Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (2024)

Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve provides a transition between two tangent strips of roadway, allowing a vehicle to negotiate a turn at a gradual rate rather than a sharp cut. The design of the curve is dependent on the intended design speed for the roadway, as well as other factors including drainage and friction. These curves are semicircles as to provide the driver with a constant turning rate with radii determined by the laws of physics surrounding centripetal force.

Contents

  • 1 Fundamental Horizontal Curve Properties
    • 1.1 Physics Properties
    • 1.2 Application of Superelevation
    • 1.3 Geometric Properties
    • 1.4 Sight Distance Properties
  • 2 Demonstrations
  • 3 Examples
    • 3.1 Example 1: Curve Radius
    • 3.2 Example 2: Determining Stationing
    • 3.3 Example 3: Stopping Sight Distance
  • 4 Sample Problem
  • 5 Demonstrations
  • 6 Additional Questions
  • 7 Variables
  • 8 Key Terms

Fundamental Horizontal Curve Properties

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Physics Properties

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Aside from momentum, when a vehicle makes a turn, two forces are acting upon it. The first is gravity, which pulls the vehicle toward the ground. The second is centrifugal force, for which its opposite, centripetal acceleration is required to keep the vehicle on a curved path. For any given velocity, the centripetal force needs to be greater for a tighter turn (one with a smaller radius) than a broader one (one with a larger radius). On a level surface, side friction Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (2) serves as a countering force to the centrifugal force, but it generally provides very little resistance/force. Thus, a vehicle has to make a very wide circle in order to make a turn on the level.

Given that road designs usually are limited by very narrow design areas, wide turns are generally discouraged. To deal with this issue, designers of horizontal curves incorporate roads that are tilted at a slight angle. This tilt is defined as superelevation, or Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (3), which is the amount of rise seen on an angled cross-section of a road given a certain run, otherwise known as slope. The presence of superelevation on a curve allows some of the centripetal force to be countered by the ground, thus allowing the turn to be executed at a faster rate than would be allowed on a flat surface. Superelevation also plays another important role by aiding in drainage during precipitation events, as water runs off the road rather than collecting on it. Generally, superelevation is limited to being less than 14 percent, as engineers need to account for stopped vehicles on the curve, where centripetal force is not present.

The allowable radius Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (4) for a horizontal curve can then be determined by knowing the intended design velocity Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (5), the coefficient of friction, and the allowed superelevation on the curve.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (6)

With this radius, practitioners can determine the degree of curve to see if it falls within acceptable standards. Degree of curve, Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (7), can be computed through the following formula, which is given in Metric.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (8)

Where:

  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (9)= Degree of curve [angle subtended by a 30.5-m (100ft) arc along the horizontal curve

Application of Superelevation

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One place you will see steep banking is at automobile racetracks. These tracks do not operate in winter, and so can avoid the problems of banking in winter weather. Drivers are also especially skilled, though crashes are not infrequent. For NASCAR fans, the following table may be of interest.

Table: Banking at US Racetracks

TrackLength (miles)Banking (degrees)
Chicago Motor Speedway10.00
Infineon Raceway1.949
Watkins Glen International2.45
Pocono Raceway2.56.00
Homestead-Miami Speedway1.58.00
Indianapolis Motor Speedway2.59.00
Memphis Motorsports Park0.7511.00
Phoenix International Raceway111.00
Las Vegas Motor Speedway1.512.00
Martinsville Speedway0.52612.00
New Hampshire Int'l Speedway1.05812.00
California Speedway214.00
Kentucky Speedway1.514.00
Richmond International Raceway0.7514.00
Kansas Speedway1.515.00
Michigan International Speedway218.00
Nashville Speedway USA0.59618.00
North Carolina Speedway1.01722.00
Darlington Raceway1.36623.00
Atlanta Motor Speedway1.5424.00
Dover Downs Int'l Speedway124.00
Lowe's Motor Speedway1.524.00
Texas Motor Speedway1.524.00
Daytona International Speedway2.531.00
Talladega Superspeedway2.6633.00
Bristol Motor Speedway0.53336.00

Source: Fantasy Racing Zone by FSN

Geometric Properties

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Horizontal curves occur at locations where two roadways intersect, providing a gradual transition between the two. The intersection point of the two roads is defined as the Point of Tangent Intersection (PI). The location of the curve's start point is defined as the Point of Curve (PC) while the location of the curve's end point is defined as the Point of Tangent (PT). The PC is a distance Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (12) from the PI, where Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (13) is defined as Tangent Length. Tangent Length can be calculated by finding the central angle of the curve, in degrees. This angle is equal to the supplement of the interior angle between the two road tangents.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (14)

Where:

  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (15)= tangent length (in length units)
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (16)= central angle of the curve, in degrees
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (17)= curve radius (in length units)

The PT is a distance Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (18) from the PC where Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (19) is defined as Curve Length. Curve length can be determined using the formula for semicircle length:

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (20)

The distance between the PI and the vertex of the curve can be easily calculated by using the property of right triangles with Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (21) and Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (22). Taking this distance and subtracting off the curve radius Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (23), the external distance Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (24), which is the smallest distance between the curve and PI, can be found.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (25)

Where:

  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (26)= external distance (in length units)

Similarly, the middle ordinate Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (27) can be found. The middle ordinate is the maximum distance between a line drawn between PC and PT and the curve. It falls along the line between the curve's vertex and the PI.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (28)

Where:

  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (29)= middle ordinate (in length units)

Similarly, the geometric formula for chord length can find Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (30), which represents the chord length for this curve.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (31)

Sight Distance Properties

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Unlike straight, level roads that would have a clear line of sight for a great distance, horizontal curves pose a unique challenge. Natural terrain within the inside of the curve, such as trees, cliffs, or buildings, can potentially block a driver's view of the upcoming road if placed too close to the road. As a result, the acceptable design speed is often reduced to account for sight distance restrictions.

Two scenarios exist when computing the acceptable sight distance for a given curve. The first is where the sight distance is determined to be less than the curve length. The second is where the sight distance exceeds the curve length. Each scenario has a respective formula that produces sight distance based on geometric properties. Determining which scenario is the correct one often requires testing both to find out which is true.

Given a certain sight distance Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (33) and a known curve length Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (34) and inner lane centerline radius Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (35), the distance a sight obstruction can be from the interior edge of the road, Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (36) can be computed in the following formulas.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (37)

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (38)

Demonstrations

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Examples

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Example 1: Curve Radius

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Problem:

A curving roadway has a design speed of 110 km/hr. At one horizontal curve, the superelevation has been set at 6.0% and the coefficient of side friction is found to be 0.10. Determine the minimum radius of the curve that will provide safe vehicle operation.

Solution:

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (41)

Example 2: Determining Stationing

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Problem:

A horizontal curve is designed with a 600 m radius and is known to have a tangent length of 52 m. The PI is at station 200+00. Determine the stationing of the PT.

Solution:

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (45)

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (46)

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (47)

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (48)

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (49)

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (50)

Example 3: Stopping Sight Distance

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Problem:

A very long horizontal curve on a one-directional racetrack has 1750-meter centerline radius, two 4-meter lanes, and a 200 km/hr design speed. Determine the closest distance from the inside edge of the track that spectators can park without impeding the necessary sight distance of the drivers. Assume that the sight distance is less than the length of the curve, a coefficient of friction of 0.3, and a perception-reaction time of 2.5 seconds.

Solution:

With a centerline radius of 1750 meters, the centerline of the interior lane is 1748 meters from the vertex (1750 - (4/2)). Using the stopping sight distance formula (See Sight Distance), SSD is computed to be 664 meters. With this, the distance from the track that spectators can be parked can easily be found.

Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (53)

This gives the distance (31.43 m) to the center of the inside lane. Subtracting half the lane width (2m in this case) would give the distance to the edge of the track, 29.43 m.

Sample Problem

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Problem (Solution)

Demonstrations

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Additional Questions

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  • Homework
  • Additional Questions

Variables

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  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (54) - Centerline Curve Radius
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (55) - Degree of curve [angle subtended by a 30.5-m (100ft) arc along the horizontal curve
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (56) - tangent length (in length units)
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (57) - Deflection angle of curve tangents. Also central angle of the curve, in degrees.
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (58) - External. Smallest distance between the curve and PI
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (59) - Middle ordinate
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (60) - Curve Length
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (61) - Chord Length
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (62) - Sight Distance
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (63) - Acceptable distance from inner edge of road for a sight obstruction to be placed without impeding sight distance
  • Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (64) - Radius of innermost lane centerline

Key Terms

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  • PC: Point of Curve
  • PI: Point of Tangent Intersect
  • PT: Point of Tangent
Fundamentals of Transportation/Horizontal Curves - Wikibooks, open books for an open world (2024)

FAQs

What are the four types of horizontal curves? ›

A curve may be simple, compound, reverse, or spiral (figure l). Compound and reverse curves are treated as a combination of two or more simple curves, whereas the spiral curve is based on a varying radius. The simple curve is an arc of a circle.

What is the purpose of the horizontal curve? ›

A horizontal curve provides a transition between two tangent strips of roadway, allowing a vehicle to negotiate a turn at a gradual rate rather than a sharp cut. The design of the curve is dependent on the intended design speed for the roadway, as well as other factors including drainage and friction.

What is PC in horizontal curve? ›

PI = Point of Intersection of back tangent and forward tangent. PC = Point of Curvature. This is the point of change from back tangent to circular curve. PCC = Point of Compound Curvature for compound horizontal curves. PT = Point of Tangency.

How to design a road curve? ›

  1. 1 Determine the design speed. The design speed is the maximum safe speed that vehicles can travel on a highway segment, under ideal conditions. ...
  2. 2 Calculate the minimum radius. ...
  3. 3 Design the superelevation. ...
  4. 4 Determine the length of curve. ...
  5. 5 Draw the curve layout. ...
  6. 6 Check the curve design. ...
  7. 7 Here's what else to consider.
Feb 21, 2024

What are the 3 types of curves? ›

A curved shape can be two-dimensional, like circles, ellipses, parabolas, and arcs. Curved shapes can also be three-dimensional figures like spheres, cones, and cylinders.

What is SSD in highway? ›

STOPPING SIGHT DISTANCE (SSD) :

➢Stopping sight distance (SSD) is the minimum sight distance available on a highway at any spot having sufficient length to enable the driver to stop a vehicle travelling at design speed, safely without collision with any other obstruction.

Why do horizontal curves have a high crash rate? ›

Improving the Safety of Horizontal Curves. The majority of these accidents and fatalities occur when drivers are speeding or not paying attention, causing them to miss the curve and leave the road. About three-quarters of curve-related fatal crashes involve single vehicles leaving the roadway.

What is the radius of a horizontal curve? ›

The allowable radius R for a horizontal curve can then be determined by knowing the intended design velocity V, the coefficient of friction, and the allowed superelevation on the curve. R=v2g(e+fs) With this radius, practitioners can determine the degree of curve to see if it falls within acceptable standards.

How to calculate the curve of a road? ›

A road is curvier if it takes a less-direct path than a separate road. By this definition, we could quantify the curvature of a road by dividing the straight-line distance between the start and end points of the road by the full length of the road.

What is the formula for super elevation? ›

The rate of change in superelevation is found by dividing the difference between normal crown and full super by the transition length. 11000 – 10971.61 = 28.39. The rate of change is the same as for the transition at the beginning end of the curve (. 0004177).

What is pi in surveying? ›

Point of Intersection (PI)

The point of intersection marks the point where the back and forward tangents intersect. The surveyor indicates it as one of the stations on the preliminary traverse.

Why are roads slanted? ›

Pavement cross slope is an important cross-sectional design element. The cross slope drains water from the roadway laterally and helps minimize ponding of water on the pavement.

How do you drive fast on a curve? ›

Once you're into the curve, keep looking as far around the curve as possible. This gives you time to react to hazards and helps you take the best and smoothest course through the curve. Unless you need to brake to slow down, keep gentle pressure on the accelerator to maintain speed through the curve. Don't coast.

Why are horizontal curves important? ›

Why are Horizontal Curves Needed? help offset centripetal forces developed as the vehicle goes around a curve. Along with friction, they are what keeps a vehicle from going off the road.

What are the four types of road curves? ›

There are several types of curves including simple, compound, reverse, and transition curves. A simple circular curve connects two tangents with a single arc, and is defined by its radius or degree.

What are the four special curves? ›

The document discusses different types of special curves including cycloids, involutes, spirals, and helices. Cycloids are curves generated by a point on a circle rolling along a straight line, and are used in gear tooth profiles.

What type of curves are used in horizontal alignment? ›

The horizontal alignment is a series of horizontal tangents (straight roadway sections), circular curves, and spiral transitions used for the roadway's geometry. This design shows the proposed roadway location in relation to the existing terrain and adjacent land conditions.

What are the different types of curves in surveying? ›

Curves are classified based on their characteristics and geometrical properties. These include circular curves, compound curves, reverse curves, and spiral curves.

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