used for any cross section where two lanes are provided in both directions of travel; this value should be used for short four-lane sections that begin and end at the same station or for any area where passing lanes in opposing directions of travel overlap.

6.8 Two-Way Left-Turn Lanes (AMF₈)

If no center TWLTL is present on a highway section, the value of AMF₈ is 1.00.

If a center TWLTL is present, the value of the AMF is determined as:

AMF₈ = 1.00 - 0.35 P_AP (A-11)

where:

P_AP = access-point-related accidents as a proportion of total accidents

The value of P_AP is determined as:

P_AP = ( 0.0047 DD + 0.0024 DD² ) / ( 1.199 + 0.0047 DD + 0.0024 DD² ) (A-12)

If the driveway density (DD) is less than five driveways per mile, the value of AMF₈ is 1.00.

6.9 Roadside Hazard Rating (AMF₉)

The AMF for roadside hazard rating (AMF₉) is determined as:

AMF₉ = exp ( -0.6869 + 0.0668 RHR ) / exp ( -0.4865 ) (A-13)

where:

RHR = roadside hazard rating for the highway segment considering both sides of the road (1 to 7 scale)

The roadside hazard rating for a highway section ranges from 1 (best roadside) to 7 (poorest roadside). This roadside hazard rating scale is explained and illustrated Report FHWA-RD-99-207, Prediction of the Expected Safety Performance of Rural Two-Lane Highways.

6.10 Reference

Report No. FHWA-RD-99-207, Prediction of the Expected Safety Performance of Rural Two-Lane Highways is available online.

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6. AMFs for Highway Segments

6.1 Lane Width (AMF1)

6.2 Shoulder Width and Type (AMF2)

6.3 Horizontal Curve Length, Radius, and Presence or Absence of Spiral Transition (AMF3)

6.4 Superelevation (AMF4)

6.5 Grades (AMF5)

6.6 Driveway Density (AMF6)

6.7 Passing Lanes and Short Four-Lane Sections (AMF7)

6.8 Two-Way Left-Turn Lanes (AMF8)

6.9 Roadside Hazard Rating (AMF9)

6.10 Reference

6.1 Lane Width (AMF₁)

6.2 Shoulder Width and Type (AMF₂)

6.3 Horizontal Curve Length, Radius, and Presence or Absence of Spiral Transition (AMF₃)

6.4 Superelevation (AMF₄)

6.5 Grades (AMF₅)

6.6 Driveway Density (AMF₆)

6.7 Passing Lanes and Short Four-Lane Sections (AMF₇)

6.8 Two-Way Left-Turn Lanes (AMF₈)

6.9 Roadside Hazard Rating (AMF₉)