5.  Horizontal Alignment Checks

This section describes each horizontal alignment element check. Included in the discussion is a definition of the check, the input data requirements, the PRM check process, boundary and rounding conditions, special conditions, and the output generated by the PRM for each check. Notes are made to illustrate the differences among the 1990, 1994, 2001 and 2004 editions of the AASHTO A Policy on Geometric Design of Highways and Streets (AASHTO policy).

There is a general consensus of state DOTs and the FHWA that there are 13 controlling geometric elements that are of sufficient importance and are basic to the operational quality of the road, and so should explicitly be considered in design exceptions. Nine of these geometric elements are reviewed in the IHSDM policy checks.

The following horizontal alignment checks are included in this section (those denoted with * are controlling criteria):

• Radius of Curve*
• Superelevation*
• Superelevation Transition Design (not available in the current release of IHSDM)
• Length of Horizontal Curve
• Compound Curve Ratio

Table 13., Summary of Input Data Requirements for Horizontal Alignment Checks summarizes the input data required to perform each horizontal alignment check.

5.1  Radius of Curve

Radius of curve is a basic design parameter for horizontal curves. Radius of curve is among the 13 controlling criteria. AASHTO design policy references a recommended minimum radius of curve for a given design speed and maximum superelevation rate (e) so as not to exceed a maximum side friction factor (f). The maximum side friction factor is a function of design speed. One set of factors is provided for rural highways, urban freeways, and high-speed urban streets; IHSDM uses this set. Another set is provided for low-speed urban streets, which is not used by IHSDM. AASHTO also provides guidance on the selection of a maximum superelevation rate (4, 6, 8, 10, or 12 percent). The recommended minimum radius of curve for a given design speed corresponds with the use of the maximum superelevation rates.

The PRM checks the radius of curve for a given design speed relative to the recommended minimum radii referenced in AASHTO Policy. Other checks evaluate the superelevation rate and superelevation transition (future release) from tangent alignment into the curve.

5.1.1  Input Data Requirements

To check radius of curve, the following data must be input by the PRM user:

• Evaluation Bounds (Start Station and End Station)
• Maximum superelevation for the evaluation (4, 6, 8, 10, and 12 percent)
• Horizontal alignment data
• Vertical alignment data
• Functional classification (local, collector, or arterial)
• Design speed
• Surface type (paved, aggregate)
• Superelevation of each curve (derived from cross slope)

5.1.2  The PRM Process

Using the maximum superelevation, design speed, and the curve radius from the IHSDM highway data, the PRM compares the road value to the recommended minimum radius referenced in Table III-6 of the 1990 and 1994 AASHTO policies or Exhibit 3-14 of the 2001 AASHTO policy or Exhibit 3-15 of the 2004 AASHTO policy. The radius of a given horizontal curve is reported to fall within controlling criteria for the specified design speed if it is greater than or equal to the recommended minimum radius referenced in AASHTO policy.

The PRM also calculates an "effective design speed" for each horizontal curve. Effective design speed, V(eff), is determined using the following equations:

V(eff) = (127*R[e+f])^1/2 ;where e = superelevation rate and f = side friction (metric)

V(eff) = (15*R[e+f])^1/2 ; where e = superelevation rate and f = side friction (U.S.)

V(eff) is the maximum speed for the radius [R] and superelevation [e] of a given curve such that the resultant side friction factor does not exceed the maximum side friction factor for that speed as specified in Table III-6 in the 1990 and 1994 AASHTO policies, or Exhibit 3-14 in the 2001 AASHTO policy or Exhibit 3-15 of the 2004 AASHTO policy. The maximum superelevation specified for the evaluation is used to calculate effective design speed.

The PRM also evaluates the maximum superelevation specified for the evaluation. The PRM reports whether the maximum superelevation falls within or outside the range of recommended values referenced in policy, which are determined as follows.

• For rural local roads, the PRM references page 425 of the 1990 AASHTO policy, page 421 of the 1994 AASHTO policy, page 387 of the 2001 AASHTO policy, and page 383 of the 2004 AASHTO policy. For 1990 and 1994 AASHTO Policies the range of recommended values for maximum superelevation is from 4 to 10 percent for paved surfaces, and from 4 to 12 percent for aggregate surface roads. For 2001 and 2004 policies the recommended range is from 4 to 12 percent regardless of the pavement type.
• For rural collector roads, the PRM references page 472 of the 1990 AASHTO policy,, page 464 of the 1994 AASHTO policy, page 428 of the 2001 AASHTO policy, and page 424 of the 2004 AASHTO policy. For all policies the recommended range is from 4 to 12 percent for collectors.
• For rural arterials, the PRM references page 496 of the 1990 AASHTO policy, page 486 of the 1994 AASHTO policy [page 450 of the 2001 AASHTO policy] and page 446 of the 2004 AASHTO policy. For all policies the recommended range is from 4 to 12 percent for arterials.

Based on all AASHTO policies, use of 4% as maximum superelevation is limited to urban areas. Therefore, if the road value for maximum superelevation is 4% then this AASHTO recommendation would be reflected in the "Comment" column of the evaluation report.

5.1.3  Boundary Conditions and Rounding

All curve radii values are rounded to the nearest 0.01 m [0.01 ft].

5.1.4  Special Conditions

Three special cases are addressed in this section: compound curves, back-to-back spiral curves, and horizontal points of intersection (PIs).

For compound curves, the PRM checks separately the radius of each of the simple circular curves in the compound curve set.

For back-to-back spiral curves, there is no section of alignment that is defined as a simple circular curve. The PRM checks the value of radius at the common point of the two spirals (SS). At this point, there is a local, effective minimum radius. This local radius is checked against the recommended minimum radius referenced in policy.

Horizontal points of intersection without curves, i.e., horizontal deflections, are not evaluated by this check. So, PRM output provides no notice or mention of this condition.

5.1.5  Output

Results of the check are summarized in two tables of the PRM Evaluation Report: one for radius of curve, and one for maximum superelevation.

In the table for the radius of curve check, each row represents a horizontal curve. The table includes the following columns:

• Stations-Start and End: the station limits of the horizontal curve.
• Radius of Curve-Road and Policy:
  • The road value is the radius of the curve within the highway segment defined by the start and end stations.
  • The policy value is the recommended minimum radius referenced in the selected policy for the specified design controls.
• Effective Design Speed
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 14., Summary of Comment Statements for Radius of Curve Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

The table for maximum superelevation includes a single row for the evaluation bounds. The table includes the following columns:

• Stations-Start and End: the evaluation bounds.
• e_max Bounds-Road and Policy:
  • The road value is the maximum superelevation specified for the evaluation.
  • The policy values are the recommended range of maximum superelevation referenced in the selected policy for the specified design controls.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 15., Summary of Comment Statements for Maximum Superelevation Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

5.2  Superelevation

Superelevation refers to the banking of the plane of the highway section through the horizontal curve to counterbalance the lateral forces developed by the vehicle as it proceeds at speed through the curve. Superelevation is among the 13 controlling criteria.

AASHTO policy references a range of recommended maximum superelevation. These maximum superelevation rates are used for the sharpest curve (i.e., minimum radius of curve) referenced for a given design speed. For curves with radii larger than the minimum, AASHTO references a recommended design superelevation rate less than the maximum rate.

This check compares the superelevation rate of a given horizontal curve relative to the values referenced in AASHTO for design superelevation rates. A future check will evaluate the superelevation transition between approach and departure tangents and the horizontal curve.

5.2.1  Input Data Requirements

To check superelevation, the following data must be input by the PRM user:

• Evaluation bounds (Start Station and End Station)
• Maximum superelevation for the evaluation (4, 6, 8, 10, and 12 percent)
• Horizontal alignment data
• Vertical alignment data
• Functional classification (local, collector, or arterial)
• Design speed
• Surface type (paved, aggregate)
• Superelevation of each curve (derived from cross slope)

5.2.2  The PRM Process

The PRM determines the full superelevation of each curve from the cross slope data specified in the IHSDM highway data for the highway being evaluated. Prior to checking superelevation, the PRM must first establish whether the radius of curve is within controlling criteria, i.e., greater than or equal to the recommended minimum radius referenced in policy. AASHTO policy tables for design superelevation reference recommended values only for radii greater than or equal to the recommended minimum radius; therefore, the superelevation check can be performed only for curves with radii within controlling criteria. If the radius of a curve is less than the minimum radius referenced in policy, there are no design superelevation policy values to reference and, therefore, the superelevation check cannot be performed.

Using the maximum superelevation and the curve radius, the PRM checks to make sure that the road value for radius is greater than or equal to the recommended minimum radius referenced in Table III-6 of the 1990 and 1994 AASHTO policies [Exhibit 3-14 of the 2001 AASHTO policy or Exhibit 3-15 of the 2004 AASHTO policy]. If the road value for radius is less than the recommended minimum radius, then the process of checking superelevation for that curve is terminated and the appropriate output message is created. If the road value for radius is greater than or equal to the recommended minimum radius, then the PRM compares the road value for superelevation to the values presented in Tables III-8 to III-12 of the 1990 AASHTO policy, Tables III-7 to III-11 and Exhibits 3-21 to 3-25 of the 2001 AASHTO policy. The PRM performs straight-line interpolation between tabular values for radius and superelevation for these policies.

For the 2004 AASHTO policy, Exhibits 3-25 to 3-29 are used without interpolation. Instead, if the curve radius is between two radii in the table, the PRM chooses the superelevation corresponding to the smaller radius.

For 1990, 1994, and 2001 policies: for conditions resulting in policy values of "NC" (normal crown) or "RC" (remove adverse crown), the PRM reports policy values as "NC" and "RC," respectively. If the policy value for a given design speed, radius, and maximum superelevation falls between "RC" and the first numeric value in Tables III-8 to III-12 of the 1990 AASHTO policy, Tables III-7 to III-11 of the 1994 AASHTO policy or Exhibits 3-21 to 3-25 of the 2001 AASHTO policy, then the PRM sets "RC" equal to the road normal cross slope and interpolates between the numeric value and the road normal cross slope. For example, for a maximum superelevation of 8 percent, design speed of 80 km/h and a curve radius of 1750 m, the superelevation in Table III-9 of the 1994 AASHTO policy falls between "RC" (for R=2000 m) and 2.4 percent (for R=1500 m). If the road value for normal cross slope is 2 percent, then the PRM interpolates between 2 and 2.4 percent to arrive at a policy value of 2.2 percent.

Boundary conditions for superelevation designated as "NC" are handled in a more direct manner and interpolation between "NC" and "RC" is not required. The minimum radius for which "NC" design is appropriate is taken directly from the appropriate look-up table. For a given design speed, radii falling between "NC" and "RC" designations are assumed to be "RC." For example, in Table III-9 in the 1994 AASHTO policy [Exhibit 3-23 in the 2001 AASHTO policy], given a design speed of 80 km/h and a radius of 2400 m, the policy value would be "RC."

For the 2004 AASHTO policy:

• If the calculated superelevation policy value is equal to the absolute values of the normal cross slope, the PRM chooses RC as the policy value.
• If the calculated superelevation policy value is less than the absolute values of the normal cross slope, the PRM chooses NC as the policy value. For this policy, there is also an adjustment if the grade is steeper than 5%. In this case, instead of the actual design speed of the highway, the next highest design speed would be used in the calculations, if available.

The PRM reports that the road value for superelevation is close to controlling criteria if it is within plus or minus 0.1 percent of the relevant policy values. For example, if the relevant policy value is 3.4 percent and the road value is within the range of 3.3 to 3.5 percent, then the PRM will report that the road value is close to controlling criteria.

The PRM also compares the maximum superelevation rate specified for the evaluation against the range of recommended values referenced in policy. The PRM reports whether the specified maximum superelevation falls within or outside the range of recommended values referenced in policy. For rural local roads, the PRM references page 425 of the 1990 AASHTO policy, page 421 of the 1994 AASHTO policy, page 387 of the 2001 AASHTO policy, and page 383 of the 2004 AASHTO policy; the range of recommended values for maximum superelevation is from 6 to 10 percent for paved surfaces, and from 6 to 12 percent for aggregate surface roads. For rural collectors, the PRM references page 472 of the 1990 AASHTO policy, page 464 of the 1994 AASHTO policy and page 428 of the 2001 AASHTO policy. For rural arterials, the PRM references page 496 of the 1990 AASHTO policy, page 486 of the 1994 AASHTO policy, page 450 of the 2001 AASHTO policy and page 446 of the 2004 AASHTO policy. For rural collectors and arterials, the range of recommended values referenced in policy is 6 to 12 percent.

5.2.3  Boundary Conditions and Rounding

Road and policy values for superelevation rates are rounded to the nearest 0.01 percent.

5.2.4  Special Conditions

Five conditions are addressed in this section. The first condition is related to projects with normal cross slope steeper than -2.0 percent. The other four conditions are related to special conditions for simple curves, compound curves, back-to-back spiral curves, and horizontal points of intersection (PIs).

The policy values for superelevation rates of 1990, 1994, and 2001 AASHTO policies (Tables III-8 through III-12 in 1990 AASHTO, Tables III-7 through III-11 in 1994 AASHTO, and Exhibits 3-21 through 3-25 in 2001 AASHTO) imply a normal cross slope of no steeper than -2.0 percent. For a given Emax, design speed, and number of lanes, very flat curves require no superelevation (NC). For slightly sharper curves, superelevation at the normal cross slope rate (RC) is recommended. The condition of "RC" relates to removing adverse crown and superelevating at the normal cross slope rate. This implies that RC relates to a superelevation of no steeper than 2.0 percent. However, if the actual (design) normal cross slope is steeper than -2.0 percent, it is possible that the recommended superelevation rate for sharper curves (i.e., curves requiring superelevation greater than "RC") will actually be less than the "RC" value implied by the normal cross slope.

For example, given a two-lane road with an Emax of 8 percent, a design speed of 70 km/h, a curve radius of 1300 m, and a normal cross slope of -3.0 percent, the recommended superelevation rate is 2.2 percent. For a (flatter) curve with radius of 1500 m, a value of "RC" is recommended, i.e., superelevation at the normal cross slope rate of 3.0 percent. In this case, the RC rate (3.0 percent) is greater than the recommended rate for a sharper curve (2.2 percent). The users should consider this apparent anomaly in their analyses.

For the 2004 AASHTO policy, the PRM interpretation of page 166 is that what is reflected in the AASHTO Exhibits are examples for normal cross slope of -1.5%. Therefore, if the normal cross slope is steeper than 1.5% the curves whose superelevations in the exhibits are flatter than the normal cross slope do not require any superelevation and the policy value for the superelevation is NC.

For the 2004 AASHTO policy, if the superelevation policy value is between 1.5% and 2.5%, a practical superelevation adjustment can be obtained by retaining the shape of the normal traveled way cross section, but rotating it around the edge or centerline of the traveled way (page 166). In this circumstance, the road superelevation is evaluated by first checking whether the shape of the cross section is maintained, then whether the adverse cross slope on the high side of the road is removed. If both conditions are satisfied then the superelevation policy is met.

For simple curves, the superelevation value used by IHSDM is the "full superelevation," as reflected in the "Cross Slope Code" field of the cross slope data. It is independent from the superelevation at the midpoint of the curve. The "full superelevation" is the maximum superelevation within a given curve, and may not equal the superelevation at the curve midpoint if the maximum does not occur at the midpoint.

For compound curves, the PRM checks separately the superelevation of each simple circular curve in the compound curve set.

For back-to-back spiral curves, there is no section of alignment that is defined as a simple circular curve. The PRM checks the superelevation at the common point of the two spirals (SS). At this point, there is a local superelevation rate. This local superelevation rate is checked against the recommended design superelevation referenced in policy.

Horizontal points of intersection without a curve, i.e., horizontal deflections, are not evaluated by this check. The PRM output provides no notice or mention of this condition.

5.2.5  Output

Results of the check are summarized in three tables of the PRM Evaluation Report: one for design superelevation of each curve, one for the evaluation of the cross slope on non-superelevated flat curves and one for maximum superelevation specified for the evaluation.

In the table for design superelevation, each row represents a horizontal curve. The table includes the following columns:

• Stations-Start and End: the station limits of the horizontal curve.
• Superelevation-Road and Policy:
  • The road value is the full superelevation rate for the curve within the highway segment defined by the start and end stations.
  • The policy value is the recommended design superelevation rate referenced in the selected policy for the specified design controls.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 16., Summary of Comment Statements for Superelevation Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

The table for evaluation of the cross slope on non-superelevated flat curves includes the following columns:

• Stations-Start and End: the station limits of the horizontal curve.
• Side of Road: The side of the road (left, right or both) facing in the direction of increasing stations.
• Cross slope-Road and Policy:
  • The road value is the cross slope for the curve within the highway segment defined by the start and end stations.
  • The policy value is the recommended design normal cross slope referenced in the selected policy for the specified design controls.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 18, Summary of Comment Statements for Superelevation Check on Non-Superelevated Flat Curves lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

The table for maximum superelevation includes a single row for the evaluation bounds. The table includes the following columns:

• Stations-Start and End: the evaluation bounds.
• e_max Bounds-Road and Policy:
  • The road value is the maximum superelevation specified for the analysis.
  • The policy values are the range of maximum superelevation referenced in the selected policy for the specified design controls.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 17., Summary of Comment Statements for e_max Bounds Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

5.3  Superelevation Transition (not available in the current release of IHSDM)

The term superelevation transition design refers to the longitudinal and lateral design of the edges of pavement in advance of a horizontal curve that requires development of superelevation. The portion of the alignment over which the pavement slope is changed from a normal cross slope design to full superelevation is referred to as the transition. AASHTO describes two ways in which the transition can be designed: without spiral curves (i.e., from tangent to circular horizontal curve), and with a simple spiral curve between the tangent and circular curve.

Development of the superelevation is a final design detail. It is part of the process wherein elevations for both edges of pavement are designed or calculated. To test for transition design adherence to policy requires that the design be completed for the centerline as well as both edges of pavement.

Transitions effected on unspiraled alignments include two elements: tangent runout, and superelevation runoff. Tangent runout is that portion of the alignment over which the adverse cross slope is removed. Superelevation runoff represents the length of highway over which the development of full superelevation occurs, i.e., from the end of runout to the point at which full superelevation is achieved in the curve.

The AASHTO policy contains criteria on the lengths of runoff and on the relationship of pavement edge profiles to centerline profiles. In the case of two-lane rural highways, the axis of rotation typically used to attain superelevation is by way of revolving the traveled way with normal cross slopes about the centerline.

Another design control for the transition is the distribution of the superelevation runoff along the transition. For unspiraled designs, AASHTO references recommended values for the percentage of runoff located prior to the point of curvature (PC). For spiral transition designs, AASHTO notes that the development of full superelevation occurs on the spiral, with full superelevation at the point of spiral to curve (SC).

In most cases, superelevation transition design is a consideration in the design of tangent to curve alignment. In rare instances, transitions also are required for compound curvature. A review of the AASHTO Policy did not show any recommended values for lengths of superelevation transitions between compound curves; therefore, the PRM does not cover this instance.

When users request the superelevation transition check, the PRM checks all aspects of transition design, including runoff length, percentage of runoff on the tangent, whether or not the transition is within a spiral curve, the length of spiral, and the maximum relative profile gradient.

5.3.1  Input Data Requirements

To check the superelevation transition design, the PRM user must provide the following data:

• Evaluation bounds (Start Station and End Station)
• Maximum superelevation for the analysis (4, 6, 8, 10, and 12 percent)
• Horizontal alignment data
• Vertical alignment data
• Design speed
• Through lane width
• Through lane cross slope
• Superelevation of each curve (derived from cross slope)

5.3.2  The PRM Process

AASHTO policy describes five methods to distribute superelevation and side friction on highway curves. Method 5 distributes superelevation and side friction in a curvilinear relation with the inverse of the radius of curve. This method is commonly used for all curves with radii greater than the minimum radius of curvature on rural highways. The PRM employs Method 5 to check superelevation transition design for horizontal curves.

The PRM identifies a transition as being either an unspiraled transition or a spiral curve transition. For unspiraled transitions (tangent to curve, or curve to tangent), the program determines the location where runoff begins and where the actual full superelevation on the given curve is achieved and calculates the length of runoff transition.

For unspiraled transitions, the computed superelevation runoff length is compared to the recommended lengths of runoff referenced in Tables III-7 through III-11 in the 1994 AASHTO policy and Exhibits 3-21 through 3-25 of the 2001 AASHTO policy. The runoff lengths included in the 1994 AASHTO policy tables are for two- or four-lane cross-sections. In the case of three- or six-lane cross-sections, the length for a two-lane transition is multiplied by 1.2 or 2.0, respectively. The 2001 AASHTO policy provides adjustment factors for number of lanes rotated in Exhibit 3-28.

For unspiraled transitions, the PRM also checks the percentage of superelevation runoff effected on the tangent. The 1994 AASHTO policy references a recommended range of between 60 percent and 80 percent of the superelevation occurring on the tangent of an unspiraled transition. The 2001 AASHTO policy references a recommended range of between 60 and 90 percent of the superelevation occurring on the tangent of an unspiraled transition.

For spiral curve transitions, the PRM determines the location where the runoff begins and ends and determines whether the superelevation runoff is "effected over the whole of the transition curve," as recommended in the 1994 and 2001 AASHTO policies, this point. If the TS is within plus or minus 2 m [10 ft] of the start of the superelevation runoff and the ST is within 2 m of the start of full superelevation, then the PRM reports that the superelevation runoff is within the spiral. Then, the PRM determines the length of spiral and compares this length to the recommended length of runoff referenced in Tables III-7 through III-11 of the 1994 AASHTO policy, or in Exhibits 3-21 through 3-25 of the 2001 AASHTO policy. The appropriate length of spiral is the same as the length of runoff. The program incorporates straight-line interpolation between tabular values for radius, superelevation, and minimum length of runoff. The AASHTO policy addresses these lengths as minimums; hence, spirals longer than those specified by AASHTO are reported by the PRM as within the recommended values referenced in policy.

The PRM also checks relative gradients for profiles between the edge of the traveled way and the centerline against the recommended maximum relative gradients referenced in Table III-13 in the 1994 AASHTO policy and Exhibit 3-27 in the 2001 AASHTO.

5.3.3  Boundary Conditions and Rounding

The road and policy values in the runoff length and length of spiral analysis tables are rounded to the nearest 0.01 m [0.01 feet]. The road and policy values in the output tables for percentage of runoff on tangent and relative profile gradient are rounded to the nearest 0.01 percent.

5.3.4  Special Conditions

The horizontal alignment may contain compound curvature. Such curvature may require different superelevation rates for the two radii. The AASHTO Policy does not provide explicit guidelines for design of superelevation transitions in such cases. Therefore, the PRM is not able to check superelevation transitions between compound curves.

Boundary conditions exist in the design procedures that are accommodated in the program. These boundary conditions are between the NC and RC sections, and between RC and superelevated sections.

When radii resulting in policy values between RC and the first numeric value in a column are used, the PRM interpolates between RC and the first numeric value in the table. For example, given a normal cross-slope of 2.0 percent, design speed = 60 km/h, radius = 1100 m, and E-max = 8 percent, the policy value (from Table III-9) would be determined by interpolating between RC and 2.2 percent. Since the normal cross-slope is 2.0 percent, RC = 2.0 percent for radius = 1000 m. The policy value for radius = 1100 m would then be (2.0 + 2.2)/2 = 2.1 percent.

Boundary conditions for superelevation designated as NC are handled in a more direct manner and interpolation between NC and RC is not required. The minimum radius for which NC design is appropriate is taken directly from the appropriate look-up table. For a given design speed, radii falling between "NC" and "RC" designations are assumed to be RC. For example, in Table III-9, given a design speed of 80 km/h and a radius of 2400 m, the policy value would be RC.

Horizontal points of intersection without a curve, i.e., horizontal deflections, are not evaluated by this check. The PRM output provides no notice or mention of this condition.

In certain instances the alignment in the vicinity of the transition may pass through an intersection. In doing so, profile values for one or both edges of pavement may not be available. This is not interpreted as a violation of policy, but it will preclude completion of the analysis as outlined above. These cases are noted in the PRM Evaluation Report.

In checking the location of the superelevation transition relative to the spiral curve, a tolerance range of plus or minus 2 m [10 ft] on each end of the spiral curve is established.

5.3.5  Output

Results of the check are summarized in a series of tables in the PRM Evaluation Report; one for each of the following dimensions: runoff length, percent runoff on tangent, Is (superelevation) transition within spiral-, length of spiral, maximum relative profile gradient. The tables have the same general format. Each row represents one of the transitions (i.e., into or out of horizontal curve). The tables include the following common columns:

• Stations-Start and End: the station limits of the horizontal curve.
• End of curve-Exit or Entry, in the direction of increasing stations.
• Dimension checked-Road and Policy: The road value for the highway segment and the relevant policy value against which it is checked.
  • The road value is the dimension of the highway being evaluated within the segment defined by the start and end stations.
  • The policy value is the limiting value within the recommended range of values referenced in the selected policy.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 18., Summary of Comment Statements for Superelevation Transition Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

5.4  Length of Horizontal Curve

The length of curve is a design parameter that results from the selection of a design radius for a given deflection angle. AASHTO policy references recommended values for minimum length of curve in its discussion of general controls for horizontal alignment. The basis for the recommendation is primarily aesthetics, i.e., to avoid the appearance of a kink in the alignment at curves with small deflection angles.

5.4.1  Input Data Requirements

To check length of horizontal curve, the PRM user must provide the following data:

• Evaluation bounds (Start Station and End Station)
• Horizontal alignment data
• Vertical alignment data
• Functional classification (local, collector, or arterial)
• Design speed

5.4.2  The PRM Process

The PRM determines the length of each horizontal curve from the IHSDM highway data file for the highway being evaluated. For simple circular curves, the length of the curve is the road value. For curves with spirals on either or both ends, the road value for length of curve is the sum of the lengths of circular and spiral curves. For compound curves, the road value is the sum of the lengths of the two simple curves comprising the compound curve. These road values are then compared to the relevant policy values, which are determined as outlined below.

AASHTO policy values for length of horizontal curve vary by functional classification are referenced on p. 224 of the 1994 AASHTO policy and pp. 233-234 of the 2001 AASHTO policy. They are a function of design speed. Table 19., Recommended minimum length of curve referenced in policy for arterials summarizes the formulas for recommended minimum lengths for main highways. Table 20., Recommended minimum length of curve with small deflection angles summarizes formulas for recommended minimum length of curves with small deflection angles, which apply to all functional classifications.

Curve lengths on arterials are checked relative to the formula in both Table 19., Recommended minimum length of curve referenced in policy for arterials and Table 20., Recommended minimum length of curve with small deflection angles. Curve lengths on collector and local roads are checked relative to only Table 20., Recommended minimum length of curve with small deflection angles.

5.4.3  Boundary Conditions and Rounding

Road and policy values for length of horizontal curve are rounded to the nearest 0.01 m [0.01 ft].

5.4.4  Special Conditions

The AASHTO Policy reference to main highways has been interpreted as meaning roads functionally classified as arterial highways.

5.4.5  Output

Results of the check are summarized in one table of the PRM Evaluation Report. In the table, each row represents a horizontal curve. The table includes the following columns:

• Stations-Start and End: the station limits of the horizontal curve.
• Computed Curve Length-Road and Policy:
  • The road value is the length of the horizontal curve within the highway segment defined by the start and end stations.
  • The policy value is the recommended minimum length of horizontal curve referenced in the selected policy for the specified design controls.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 21., Summary of Comment Statements for Superelevation Transition Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The design controls for the highway being evaluated that are used to determine the relevant policy value.

5.5  Compound Curve Ratio

Compound curves are circular horizontal curves of different radii, with alignment in the same direction (i.e., not reverse curvature), with no tangent alignment between the curves. (Alignment comprised of consecutive curvature separated by a short tangent is referred to as broken-back alignment.) In its discussion of general controls for horizontal alignment, AASHTO policy references a recommended range of values for the ratio of the radii of the adjoining circular curves comprising the compound curve.

5.5.1  Input Data Requirements

To check compound curve ratio, the PRM user must provide the following data:

• Evaluation bounds (Start Station and End Station)
• Horizontal alignment data
• Vertical alignment data

5.5.2  The PRM Process

The PRM determines the curve radii for two circular curves that share a common point (i.e., point of compound curvature) from the IHSDM highway data for the highway being evaluated. The compound curve ratio is computed by dividing the larger radius by the smaller radius. These road values are then compared to the relevant policy values, which are determined as outlined below.

AASHTO (Pages 201 and 225 of the 1990 policy; Pages 199 and 225 of the 1994 policy; Pages 205 and 234 of the 2001 policy and Pages 201 and 230 of the 2004 policy) recommends that the ratio of the larger radius to the smaller radius should be not exceed a maximum of 1.5.

5.5.3  Boundary Conditions and Rounding

Road and policy values for compound curve ratio are rounded to the nearest 0.01.

5.5.4  Special Conditions

No special conditions are identified for compound curve ratio. Where no compound curve exists, the PRM review for compound curve ratio does not apply.

5.5.5  Output

Results of the check are summarized in one table of the PRM Evaluation Report. In the table, each row represents a compound curve. The table includes the following columns:

• Stations-Start and End: the station limits of the compound curve.
• Compound Curve Ratio-Road and Policy:
  • The road value is the ratio of the radii comprising the compound curve within the highway segment defined by the start and end stations.
  • The policy value is the maximum recommended ratio referenced in the selected policy.
• Comment: A statement summarizing the comparison of the road value and policy value for the highway segment. Table 22., Summary of Comment Statements for Compound Curve Ratio Check lists the possible comments for this check and provides a more detailed description of the situation they represent.
• Attributes: The station limits of each simple circular curve in the compound curve set.