Office of Planning, Environment, & Realty (HEP)

Parameters and Defaults Values for Use with the BPR Formula for Estimating Speed

As described in Section 3, use of the BPR-type formulas (and other methods) requires three inputs: free-flow speed, roadway capacity, and traffic volume. Traffic volume information is developed as described in Section 2 of this report. The accuracy of this method is highly dependent on the accuracy of the capacity and free-flow speed inputs. This appendix described in detail the procedures for developing these two inputs, including default parameter values and some examples.

Free-flow speed estimation

NCHRP Report 387 recommends estimating free-flow speed by link using separate equations for unsignalized and signalized facilities.

Free-flow speed equation for unsignalized facilities:

*Free-flow speed = 0.88*S _{p }+ 14* (High-speed facilities have posted speed>50 mph)

*Free-flow speed = 0.79*S _{p }+ 12* (Low-speed facilities have posted speed<=50 mph)

*where S _{p} = posted speed limit in mph*

Free-flow speed equation for signalized facilities:

*where: L = length of facility (in miles)*

*S _{mb} = mid-block free-flow speed = 0.79*posted speed + 12 mph*

*N = number of signalized intersections on length, L*

*D = average delay per signal*

*D = DF * 0.5 * C(1-g/C) ^{2}*

*where: D = total signal delay per vehicle (sec)*

*g = effective green time (sec)*

*C = cycle length (sec)*

*If signal timing data are not available, the following default values can*

*be used:*

*C = 120 seconds*

*g/C = 0.45*

*DF = (1 - P)/(1 - g/C), where P= proportion of vehicles arriving on green*

*If P is unknown, the following defaults can be used for DF:*

*DF = 0.9 for uncoordinated traffic actuated signals*

*= 1.0 for uncoordinated fixed time signals*

*= 1.2 for coordinated signals with unfavorable progression*

*= 0.90 for coordinated signals with favorable progression*

*= 0.60 for coordinated signals with highly favorable progression*

When using these equations to estimate free-flow speed on a large number of links, it is typically impractical to apply the equations individually for each link. Instead, the equations are used to develop look-up tables of free-flow speeds by facility type and area type. The look-up table is then used to quickly assign free-flow speeds to each link. Below is an example if such a look-up table.

Free-flow speeds (mph) | |||||
---|---|---|---|---|---|

Freeway | Expressway | Arterial | Collector | Local | |

CBD | 50 | 45 | 40 | 35 | 30 |

Urban | 55 | 50 | 45 | 40 | 35 |

Suburban | 60 | 55 | 50 | 45 | 40 |

Rural | 65 | 60 | 55 | 50 | 45 |

Source: *Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications*,

NCHRP Report 387, Transportation Research Board, 1997.

Free-flow speeds can be determined using other more simplistic methods. Some regions estimate flow speeds by facility type based on the posted speed limit, such as adding or subtracting a fixed amount to/from the speed limit (e.g., speed limit plus 5 mph for highways) or multiply the speed limit by a fixed percentage (e.g., 62% of speed limit for collectors). These simple adjustments to posted speed limits are usually based on a limited sample of measured local speeds that are available for the desired roadway classification. When using these rules for estimating free-flow speeds, the equations often differ based on area type (e.g., CBD, rural, etc.). Other regions estimate free-flow speeds by facility type using observed off-peak speeds.

Roadway capacity estimation

NCHRP Report 387 recommends a set of equations for estimating capacity that are based on the 1994 *Highway Capacity Manual*. There are separate equations for freeways, 2-lane unsignalized roads, and signalized arterials.

Capacity equation for freeways and unsignalized multilane roads:

*Capacity (vph) = Ideal Cap * N * F _{hv} * PHF*

*Where:*

*Ideal Cap = 2,400 (pcphl) for freeways with >=70 mph free-flow speed*

*= 2,300 (pcphl) for all other freeways (free-flow speed < 70 mph)*

*N = number of through lanes (Ignore auxiliary lanes and "exit only" lanes)*

*F _{hv} = heavy vehicle adjustment factor*

*= 100/(100 + 0.5 * HV) for level terrain*

*= 100/(100 + 2.0 * HV) for rolling terrain*

*= 100/(100 + 5.0 * HV) for mountainous terrain*

*(HV = proportion of heavy vehicles, including trucks, buses, recreational vehicles, in the traffic flow. If HV is unknown, use 0.05 heavy vehicles as default.)*

*PHF = peak-hour factor (ratio of the peak 15-min flow rate to the average hourly flow rate) (If unknown, use default value of 0.90.)*

Capacity equation for two-lane unsignalized roads:

*Capacity (vph) = Ideal Cap * N * F _{w} * F_{hv} * PHF * F_{dir} * F_{nopass}*

*Where: Ideal Cap = 1,400 (pcphl) for all two-lane rural roads*

*N = number of lanes*

*F _{w} = lane width and lateral clearance factor*

*= 0.80 if narrow land and/or narrow shoulders are present*

*= 1.00 otherwise*

*(Narrow lanes are less than 12 ft. (3.6 m) wide; narrow shoulders are less than 3 ft (1.0 m) wide.)*

*F _{hv} = heavy vehicle adjustment factor*

*= 100/(100 + 1.0 * HV) for level terrain*

*= 100/(100 + 4.0 * HV) for rolling terrain*

*= 100/(100 + 11.0 * HV) for mountainous terrain*

*(HV = proportion of heavy vehicles, including trucks, buses, recreational vehicles, in the traffic flow. If HV is unknown, use 0.05 heavy vehicles as default.)*

*PHF = peak-hour factor (ratio of the peak 15-min flow rate to the average hourly flow rate) (If unknown, use default value of 0.90.)*

*F _{dir} = directional adjustment factor*

*= 0.71 + 0.58 * (1.00 - peak direction proportion) (Peak direction proportion of two-way traffic going in peak direction. If not known, use default of 0.55 peak direction.)*

*F _{nopass} = no-passing zone factor*

*= 0.97 - 0.07 * (NoPass) for rolling terrain*

*= 0.91 - 0.13 * (NoPass) for mountainous terrain*

*(NoPass is the proportion of length of facility for which passing is prohibited. If NoPass is unknown, use 0.60 NoPass for rolling terrain and 0.80 for mountainous terrain.)*

Capacity equation for signalized arterials:

*Capacity (vph) = Ideal Sat * N * F _{hv} * PHF * F_{park} * F_{bay} * F_{CBD }** g/C * F

*Where: Ideal Sat = ideal saturation flow rate (vehicles per lane per hour of green)*

*= 1,900*

*N = number of through lanes (Exclude exclusive turn lanes and short lane additions.)*

*F _{hv }= heavy vehicle adjustment factor*

*= 1.00/(1.00 + HV)*

*(HV = proportion of heavy vehicles, including trucks, buses, recreational vehicles, in the traffic flow. If HV is unknown, use 0.05 heavy vehicles as default.)*

*PHF = peak-hour factor (ratio of the peak 15-min flow rate to the average hourly flow rate) (If unknown, use default value of 0.90.)*

*F _{park} = on-street parking adjustment factor*

*= 0.90 if on-street parking is present and time limit is 1 hr or less*

*= 1.00 otherwise*

*F _{bay }= left turn bay adjustment factor*

*= 1.10 if exclusive left turn lanes (often as left turn bay) are present*

*= 1.00 otherwise*

*F _{CBD} = central business district adjustment factor*

*= 0.90 if located in CBDs*

*= 1.00 elsewhere*

*g/C = ratio of effective green time per cycle*

*If no data are available, use the following defaults:*

*Protected left turn phase present: g/C = 0.40*

*Protected left turn phase not present: g/C = 0.45*

*Other defaults may be developed by the local planning agency based on local conditions. Additional defaults might be based on the functional class of major and crossing streets.*

*F _{c} = optional user-specified calibration factor necessary to match estimated capacity with field measurements or other independent estimates of capacity (no units) (can be used to account for the capacity-reducing effects of left and right turns made from through lanes)*

As with free-flow speeds, it is usually impractical to apply the capacity equations individually for every link, so look-up tables are developed.

One-way LOS "C", vehicles per lane per hour | |||||
---|---|---|---|---|---|

Freeway | Expressway | 2-Way Arterial (w/ parking) | One-Way Arterial (w/ parking) | Two-Way Arterial (no parking) | |

CBD | 1750 | 800 | 600 | 700 | 600 |

Fringe | 1750 | 1000 | 550 | 550 | 800 |

Outer CBD | 1750 | 1000 | 550 | 650 | 800 |

Rural/Residential | 1750 | 1000 | 550 | 900 | 800 |

Source: *Planning Techniques to Estimate Speeds and Service Volumes for Planning Applications*, NCHRP Report 387, Transportation Research Board, 1997.

If traffic volume data is on a daily basis (AADT), then hourly capacity must be converted to an effective daily capacity. In one approach to calculate 24-hour capacity, the hourly capacity per lane is divided by the ratio of AADT that occurs in the peak hour. This figure is then multiplied by the number of lanes in the peak direction, and in the off peak direction is multiplied by the number of lanes and a directional adjustment factor. A 24-hour volume-to-capacity (V/C) ratio is then calculated by dividing AADT by 24-hour capacity.

*Construction of a Localized Capacity Look-Up Table*

Because the accuracy of capacity estimates is essential to the accuracy of speed estimates, NCHRP Report 387 recommends that planning agencies use the specific capacities of the selected study section. When that is not possible, the following tables demonstrate the procedure for selecting default values and computing a look-up table of capacities, according to facility, area, and terrain type. The first table is for two-lane, rural undivided arterials, but additional rows of data could be added for multilane rural undivided arterials. The second table provides a sample computation.

Functional Class | Area Type | Terrain Type | Lanes | Free Speed | Lane Width | PHF | % Heavy Vehicles | Direction Split | % No Pass | Parking | Left Turn Bay | g/C |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Freeway | Rural | Level | all | >70 mph | 0.85 | 5% | ||||||

Rolling | all | >70 mph | 0.85 | 5% | ||||||||

Mountain | all | <70 mph | 0.85 | 5% | ||||||||

Urban | all | all | <70 mph | 0.90 | 2% | |||||||

Divided Arterial | Rural | Level | >2 | 60 mph | 0.85 | 5% | ||||||

Rolling | >2 | 55 mph | 0.85 | 5% | ||||||||

Mountain | >2 | 50 mph | 0.85 | 5% | ||||||||

Suburban | all | all | 0.90 | 2% | no | yes | 0.45 | |||||

Urban | all | all | 0.90 | 2% | yes | yes | 0.45 | |||||

CBD | all | all | 0.90 | 2% | yes | yes | 0.45 | |||||

Undivided Arterial | Rural | Level | 2 | standard | 0.85 | 5% | 55% | 0% | ||||

Rolling | 2 | standard | 0.85 | 5% | 55% | 60% | ||||||

Mountain | 2 | narrow | 0.85 | 5% | 55% | 80% | ||||||

Suburban | all | all | 0.90 | 2% | no | no | 0.45 | |||||

Urban | all | all | 0.90 | 2% | yes | no | 0.45 | |||||

CBD | all | all | 0.90 | 2% | yes | no | 0.45 | |||||

Collector | Urban | all | all | 0.85 | 2% | yes | no | 0.40 |

Functional Class | Area Type | Terrain Type | Lanes | Ideal Cap | PHF | Fhv | FW | Fdir | Fno- pass | Fpark | Fleft | Fcbd | g/C | Cap/ Lane |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Freeway | Rural | Level | all | 2400 | 0.85 | 0.98 | 2000 | |||||||

Rolling | all | 2400 | 0.85 | 0.91 | 1900 | |||||||||

Mountain | all | 2300 | 0.85 | 0.80 | 1600 | |||||||||

Urban | all | all | 2300 | 0.90 | 0.98 | 2000 | ||||||||

Divided Arterial | Rural | Level | >2 | 2200 | 0.85 | 0.98 | 1800 | |||||||

Rolling | >2 | 2100 | 0.85 | 0.91 | 1600 | |||||||||

Mountain | >2 | 2000 | 0.95 | 0.80 | 1400 | |||||||||

Suburban | all | all | 1900 | 0.90 | 0.98 | 1.00 | 1.10 | 1.00 | 0.45 | 850 | ||||

Urban | all | all | 1900 | 0.90 | 0.98 | 0.90 | 1.10 | 1.00 | 0.45 | 750 | ||||

CBD | all | all | 1900 | 0.90 | 0.98 | 0.90 | 1.10 | 0.90 | 0.45 | 650 | ||||

Undivided Arterial | Rural | Level | 2 | 1400 | 0.85 | 0.95 | 1.00 | 0.97 | 1.00 | 1100 | ||||

Rolling | 2 | 1400 | 0.85 | 0.83 | 1.00 | 0.97 | 0.93 | 900 | ||||||

Mountain | 2 | 1400 | 0.85 | 0.65 | 0.80 | 0.97 | 0.81 | 500 | ||||||

Suburban | all | all | 1900 | 0.90 | 0.98 | 1.00 | 1.00 | 1.00 | 0.45 | 750 | ||||

Urban | all | all | 1900 | 0.90 | 0.98 | 0.90 | 1.00 | 1.00 | 0.45 | 700 | ||||

CBD | all | all | 1900 | 0.90 | 0.98 | 0.90 | 1.00 | 0.90 | 0.45 | 600 | ||||

Collector | Urban | all | all | 1900 | 0.85 | 0.98 | 0.90 | 1.00 | 1.00 | 0.40 | 550 |

Computing average speed

The updated BPR formula is as follows:

*where: s = predicted mean speed*

* s _{f}= free-flow speed*

* v = volume*

* c = practical capacity*

* a = 0.05 for facilities with signals spaced 2 mi apart or less*

* = 0.20 for all other facilities*

* b = 10*

Many regions have modified the parameters *a* and *b* so that the formula calculates speeds that more closely reflect observed local speeds. The original BPR formula uses *a = 0.15* and *b = 4*. Other regions have used values of *a* as high as 1.0 and values of *b* as high as 11.

**Advantages**-
- Able to produce highly accurate speed estimates if applied properly.
- Accounts for future congestion impacts on speed.

**Limitations**-
- In order to produce accurate speed results, requires accurate local information on capacity and free-flow speed. Use of default look-up tables for these values often leads to inaccurate speed estimates.
- To apply this method for individual links, requires detailed information regarding signalization characteristics, traffic characteristics, etc.

**Example Location**- Ohio DOT used the original form of the BPR formula (
*a = 0.15*and*b = 4*) to estimate speed in rural areas not covered by a TDF model. To estimate free-flow speeds, Ohio DOT used the upper bound of the table provided in the HCM for each functional class.