Transcript HSM Predicting Highway Safety for Curves on Two

HSM Practitioner’s Guide for Two-Lane
Rural Highways Workshop
Predicting Highway Safety for
Curves on Two-Lane Rural Highway
- Session #4
4-1
Predicting Highway Safety for Curves on
Two-Lane Rural Highways
Learning Outcomes:
► Describe the crash prediction method
for Crash Performance on Horizontal
Curves
► Identify low-cost safety improvements
for horizontal curves
4-2
….Curves present particular safety
problems to designers
Crash Rate
8
6.7
7
6
5
4
3
2
3.93
2.21
1
0
Tangent
segments
CRASH RATES
(Crashes per 1
km segment--3
year timeframe)
The risk of a
reported crash is
about three times
greater on a curve
than on a tangent
Segments Curved portion only
w/curve
(Curve plus transitions)
Source: Glennon, et al,
1985 study for FHWA
4-3
%RSME = 16.27%
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
1000
2000
3000
4000
5000
6000
Actual Radius (ft)
7000
8000
9000
10000
%RSME = 29.23%
Lactual vs Lpredicted
Predicted Length (ft)
Predicted Radius (ft)
Ractual vs Rregression
4000
3000
2000
1000
0
0
500
1000
1500
2000
Actual Length (ft)
2500
3000
3500
4-4
4-5
4-6
4-7
4-8
Actual Driver Operations on Curves
 Drivers ‘overshoot’
the curve (track a path
sharper than the
radius)
 Path is a spiral
 Path overshoot
behavior is
independent of speed
Driver tracks a ‘critical radius’
sharper than that of the curve
just past the PC
Source: Bonneson, NCHRP 439
and Glennon et al (FHWA)
4-9
Driver “overshoot” behavior on
curves (from Glennon, et al)
700
Example -- a 1000-ft radius
curve is driven by a 95th percentile
driver at about a 700 ft radius
at some point in the curve
4-10
Research confirms differences in actual
operations versus AASHTO assumptions
Curves driven faster
than Policy assumption
Curves driven
slower
than Policy
assumption
• Drivers’ selected
speed behavior does
not match design
assumptions
• Sharper curves (<80
km/h or 50 mph) are
driven faster (drivers
are more comfortable)
4-11
Speed Prediction Model for Horizontal
Curves (Otteson and Krammes)
V85 = 41.62 - 1.29D + 0.0049L - 0.12DL + 0.95 Vt
Where
V85 = 85th percentile speed on the curve
D = degree of curve
L = length of curve (mi)
Vt = 85th percentile approach speed (mph)*
*this should be measured in the field
4-12
A ‘risk assessment’ tool for speed profiles
V85 - Vdesign = Vdelta
Higher risk curves may be those with V delta high
(i.e., operating speeds significantly greater than
design speed)
 Vdelta > 12 mph (20 km/h); high risk
 6 mph (10 km/h) < Vdelta < 12 mph (20 km/h);
caution
4-13
FHWA’s IHSDM Speed Consistency Model
Addresses Continuous Speed Behavior
4-14
Truck operations on curves may in some
cases be critical (Harwood and Mason)
Under certain conditions,
trucks will roll over before they
skid
Trucks with high centers of
gravity overturn before losing
control due to skidding
Margin of safety for ‘f’ is
therefore lower for trucks
Trucks on downgrade curves
generate greater lateral friction
(superelevation is not as
effective)
4-15
Summary of Research on Superelevation
and Transition Design
Studies confirm small but significant effect of
superelevation on crashes
• FHWA (Zegeer) study noted 5 to 10%
greater crashes when superelevation is
“deficient”
• 1987 study of fatal crash sites on curves
noted “deficiencies in available
superelevation”
4-16
Spirals
provides e
transition
leading
into the
curve
Radius (m)
Research confirms benefits of spirals and
recommends optimal transition design
Source:
NCHRP
Report 439
• Zegeer et al found safety benefits in HSIS study of Washington
• Bonneson confirmed operational benefits noted by Glennon, etal
4-17
Zegeer et al. FHWA Study “Cost-Effective
Geometric Improvements for Safety
Upgrading of Horizontal Curves” (1991)
Data Bases
• 10,900 Curves in Washington State
• 7-state data base of 5000 mi
• 78 curves in New York State
• Glennon 4-state data base of 3277 curve
segments
Statistical Analysis and Model Development
Identified as key effort in TRB SR 214, recent
NCHRP review by BMI, and key reference for
IHSDM
4-18
Summary of findings from Zegeer study
Features related to crashes include:
• Degree and length of curve
• Width through the curve
• Superelevation and,
• Spiral presence
For typical volumes on 2-lane highways, expect
1 to 3 crashes per 5 years on a curve
4-19
Safety Effects for Horizontal Curves
(CMF3r)
CMF3r = 1.55 Lc + (80.2/R) - 0.012 * S
1.55Lc
Where:
Lc = Length of Curve including spirals, (mi)
R = Radius of Curve (ft)
S = 1 if spiral transition is present, 0 if not present
4-20
Safety Effects of Horizontal Curves (CMF3r):
Example with no Spiral present
For: Lc = 480 feet = 0.091 miles
R = 350’; no spiral transition
CMF3r = {1.55 Lc + (80.2/R) – 0.012S } / 1.55Lc
= (1.55 x 0.091) + (80.2/350) – 0.012x0
1.55x 0.091
= 2.62
4-21
Safety Effects of Horizontal Curves (CMF3r):
Example with Spiral Transition
For: Lc = 480 feet = 0.091 miles
R = 350’; with spiral transition
CMF3r = {1.55 Lc + (80.2/R) – 0.012S } / 1.55Lc
= (1.55 x 0.091) + (80.2/350) – 0.012x1
1.55x 0.091
== ?*2.54
*Without spiral CMF3r = 2.62, with spiral CMF3r=
2.54, Difference = 8% potential for fewer crashes
with a spiral transition in this segment.
4-22
Crash Modification Function for
Horizontal Curves: Superelevation
CMF4r is based on “Superelevation variance” or SV
For SV less than 0.01: CMF4r = 1.00
For 0.01 < SV < 0.02: CMF4r = 1.00 + 6(SV-0.01)
For SV > 0.02: CMF4r = 1.06 + 3(SV-0.02)
Example: Design e = 4%, Actual e = 2%
SV = 0.04 – 0.02 = 0.02
CMF4r = 1.06 + 3(0.02-0.02) = 1.06 + 3(0.0) = 1.06
4-23
HSM Applications to
Two-Lane Rural Highway Segments
HSM Crash Prediction Method for TwoLane Rural Highway Segments:
• Applying SPF and CMFs
• Example Problem
4-24
Crash Prediction for Roadway Segment for
Existing Conditions – Example Calculation:
Two-Lane Rural Roadway, CR 123 Anywhere, USA
(MP 10.00 – 15.02)
► AADT = 3,500 vpd for the current year
► Length = 26,485 feet = 5.02 miles
• Lane Width = 11.0 ft
• Shoulder Width = 2 ft; Shoulder Type = Gravel
► Horizontal Curve on Grade (MP 12.00-12.186):
• Lc = 0.186 miles, R = 650’; with no spiral transition
• Grade = 4.5%
• Superelevation Variance = .02
►Tangent Section on Grade (MP 13.45-14.00):
• L = 0.55 miles; Grade = -6.3%
4-25
Crash Prediction for Roadway Segment for
Existing Conditions – Example:
► Divide Two-Lane Rural Roadway into Individual
Segments:
Segment
Length
(miles)
Horizontal
Curve
Radius (ft)
Superelevation
Variance
Grade
(%)
Driveway
Density
(per mile)
RHR
10.00 –
12.00
2.000
Tangent
N/A
2.0%
8
5
*12.00 –
12.186
0.186
650
.02
4.5%
0
5
12.186 13.45
1.264
Tangent
N/A
3.0%
4
5
13.4514.00
0.550
Tangent
N/A
- 6.3%
0
5
140015.02
1.020
Tangent
N/A
- 3.0%
6
5
4-26
Safety Performance Function (SPF) for Base
Conditions: Example Calculation
Segment 2 (MP 12.00-12.186): Horizontal Curve on
a 4.5% Grade
Where:
AADT = 3,500 vpd (current year)
Length = 0.186 miles
Nspf-rs = (AADTn) (L) (365) (10-6) e-0.312
Nspf-rs = (3,500) (0.186) (365) (10-6) e-0.312
= (3,500) (0.186) (365) (10-6) (0.7320)
= 0.17 crashes per year
4-27
CMF for Lane Width (CMF1r): Calculation
Segment 2: 11 foot wide lane:
From Table 10-8: CMFra = 1.05
►Adjustment for lane width and shoulder width related
crashes (Run off Road + Head-on + Sideswipes) to obtain
total crashes using default value for pra = 0.574
CMF1r = (CMFra - 1.0) pra + 1.0
= (1.05 - 1.0) * 0.574 + 1.0
= (0.05) (0.574) + 1.0
= 1.03
4-28
CMF or Shoulder Width and Type (CMF2r):
Calculation
Segment 2: 2 ft wide gravel shoulder:
CMFwra = 1.30 (Table10-9) and CMFtra = 1.01 (Table10-10)
►Adjustment from crashes related to lane and
shoulder width (Run off Road + Head-on + Sideswipes)
to total crashes using default value for pra = 0.574
CMF2r = (CMFwra CMFtra - 1.0) pra + 1.0
= ((1.30)(1.01) - 1.0) * 0.574 + 1.0
= (0.313) (0.574) + 1.0
= 1.18
4-29
CMF for Horizontal Curve (CMF3r): Calculation
Segment 2: Horizontal Curve
For: Lc = 0.186 miles
R = 650’; with no spiral transition
CMF3r = {1.55 Lc + (80.2/R) – 0.012S } / 1.55Lc
= (1.55 x 0.186) + (80.2/650) – 0.012x0
1.55x 0.186
= 1.43
4-30
CMF for Superelevation on Horizontal
Curves (CMF4r)
Segment 2: Horizontal Curve Superelevation
Variance = 0.02
►For SV > 0.02: CMF4r = 1.06 + 3(SV-0.02)
CMF4r = 1.06 + 3(0.02-0.02)
= 1.06 + 3(0.0)
= 1.06
4-31
CMF for Percent (%) Grade on Roadway
Segments (CMF5r)
Segment 2: 4.5% Grade
CMF5r = 1.10
4-32
CMF Roadside Design (CMF10r): Example
Calculation
Segment 2: RHR = 5
CMF10r = e(-0.6869 + (0.0668xRHR)) /e-0.4865
= e(-0.6869 + (0.0668x5)) /e-0.4865
= 1.14
4-33
Applying CMFs to the SPF Base
Prediction Model
CRASH MODIFCATION FACTORS
Lane Width = 11 ft
CMF1r = 1.03
Segment 2: SPF
and CMF Values:
Shoulder Width = 2 ft gravel
CMF2r = 1.18
Horizontal Curve
CMF3r = 1.43
AADT = 3,500 vpd,
Length = 0.186 mi
Radius = 650 ft
Superelevation Variance (0.02)
CMF4r = 1.06
Percent Grade = 4.5%
CMF5r = 1.10
Driveway Density, None
CMF6r = 1.00
Centerline Rumble, None
CMF7r = 1.00
Passing/Climbing Lanes, None
CMF8r = 1.00
TWLTLs, None
CMF9r = 1.00
Roadside Design, RHR = 5
CMF10r = 1.14
Lighting, None
CMF11r = 1.00
Automated Enforcement, None
CMF12r = 1.00
Nspf-rs = 0.17
crashes per year
CMFtotal = 2.31
4-34
Applying CMFs to the SPF Base Prediction Model
Npredicted-rs = Nspf-rs x (CMF1r … CMF12r) Cr
Segment 2: Apply CMFs to SPF for Base
Conditions: (letting Cr = 1.0)
Npredicted-rs = 0.17 x (1.03 x 1.18 x 1.43 x 1.06 x 1.10 x
1.00 x 1.00 x 1.00 x 1.00 x 1.14 x 1.000
x 1.00) x 1.00
= 0.17 x 2.31 x 1.00
= 0.4 crashes per year, 1 crash every 2.5 yrs
4-35
Crash Prediction for Roadway Segment for
Existing Conditions – Example Calculation:
For each Two-Lane Rural Roadway Segment: Table with SPF
predicted crahses, CMFs, and Adjusted Total Crashes
CRASH PREDICTION METHOD – TOTAL CRASHES
Seg
No.
SPF
base
CMF1r
LW
CMF2r
SW&ST
CMF3r
ST
CMF4r
e
CMF5r
Grade
CMF6r
DD
CMF7r
CLRS
CMF8r
PassLn
CMF9r
TWLTL
CMF10
r RD
CMF11r
Light
CMF12
r Spd
Enf
Total
CMF
Total
Adjusted
Crashes
1
1.87
1.03
1.18
1.00
1.00
1.00
1.07
1.00
1.00
1.00
1.14
1.00
1.00
1.49
2.8
2
0.17
1.03
1.18
1.43
1.06
1.10
1.00
1.00
1.00
1.00
1.14
1.00
1.00
2.31
0.40
3
1.27
1.03
1.18
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.14
1.00
1.00
1.39
1.8
4
0.51
1.03
1.18
1.00
1.00
1.16
1.00
1.00
1.00
1.00
1.14
1.00
1.00
1.61
0.8
5
0.95
1.03
1.18
1.00
1.00
1.00
1.02
1.00
1.00
1.00
1.14
1.00
1.00
1.42
1.4
Total:
7.2
4-36
Predicting Crash Frequency
Performance
Total Predicted Crash Frequency within
the limits of the roadway being analyzed:
Ntotal crashes = ∑Npredicted-rs + ∑ Npredicted-int
Ntotal crashes = 7.2 crashes/yr + ∑ Npredicted-int
4-37
Overview of Good Alignment Design
Practice (suggested by safety and
operational research)
►Curves and grades are
necessary features of
alignment design (reflect the
topography, terrain, and
“context”)
►Pay particular attention to
roadside design adjacent to
curves
►Avoid long, sharp curves
►Adjust alignment design
to reflect expected speeds
on curves
4-38
Overview of Good Alignment Design
Practice (continued)
►Avoid minimum radius designs where
 actual speeds will be higher than design
speeds
 truck volumes will be substantial
 combined with steep grades
►Use spiral transition curves,
particularly for higher speed roads and
sharper curves
4-39
Overview of Good Alignment Design
Practice (continued)
► Minimize grades within terrain context
► Widen lanes and shoulders through
curves
► Pay attention to access points related
to horizontal and vertical curve locations
4-40
Low and Lower Cost Safety Improvements
for Horizontal Curves
► Signing
► Shoulders
► Lighting
4-41
Low Cost Intersection Safety Measures –
Signing Countermeasures
Injury
Crashes
CMF = 0.87
CRF = 13%
Advance
Warning
With Speed
Advisory
PDO
Crashes
CMF = 0.71
CRF = 29%
*CMF Clearinghouse
http://www.cmfclearinghouse.org
4-42
Safety Effects of Installing
Combination Horizontal
Alignment Warning +
Advisory Speed Signs
4-43
Signing Countermeasure for Horizontal
Curves:
Chevrons Signs
*CRF = 35%
CMF = 0.65
*CMF Clearinghouse
http://www.cmfclearinghouse.org
4-44
Safety Effects of Installing RPM’s
4-45
Low Cost Intersection Safety Measures
– Signing Countermeasures
Double Up Advance Warning Signs
CRF = 31%
CMF = 0.69
4-46
Low Cost Intersection Safety Measures –
Signing Countermeasures
Sharp 10 mph curve to
right just over hill
Activated
Warning
Beacon
 Radar activated
flasher when
speed is fast for
10mph curve
4-47
Examples of Improving Safety of Existing
Curves
• Widen 2’ Shoulder to
6’ Shoulder – NY Rte 82
north of Millbrook
Widen
Shoulders
6’
2’
4-48
Examples of Improving Safety of
Existing Curves
Widen Shoulder
Widening on
Inside of Curves
on Inside of Tight
Curve
NCHRP 500,
Strategy 15.2 A11–
Widening in Curves
4-49
Low Cost Intersection Safety Measures –
Signing Countermeasures
CRF = 28% for
injury crashes
highway lighting
9. Illumination of
Rural Curves
Route 376 near
Poughkeepsie,
NY
4-50
Predicting Highway Safety for Curves on
Two-Lane Rural Highways
Learning Outcomes:
► Described the equation for prediction
of Crash Performance on Horizontal
Curves
►Identified low-cost safety improvements
for horizontal curves
4-51
Questions and Discussion:
4-52