• Equation 22-10: Heavy vehicle adjustment factor.

  $f_{HV}=\frac{1}{1+P_T\left(E_T-1\right)}$

  (HCM7 Eq. 22-10)

Step 3: Determine Circulating and Exiting Flow Rates

The circulating flow rate (v_c) that opposes traffic entering the roundabout from a given leg comprises the following movements (assuming a four-leg roundabout):

• U-turn movement of the leg immediately to the right of the subject leg.
• U-turn and left-turn movements of the leg opposite of the subject leg.
• U-turn, left-turn, and through movements of the leg immediately to the left of the subject leg.

For example, the calculation of the circulating flow rate opposing the northbound entry leg is given by Equation 22-11 (uses results from Equation 22-9).

v_c,NB,pce = v_WBU,pce + v_SBL,pce + v_SBU,pce + v_EBT,pce + v_EBL,pce + v_EBU,pce

The exiting flow rate (v_ex) for a given leg comprises the following movements (assuming a four-leg roundabout):

• U-turn movement of the subject leg.
• Left-turn movement of the leg immediately to the right of the subject leg.
• Through movement of the leg opposite of the subject leg.
• Right-turn movement of the leg immediately to the left of the subject leg.

For example, the calculation of the exiting flow rate for the southbound exit leg is given by Equation 22-12 (uses results from Equation 22-9). Note that if a bypass lane is present on the immediate upstream entry (e.g., eastbound entry leg for a southbound exit leg), the right-turning flow using the bypass lane is deducted from the exiting flow.

v_ex,SB,pce = v_NBU,pce + v_WBL,pce + v_SBT,pce + v_EBR,pce − v_{EBR,pce,bypass}

Step 4: Determine Entry Flow Rates by Lane

• Exhibit 22-14: Assumed (de facto) lane assignments.
• Exhibit 22-15: Volume assignments for two-lane entries.

Step 5: Determine the Capacity of Each Entry Lane and Bypass Lane as Appropriate in Passenger Car Equivalents

• Exhibit 22-16: Capacity equations for entry lanes.

This exhibit identifies the capacity equation to use for different combinations of number of entry lanes (1 or 2) and number of circulating lanes (1 or 2). Due to the simplification of this analysis methodology for rural highways, that is, only considering roundabouts with single lane entries (with no bypass lane) and single circulating lanes, only Equation 22-1 is applicable.

c_e,pce = 1,380e^{(−1.02 × 10 −3)}v_c,pce (HCM7 Eq. 22-1)

• Exhibit 22-17: Capacity equations for bypass lanes.

Again, because bypass lanes are not considered in the rural highway methodology, this calculation is skipped.

Step 6: Determine Pedestrian Impedance to Vehicles

Step 7: Convert Lane Flow Rates and Capacities into Vehicles per Hour

• Equation 22-13: Convert lane i flow rate from units of pc/h to veh/h; uses results from Equation 22-9 and Equation 22-15.

  v_i = v_i,PCE × f_hv,e (HCM7 Eq. 22-13)

• Equation 22-14: Calculate lane i capacity, in units of veh/h; uses results from Equation 22-15.

  c_i = c_i,PCE × f_hv,e × f_ped (HCM7 Eq. 22-14)

• Equation 22-15: Heavy vehicle adjustment factor for the entry lane; uses results from Equation 22-9.

Step 8: Compute Volume-to-Capacity Ratio for Each Lane

• Equation 22-16: Calculation of the volume-to-capacity ratio for lane i.

  $x_i=\frac{v_i}{c_i}$

  (HCM7 Eq. 22-16)

Step 9: Compute the Average Control Delay for Each Lane

• Equation 22-17: Calculation of the control delay for lane i.

  $d_i=\frac{3,600}{c}+900T\left[x-1+\sqrt{{\left(x-1\right)}^2+\frac{\left(\frac{3,600}{c}\right)x}{450T}}\right]+5\times \min \left[x,1\right]$

  (HCM7 Eq. 22-17)

Step 10: Determine LOS for Each Lane on Each Approach

The LOS for each approach, limited to a single lane per approach, is determined from Exhibit 22-8 based on the corresponding values of control delay.

Step 11: Compute the Average Control Delay and Determine LOS for Each Approach and the Roundabout As a Whole

• Equation 22-18: Calculation of the control delay for approach.

Because the analysis is limited to single-lane approaches, the approach delay value is equal to the lane delay value from Step 9.

• Equation 22-19: Calculation of the control delay for intersection.

  $d_{intersection}=\frac{{\displaystyle \sum d_i{v}_i}}{{\displaystyle \sum v_i}}$

  (HCM7 Eq. 22-19)

• Exhibit 22-8: LOS criteria (motorized vehicle mode); the LOS is determined for the major roadway through movement for the analysis direction.

  Control Delay (s/veh)	LOS
  –10	A
  >10–15	B
  >15–25	C
  >25–35	D
  >35–50	E
  >50	F

  If the v/c > 1.0, the LOS is F.

Step 12: Compute 95th Percentile Queues for Each Lane

9.2 Nomenclature

The following notations are used, individually or in combination, to designate vehicle movements and lanes at the roundabout:

• PCE: passenger car equivalent.

Direction

• NB: Northbound.
• EB: Eastbound.
• SB: Southbound.
• WB: Westbound.

Movement

• T: Through.
• L: Left turn.
• R: Right turn.
• U: U-turn.

For example, the circulating flow rate for the northbound approach, in units of passenger cars, would be notated as v_c,NB,pce. The volume for the southbound left-turn movement would be notated as v_SBL.