Skip to content

Basic Freeway Segment Highway Capacity

Transportation · FE Reference Handbook section

Transportation
33 formulas
10 exam-style examples
~60 min
All Transportation lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

  • Speed Flow Relationship for Basic Freeway Segments
  • * All equations are based on Exhibit 12-6 and Equation 12-1 from the HCM 6th Edition assuming
  • all calibration factors (CAF and SAF) set to 1.0
  • Average Lane Width (ft) Reduction in FFS, fLW (mph)
  • HCM: Highway Capacity Manual, 6th ed., A Guide for Multimodal Mobility Analysis, Transportation

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1
Basic Freeway Segment Highway Capacity — solve for flow rate — Basic Freeway Segment Highway Capacity

a basic freeway segment highway capacity analysis for a level-terrain freeway Given hourly volume (V) = 3,050 veh/h; peak hour factor (PHF) = 0.9100; number of lanes (N) = 4.0000; heavy vehicle adjustment factor (f_HV) = 0.8700; driver population factor (f_p) = 0.9600, determine the flow rate (v_p) in pc/h/ln.

Given

  • hourlyvolume(V)=3,050veh/hhourly volume (V) = 3,050 veh/h
  • peakhourfactor(PHF)=0.9100peak hour factor (PHF) = 0.9100
  • numberoflanes(N)=4.0000number of lanes (N) = 4.0000
  • heavyvehicleadjustmentfactor(fHV)=0.8700heavy vehicle adjustment factor (f_HV) = 0.8700
  • driverpopulationfactor(fp)=0.9600driver population factor (f_p) = 0.9600

Find

flow rate (v_p), in pc/h/ln

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except v_p is given, so isolate v_p symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that v_p stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 3,050 veh/h, peak hour factor (PHF) = 0.9100, number of lanes (N) = 4.0000, heavy vehicle adjustment factor (f_HV) = 0.8700, driver population factor (f_p) = 0.9600.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    vp=1003 pc/h/lnv_{p} = 1003\ \text{pc/h/ln}
  6. Step 6 — Check: returning v_p = 1,003 pc/h/ln to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
vp=1003 pc/h/lnv_{p} = 1003\ \text{pc/h/ln}

Why the other options are there

  • 2,006 — kept a factor of two that cancels in the correct rearrangement.
  • 501.6 — dropped that same factor in the other direction.
  • 1,104 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 2
Basic Freeway Segment Highway Capacity — solve for hourly volume — Basic Freeway Segment Highway Capacity (2)

highway capacity analysis of a basic freeway segment during peak hour Given peak hour factor (PHF) = 0.9100; number of lanes (N) = 3.0000; heavy vehicle adjustment factor (f_HV) = 0.9400; driver population factor (f_p) = 0.9400; flow rate (v_p) = 1,650 pc/h/ln, determine the hourly volume (V) in veh/h.

Given

  • peakhourfactor(PHF)=0.9100peak hour factor (PHF) = 0.9100
  • numberoflanes(N)=3.0000number of lanes (N) = 3.0000
  • heavyvehicleadjustmentfactor(fHV)=0.9400heavy vehicle adjustment factor (f_HV) = 0.9400
  • driverpopulationfactor(fp)=0.9400driver population factor (f_p) = 0.9400
  • flowrate(vp)=1,650pc/h/ln⁡flow rate (v_p) = 1,650 pc/h/\ln

Find

hourly volume (V), in veh/h

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

  3. Step 3 — List the givens: peak hour factor (PHF) = 0.9100, number of lanes (N) = 3.0000, heavy vehicle adjustment factor (f_HV) = 0.9400, driver population factor (f_p) = 0.9400, flow rate (v_p) = 1,650 pc/h/ln.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    V=3980 veh/hV = 3980\ \text{veh/h}
  6. Step 6 — Check: returning V = 3,980 veh/h to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
V=3980 veh/hV = 3980\ \text{veh/h}

Why the other options are there

  • 7,960 — kept a factor of two that cancels in the correct rearrangement.
  • 1,990 — dropped that same factor in the other direction.
  • 4,378 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 3
Basic Freeway Segment Highway Capacity — solve for number of lanes — Basic Freeway Segment Highway Capacity (3)

basic freeway segment capacity with heavy-vehicle traffic Given hourly volume (V) = 4,650 veh/h; peak hour factor (PHF) = 0.8600; heavy vehicle adjustment factor (f_HV) = 0.8800; driver population factor (f_p) = 0.8800; flow rate (v_p) = 1,880 pc/h/ln, determine the number of lanes (N).

Given

  • hourlyvolume(V)=4,650veh/hhourly volume (V) = 4,650 veh/h
  • peakhourfactor(PHF)=0.8600peak hour factor (PHF) = 0.8600
  • heavyvehicleadjustmentfactor(fHV)=0.8800heavy vehicle adjustment factor (f_HV) = 0.8800
  • driverpopulationfactor(fp)=0.8800driver population factor (f_p) = 0.8800
  • flowrate(vp)=1,880pc/h/ln⁡flow rate (v_p) = 1,880 pc/h/\ln

Find

number of lanes (N)

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except N is given, so isolate N symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that N stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 4,650 veh/h, peak hour factor (PHF) = 0.8600, heavy vehicle adjustment factor (f_HV) = 0.8800, driver population factor (f_p) = 0.8800, flow rate (v_p) = 1,880 pc/h/ln.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    N=3.7139N = 3.7139
  6. Step 6 — Check: returning N = 3.7139 to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
N=3.7139N = 3.7139

Why the other options are there

  • 7.4278 — kept a factor of two that cancels in the correct rearrangement.
  • 1.8570 — dropped that same factor in the other direction.
  • 4.0853 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 4
Basic Freeway Segment Highway Capacity — solve for flow rate (case 2) — Basic Freeway Segment Highway Capacity (4)

a basic freeway segment highway capacity analysis for a level-terrain freeway Given hourly volume (V) = 1,500 veh/h; peak hour factor (PHF) = 0.9600; number of lanes (N) = 4.0000; heavy vehicle adjustment factor (f_HV) = 0.9000; driver population factor (f_p) = 1.0000, determine the flow rate (v_p) in pc/h/ln.

Given

  • hourlyvolume(V)=1,500veh/hhourly volume (V) = 1,500 veh/h
  • peakhourfactor(PHF)=0.9600peak hour factor (PHF) = 0.9600
  • numberoflanes(N)=4.0000number of lanes (N) = 4.0000
  • heavyvehicleadjustmentfactor(fHV)=0.9000heavy vehicle adjustment factor (f_HV) = 0.9000
  • driverpopulationfactor(fp)=1.0000driver population factor (f_p) = 1.0000

Find

flow rate (v_p), in pc/h/ln

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except v_p is given, so isolate v_p symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that v_p stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 1,500 veh/h, peak hour factor (PHF) = 0.9600, number of lanes (N) = 4.0000, heavy vehicle adjustment factor (f_HV) = 0.9000, driver population factor (f_p) = 1.0000.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    vp=434.0 pc/h/lnv_{p} = 434.0\ \text{pc/h/ln}
  6. Step 6 — Check: returning v_p = 434.0 pc/h/ln to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
vp=434.0 pc/h/lnv_{p} = 434.0\ \text{pc/h/ln}

Why the other options are there

  • 868.1 — kept a factor of two that cancels in the correct rearrangement.
  • 217.0 — dropped that same factor in the other direction.
  • 477.4 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 5
Basic Freeway Segment Highway Capacity — solve for hourly volume (case 2) — Basic Freeway Segment Highway Capacity (5)

highway capacity analysis of a basic freeway segment during peak hour Given peak hour factor (PHF) = 0.9000; number of lanes (N) = 3.0000; heavy vehicle adjustment factor (f_HV) = 0.8800; driver population factor (f_p) = 0.9200; flow rate (v_p) = 900.0 pc/h/ln, determine the hourly volume (V) in veh/h.

Given

  • peakhourfactor(PHF)=0.9000peak hour factor (PHF) = 0.9000
  • numberoflanes(N)=3.0000number of lanes (N) = 3.0000
  • heavyvehicleadjustmentfactor(fHV)=0.8800heavy vehicle adjustment factor (f_HV) = 0.8800
  • driverpopulationfactor(fp)=0.9200driver population factor (f_p) = 0.9200
  • flowrate(vp)=900.0pc/h/ln⁡flow rate (v_p) = 900.0 pc/h/\ln

Find

hourly volume (V), in veh/h

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

  3. Step 3 — List the givens: peak hour factor (PHF) = 0.9000, number of lanes (N) = 3.0000, heavy vehicle adjustment factor (f_HV) = 0.8800, driver population factor (f_p) = 0.9200, flow rate (v_p) = 900.0 pc/h/ln.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    V=1967 veh/hV = 1967\ \text{veh/h}
  6. Step 6 — Check: returning V = 1,967 veh/h to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
V=1967 veh/hV = 1967\ \text{veh/h}

Why the other options are there

  • 3,935 — kept a factor of two that cancels in the correct rearrangement.
  • 983.7 — dropped that same factor in the other direction.
  • 2,164 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 6
Basic Freeway Segment Highway Capacity — solve for number of lanes (case 2) — Basic Freeway Segment Highway Capacity (6)

basic freeway segment capacity with heavy-vehicle traffic Given hourly volume (V) = 2,250 veh/h; peak hour factor (PHF) = 0.8800; heavy vehicle adjustment factor (f_HV) = 0.9300; driver population factor (f_p) = 0.8700; flow rate (v_p) = 2,020 pc/h/ln, determine the number of lanes (N).

Given

  • hourlyvolume(V)=2,250veh/hhourly volume (V) = 2,250 veh/h
  • peakhourfactor(PHF)=0.8800peak hour factor (PHF) = 0.8800
  • heavyvehicleadjustmentfactor(fHV)=0.9300heavy vehicle adjustment factor (f_HV) = 0.9300
  • driverpopulationfactor(fp)=0.8700driver population factor (f_p) = 0.8700
  • flowrate(vp)=2,020pc/h/ln⁡flow rate (v_p) = 2,020 pc/h/\ln

Find

number of lanes (N)

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except N is given, so isolate N symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that N stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 2,250 veh/h, peak hour factor (PHF) = 0.8800, heavy vehicle adjustment factor (f_HV) = 0.9300, driver population factor (f_p) = 0.8700, flow rate (v_p) = 2,020 pc/h/ln.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    N=1.5644N = 1.5644
  6. Step 6 — Check: returning N = 1.5644 to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
N=1.5644N = 1.5644

Why the other options are there

  • 3.1288 — kept a factor of two that cancels in the correct rearrangement.
  • 0.7822 — dropped that same factor in the other direction.
  • 1.7208 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 7
Basic Freeway Segment Highway Capacity — solve for flow rate (case 3) — Basic Freeway Segment Highway Capacity (7)

a basic freeway segment highway capacity analysis for a level-terrain freeway Given hourly volume (V) = 600.0 veh/h; peak hour factor (PHF) = 0.9200; number of lanes (N) = 3.0000; heavy vehicle adjustment factor (f_HV) = 0.9800; driver population factor (f_p) = 0.8700, determine the flow rate (v_p) in pc/h/ln.

Given

  • hourlyvolume(V)=600.0veh/hhourly volume (V) = 600.0 veh/h
  • peakhourfactor(PHF)=0.9200peak hour factor (PHF) = 0.9200
  • numberoflanes(N)=3.0000number of lanes (N) = 3.0000
  • heavyvehicleadjustmentfactor(fHV)=0.9800heavy vehicle adjustment factor (f_HV) = 0.9800
  • driverpopulationfactor(fp)=0.8700driver population factor (f_p) = 0.8700

Find

flow rate (v_p), in pc/h/ln

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except v_p is given, so isolate v_p symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that v_p stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 600.0 veh/h, peak hour factor (PHF) = 0.9200, number of lanes (N) = 3.0000, heavy vehicle adjustment factor (f_HV) = 0.9800, driver population factor (f_p) = 0.8700.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    vp=255.0 pc/h/lnv_{p} = 255.0\ \text{pc/h/ln}
  6. Step 6 — Check: returning v_p = 255.0 pc/h/ln to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
vp=255.0 pc/h/lnv_{p} = 255.0\ \text{pc/h/ln}

Why the other options are there

  • 509.9 — kept a factor of two that cancels in the correct rearrangement.
  • 127.5 — dropped that same factor in the other direction.
  • 280.5 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 8
Basic Freeway Segment Highway Capacity — solve for hourly volume (case 3) — Basic Freeway Segment Highway Capacity (8)

highway capacity analysis of a basic freeway segment during peak hour Given peak hour factor (PHF) = 0.8800; number of lanes (N) = 3.0000; heavy vehicle adjustment factor (f_HV) = 0.9700; driver population factor (f_p) = 0.9100; flow rate (v_p) = 640.0 pc/h/ln, determine the hourly volume (V) in veh/h.

Given

  • peakhourfactor(PHF)=0.8800peak hour factor (PHF) = 0.8800
  • numberoflanes(N)=3.0000number of lanes (N) = 3.0000
  • heavyvehicleadjustmentfactor(fHV)=0.9700heavy vehicle adjustment factor (f_HV) = 0.9700
  • driverpopulationfactor(fp)=0.9100driver population factor (f_p) = 0.9100
  • flowrate(vp)=640.0pc/h/ln⁡flow rate (v_p) = 640.0 pc/h/\ln

Find

hourly volume (V), in veh/h

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that V stands alone on the left-hand side.

  3. Step 3 — List the givens: peak hour factor (PHF) = 0.8800, number of lanes (N) = 3.0000, heavy vehicle adjustment factor (f_HV) = 0.9700, driver population factor (f_p) = 0.9100, flow rate (v_p) = 640.0 pc/h/ln.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    V=1491 veh/hV = 1491\ \text{veh/h}
  6. Step 6 — Check: returning V = 1,491 veh/h to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
V=1491 veh/hV = 1491\ \text{veh/h}

Why the other options are there

  • 2,983 — kept a factor of two that cancels in the correct rearrangement.
  • 745.7 — dropped that same factor in the other direction.
  • 1,641 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 9
Basic Freeway Segment Highway Capacity — solve for number of lanes (case 3) — Basic Freeway Segment Highway Capacity (9)

basic freeway segment capacity with heavy-vehicle traffic Given hourly volume (V) = 3,200 veh/h; peak hour factor (PHF) = 0.9500; heavy vehicle adjustment factor (f_HV) = 0.9400; driver population factor (f_p) = 0.9200; flow rate (v_p) = 1,630 pc/h/ln, determine the number of lanes (N).

Given

  • hourlyvolume(V)=3,200veh/hhourly volume (V) = 3,200 veh/h
  • peakhourfactor(PHF)=0.9500peak hour factor (PHF) = 0.9500
  • heavyvehicleadjustmentfactor(fHV)=0.9400heavy vehicle adjustment factor (f_HV) = 0.9400
  • driverpopulationfactor(fp)=0.9200driver population factor (f_p) = 0.9200
  • flowrate(vp)=1,630pc/h/ln⁡flow rate (v_p) = 1,630 pc/h/\ln

Find

number of lanes (N)

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except N is given, so isolate N symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that N stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 3,200 veh/h, peak hour factor (PHF) = 0.9500, heavy vehicle adjustment factor (f_HV) = 0.9400, driver population factor (f_p) = 0.9200, flow rate (v_p) = 1,630 pc/h/ln.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    N=2.3896N = 2.3896
  6. Step 6 — Check: returning N = 2.3896 to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
N=2.3896N = 2.3896

Why the other options are there

  • 4.7792 — kept a factor of two that cancels in the correct rearrangement.
  • 1.1948 — dropped that same factor in the other direction.
  • 2.6285 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

Example 10
Basic Freeway Segment Highway Capacity — solve for flow rate (case 4) — Basic Freeway Segment Highway Capacity (10)

a basic freeway segment highway capacity analysis for a level-terrain freeway Given hourly volume (V) = 3,050 veh/h; peak hour factor (PHF) = 0.9300; number of lanes (N) = 4.0000; heavy vehicle adjustment factor (f_HV) = 0.8600; driver population factor (f_p) = 0.9300, determine the flow rate (v_p) in pc/h/ln.

Given

  • hourlyvolume(V)=3,050veh/hhourly volume (V) = 3,050 veh/h
  • peakhourfactor(PHF)=0.9300peak hour factor (PHF) = 0.9300
  • numberoflanes(N)=4.0000number of lanes (N) = 4.0000
  • heavyvehicleadjustmentfactor(fHV)=0.8600heavy vehicle adjustment factor (f_HV) = 0.8600
  • driverpopulationfactor(fp)=0.9300driver population factor (f_p) = 0.9300

Find

flow rate (v_p), in pc/h/ln

Start with the thinking

  • The governing relation printed in this handbook section is Basic Freeway Segment Highway Capacity.
  • Everything except v_p is given, so isolate v_p symbolically first — never rearrange after the numbers are in.
  • Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
  • The basic freeway segment highway capacity relation converts hourly volume into an equivalent passenger-car flow rate per lane.

Step-by-step solution

  1. Step 1 — State the governing relation:

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}
  2. Step 2 — Rearrange the relation so that v_p stands alone on the left-hand side.

  3. Step 3 — List the givens: hourly volume (V) = 3,050 veh/h, peak hour factor (PHF) = 0.9300, number of lanes (N) = 4.0000, heavy vehicle adjustment factor (f_HV) = 0.8600, driver population factor (f_p) = 0.9300.

  4. Step 4 — Substitute the given values into the rearranged relation.

  5. Step 5 — Evaluate:

    vp=1025 pc/h/lnv_{p} = 1025\ \text{pc/h/ln}
  6. Step 6 — Check: returning v_p = 1,025 pc/h/ln to

    vp=VPHF⋅N⋅fHV⋅fpv_p = \dfrac{V}{PHF \cdot N \cdot f_{HV} \cdot f_p}

    reproduces the given quantities, and both sides carry the same units.

Answer:
vp=1025 pc/h/lnv_{p} = 1025\ \text{pc/h/ln}

Why the other options are there

  • 2,050 — kept a factor of two that cancels in the correct rearrangement.
  • 512.6 — dropped that same factor in the other direction.
  • 1,128 — rounded an intermediate value before the final step.

Reference: FE Handbook — Basic Freeway Segment Highway Capacity

© 2026 Dr. Steve Efe. Civil Engineering Capstone Studio. All rights reserved.