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REPORT
This report is an archived publication and may contain dated technical, contact, and link information
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Publication Number:  FHWA-HRT-17-098     Date:  January 2018
Publication Number: FHWA-HRT-17-098
Date: January 2018

 

Self-Enforcing Roadways: A Guidance Report

APPENDIX A. OPERATING SPEED EQUATIONS

Table 33. Equations from literature used to determine operating speeds.
Study Year No. Equation R2 Variables Units Conditions/Notes
Fitzpatrick et al. 2005 1 *FF subscript 85 equals 12.4 plus the sum of 0.98 open parentheses SL close parentheses. 0.904 SL Metric —
Fitzpatrick et al. 2005 2 *FF subscript 85 equals 25.9 plus the sum of 0.83 open parentheses SL close parentheses minus the sum of 0.054 open parentheses AD close parentheses. 0.923 SL, AD Metric For sites with posted speed limit of 45 mph (73 km/h) or less
Fitzpatrick et al. 2005 3 *FF subscript 85 equals 65.0 minus 12.2 park. 0.50 park Metric For sites with 30 mph (48 km/h) posted speed limit
Misaghi and Hassan 2005 1 †V subscript 85MC equals 91.85 plus 9.81 multiplied by 10 to the negative third power times R. 0.464 R Metric —
Misaghi and Hassan 2005 2 †V subscript 85MC equals 94.30 plus 8.67 multiplied by 10 to the negative sixth power times R squared. 0.524 R Metric —
Misaghi and Hassan 2005 3 †Delta subscript 85 times V equals negative 83.63 plus 0.93V subscript T plus e to the power of negative 8.93 plus 3507.10 divided by R. 0.649 R, VT Metric —
Misaghi and Hassan 2005 4 †Delta subscript 85 times V equals negative 194.74 plus the sum of 21.42 open parentheses square root V subscript T close parentheses plus 0.11DFC minus 4.55SW minus 5.36 open parentheses curve minus dir close parentheses plus 1.30G plus 4.22 open parentheses drv subscript flag close parentheses. 0.889 VT, DFC, SW, curve direction, G, drvflag Metric —
Fitzpatrick et al. 2003 1 EV subscript 85 equals 7.675 plus the sum of 0.98 open parentheses PSL close parentheses. 0.904 PSL U.S. customary All roadways
Fitzpatrick et al. 2003 2 EV subscript 85 equals 8.666 plus the sum of 0.963 open parentheses PSL close parentheses. 0.86 PSL U.S. customary Suburban/urban arterial
Fitzpatrick et al. 2003 3 EV subscript 85 equals 21.131 plus the sum of 0.639 open parentheses PSL close parentheses. 0.41 PSL U.S. customary Suburban/urban collector
Fitzpatrick et al. 2003 4 EV subscript 85 equals 10.315 plus the sum of 0.776 open parentheses PSL close parentheses. 0.14 PSL U.S. customary Suburban/urban local
Fitzpatrick et al. 2003 5 EV subscript 85 equals 36.453 plus the sum of 0.517 open parentheses PSL close parentheses. 0.81 PSL U.S. customary Rural arterial
Schurr et al. 2002 1 ‡V subscript 85 comma midpoint equals 103.3 minus 0.1253 delta plus 0.0238L plus 1.039G subscript 1. 0.46 Δ, LC, G1 Metric —
Schurr et al. 2002 2 ‡V subscript 85 comma approach equals 70.2 plus 0.434V subscript p minus 0.001307T subscript ADT. 0.19 Vp, TADT Metric —
Schurr et al. 2002 3 ‡V subscript 95 comma midpoint equals 113.9 minus 0.122 delta plus 0.0178L minus 0.00184T subscript ADT. 0.41 Δ, LC, TADT Metric —
Schurr et al. 2002 4 ‡V subscript 95 comma approach equals 84.4 plus 0.352V subscript p minus 0.001399T subscript ADT. 0.22 Vp, TADT Metric —
Fitzpatrick et al. 2000a 1 V subscript 85 equals 106.30 minus the quotient of 3595.29 divided by R. 0.92 R Metric Horizontal curve on grade: 0 ≤ G < 4 or horizontal curve combined with sag vertical curve
Fitzpatrick et al. 2000a 2 V subscript 85 equals 96.46 minus the quotient of 2744.49 divided by R. 0.56 R Metric Horizontal curve on grade: 4 ≤ G < 9
Fitzpatrick et al. 2000a 3 V subscript 85 equals 100.87 minus the quotient of 2720.78 divided by R. 0.59 R Metric Horizontal curve on grade:
-9 ≤ G< 0
Fitzpatrick et al. 2000a 4 V subscript 85 equals 101.90 minus the quotient of 3283.01 divided by R. 0.78 R Metric Horizontal curve combined with limited sight distance crest vertical curve
Fitzpatrick et al. 2000a 5 V subscript 85 equals 111.07 minus the quotient of 175.98 divided by K. 0.54 K Metric Vertical crest curve with limited sight distance on horizontal tangents
Fitzpatrick et al. 2000a 6 V subscript 85 equals 100.19 minus the quotient of 126.07 divided by K. 0.68 K Metric Sag vertical curve on horizontal tangent
Polus et al. 2000 1 ‡SP equals 102.5 minus the quotient of 37.34 divided by e to the power of open parentheses 0.00668 multiplied by GM subscript L close parentheses. 0.332 GML Metric GML ≤ 200; maximum speed = 63.69 mph (102.5 km/h)
Polus et al. 2000 2 ‡SP equals 105.00 minus the quotient of 21.30 divided by e to the power of open parentheses 0.00092 multiplied by GM subscript L close parentheses. 0.228 GML Metric GML ≤ 1000; maximum speed = 65.25 mph (105 km/h)
Polus et al. 2000 3 ‡SP equals 101.11 minus the quotient of 3420 divided by GM subscript S. 0.553 GMS Metric Small radii and small TL; R≤ 250 m; TL < 150 m
Polus et al. 2000 4 ‡SP equals 98.405 minus the quotient of 3184 divided by GM subscript L. 0.684 GML Metric Small radii and intermediate TL; R ≤ 250 m; 150 m < TL < 1000 m; GML ≤ 1500
Polus et al. 2000 5 ‡SP equals 105.00 minus the quotient of 28.107 divided by e to the power of open parentheses 0.00108 multiplied by GM subscript L close parentheses. 0.742 GML Metric If maximum 85th-percentile speed is 65.25 mph (105 km/h)
Polus et al. 2000 6 ‡SP equals 105.00 minus the quotient of 22.953 divided by e to the power of open parentheses 0.00012 multiplied by GM subscript L close parentheses. 0.838 GML Metric Large TL and any reasonable radius;
TL< 1000 m
Krammes et al. 1995 1 V subscript 85 equals 103.66 minus 1.95D. 0.80-0.82 D Metric 85th-percentile speed on long tangents overestimated
Krammes et al. 1995 2 V subscript 85 equals 102.45 minus 1.57D plus 0.0037L minus 0.10I. 0.82 D, LC, I Metric —
Krammes et al. 1995 3 V subscript 85 equals 41.62 minus 1.29D plus 0.0049L minus 0.12I plus 0.95V subscript t. 0.90 D, LC, I, VT Metric —
Lamm and Choueiri 1987 1 ‡V subscript 85 equals 34.700 minus 1.00 open parentheses DC close parentheses plus 2.081 open parentheses LW close parentheses plus 0.174 open parentheses SW close parentheses plus 0.0004 open parentheses AADT close parentheses open bracket mph close bracket.[mph] 0.842 DC, LW, SW, AADT U.S. customary —
Lamm and Choueiri 1987 2 ‡V subscript 85 equals 58.656 minus 1.135 open parentheses DC close parentheses open bracket mph close bracket. [mph] 0.787 DC U.S. customary —
Lamm and Choueiri 1987 3 ‡V subscript 85 equals 55.132 minus 0.042 open parentheses CCR close parentheses open bracket mph close bracket. [mph] 0.846 CCR U.S. customary Lane width = 10 ft
Lamm and Choueiri 1987 4 ‡V subscript 85 equals 55.646 minus 1.019 open parentheses DC close parentheses open bracket mph close bracket. [mph] 0.753 DC U.S. customary Lane width = 10 ft
Lamm and Choueiri 1987 5 ‡V subscript 85 equals 57.602 minus 0.040 open parentheses CCR close parentheses. 0.731 CCR U.S. customary Lane width = 11 ft
Lamm and Choueiri 1987 6 ‡V subscript 85 equals 58.310 minus 1.052 open parentheses DC close parentheses. 0.746 DC U.S. customary Lane width = 11 ft
Lamm and Choueiri 1987 7 ‡V subscript 85 equals 59.515 minus 0.038 open parentheses CCR close parentheses. 0.836 CCR U.S. customary Lane width = 12 ft
Lamm and Choueiri 1987 8 ‡V subscript 85 equals 59.746 minus 0.998 open parentheses DC close parentheses. 0.824 DC U.S. customary Lane width = 12 ft
McLean 1979 1 ‡V subscript 85 equals 53.8 plus 0.464V subscript F minus 3.26 open parentheses the quotient of 1 divided by R close parentheses multiplied by 10 to the third power plus 8.5 open parentheses the quotient of 1 divided by R close parentheses to the second power multiplied by 10 to the fourth power. 0.92 VF, R Metric —
Fitzpatrick et al. 1995 1 V subscript 85 comma tan equals 74.91 plus the quotient of 22.29 divided by AD. 0.71 AD Metric Suburban highways, tangent sections
Fitzpatrick et al. 1995 2 V subscript 85 comma curve equals 54.18 plus 1.061R to the 0.5th power. 0.72 R Metric Suburban highways, curve sections
Fitzpatrick et al. 1995 3 V subscript 85 comma curve equals 56.34 plus 0.808R to the 0.5th power plus the quotient of 9.34 divided by AD. 0.81 R, AD Metric Suburban highways, curve sections
Banihashemi et al. 2011 1 ‡V subscript T85 equals 35.15 plus 0.26PS minus the quotient of 1132 divided by R subscript p. 0.49 RP U.S. customary Tangents with LT < 150 ft
Banihashemi et al. 2011 2 ‡V subscript T85 equals 26.04 plus 0.53PS minus 0.89RHR plus 0.005L subscript T. 0.29 PS, RHR, LT U.S. customary Tangents with LT ≥ 150 ft
Banihashemi et al. 2011 3 ‡V subscript C85 equals 44.25 minus the quotient of 1462 divided by R. 0.37 R U.S. customary Curve speed

*©ASCE. Reproduced with the express written authority of the American Society of Civil Engineers (ASCE). Excerpted from the ASCE publication

Journal of Transportation Engineering, 131(4), ASCE, April 2005, pp. 261-269.

†©ASCE. Reproduced with the express written authority of the American Society of Civil Engineers (ASCE). Excerpted from the ASCE publication

Journal of Transportation Engineering, 131(4), ASCE, April 2005, pp. 408-418.

‡©TRB.

—No information.

FF85 = 85th-percentile free-flow operating speed (mph (km/h));
SL = posted speed limit (mph (km/h));
AD = access density;
park = indicator variable for the presence of parking;
V85MC = 85th-percentile speed at middle of curve (mph (km/h));
Δ85V = 85th-percentile speed differential calculated as 85th-percentile value of speed differentials of individual drivers;
VT = approach tangent speed (mph (km/h));
DFC = deflection angle of circular curve (degrees);
SW = shoulder width (ft (m));
curve - dir = curve direction;
drvflag = driveway flag; EV85 = estimated 85th-percentile speed (mph (km/h));
PSL = posted speed limit (mph (km/h));
V85, midpoint = 85th-percentile speed at free-flow passenger cars at the curve midpoint (mph (km/h));
Δ = deflection or intersection angle of horizontal curve (degrees);
LC = length of horizontal curve (ft (m));
G1 = approach grade (percent);
V85, approach = 85th-percentile speed at the approach location (mph (km/h));
Vp = posted speed limit (mph (km/h));
TADT = average daily traffic (vehicles per day);
V95, midpoint = 95th-percentile operating speed at the midpoint of the horizontal curve (mph (km/h));
V95, approach = 95th-percentile operating speed on the approach tangent to the horizontal curve (mph (km/h));
K = rate of vertical curvature (ft/percent (m/percent));
SP = posted speed limit (mph (km/h));
GML = geometric measure for long tangents between horizontal curves (ft2 (m2));
GMS = geometric measure for short tangents between horizontal curves (ft2 (m2));
D = degree of curvature;
I = deflection or intersection angle of horizontal curve (degrees);
LW = lane width (ft (m));
CCR = curvature change rate (degrees per half mile);
VF = desired speed of the 85th-percentile car (mph (km/h));
V85, tan = estimated 85th-percentile operating speed on tangent (mph (km/h));
V85, curve = 85th-percentile speed on the curve (mph (km/h));
VT85 = estimated 85th-percentile operating speed on tangent (mph (km/h));
PS = posted speed limit (mph (km/h));
Rp = radius of preceding horizontal curve (ft (m));
RHR = roadside hazard rating;
LT = length of approach tangent (ft (m));
VC85 = estimated 85th-percentile operating speed on the curve (mph (km/h)).

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