Road design and analysis in highway engineering involve the proper positioning of the physical elements of the roadways by the standards and constraints. The main objectives of road design and analysis are to ensure safety, optimize efficiency and as well minimize environmental damage and construction cost. Road design and analysis also take into consideration community goals, such as providing access to employment, schools, businesses, and residences to accommodate a range of travel modes such as automobiles, bicycling, transit, and walking, as well as minimizing emissions, fuel use, and other environmental damages.

Roadway design and analysis can be subdivided into three main parts which provide a three-dimensional layout for a roadway as follows:

**Profile:**That is the vertical aspect of the road, including sag curves and crest, and the straight grade lines that connect them.**Alignment:**This is the route of the road, defined as a series of horizontal tangents and curves.**Cross-section**: This shows the position and number of vehicle and bicycle lanes, and sidewalks, alongside their cross slope and likewise drainage features, pavement structure, and other items outside the design category.

## Road Design Standards

Generally, roads are designed by design guidelines and standards adopted by national or sub-national authorities such as states, provinces, territories, or municipalities. Usually, design guidelines take into consideration vehicular speed, vehicle type, road slopes, stopping distance, and view obstructions. A good engineering judgment alongside the proper application of design standards and guidelines, an engineer can afford a design of roadway that is safe, comfortable, and aesthetically appealing.

The US road design guidelines are found in a Policy on Geometric Design of Highways and Streets published by AASHTO. Other design standards and guidelines include the Australian Guide to Road Design and the British Design Manual for Roads.

## Road Profile

Road profile usually consists of road slopes, also known as grades, which are connected by vertical curves. These curves are used to provide a subtle change from one road grade to another, to ensure smooth navigation of vehicles along with the grade changes as they travel.

### Sag Vertical Curves

Sag vertical curves are curves with a higher tangent slope or grade at the end of the curve compared to the beginning of the curve. Usually, a sag curve on a road would appear as a depression or a valley, with the moving vehicle going downhill first before reaching the bottom of the curve and continuing uphill.

In sag vertical curves design, the most important design criterion is the headlight sight distance. When driving on a sag curve at night, the headlight sight distance is limited by the higher slope in front of the vehicle. This distance must be long enough to enable the driver to see any form of obstruction on the road to stop the vehicle within the headlight sight distance. Usually, the headlight sight distance is determined by the angle of the headlight and the angle of the tangent grade at the end of the curve. In finding the headlight sight distance and then calculating the curve length (L) as seen in the equations below, the curve length can be accurately determined.

Unit |
Headlight Sight Distance < Curve Length (S < L) |
Headlight Sight Distance > Curve Length (S > L) |

Metric(S in metres) |
L= AS^{2} /(120 + 3.5S) |
L = 2S – (120 + 3.5S) / A |

### Crest Vertical Curves

Crest vertical curves are also curves that have a lower tangent grade at the end of the curve compared to the beginning of the curve. For a moving vehicle driving on a crest curve, the road appears as a hill, with the moving vehicle first going uphill before reaching the top of the curve and then going downhill.

In crest vertical curves design the most important criterion for designing such curves is stopping sight distance. This distance is the maximum distance a driver can view over the crest of the curve. It is determined by the vehicular speed of traffic on a roadway by finding the stopping sight distance (S) and then calculating the curve length (L) in each of the equations below. The accuracy of the equation depends on whether the crest vertical curve is shorter or longer than the available sight distance. Both equations are solved, and then the results are compared to the curve length.

Unit |
Headlight Sight Distance < Curve Length (S < L) |
Headlight Sight distance > Curve Length (S > L) |

Metric(S in metres) |
L= AS^{2} /200(√h1 + √h2)^{2} |
L = 2S – 200(√h1 + √h2)^{2} / A |

### Symbols Used For Road Profiling

- BVC = Beginning of Vertical Curve
- EVC = End of Vertical Curve
- PVI = Point of Vertical Interception (intersection of initial & final slopes)
*A*= Absolute value of the difference in slopes (initial minus final), usually expressed in %*S*= headlight sight distance*L*= curve length (along the*x*-axis)*x*= horizontal distance from BVC*Y*= Vertical Distance from the Initial tangent point to a point on the curve*Y*′ = Curve Elevation = T_{g}—*Y (offset)*- = initial roadway slope, expressed in %
- = final roadway slope, expressed in %
- = height of eye above the roadway, measured in meters or feet
- = height of an object above the roadway, measured in meters or feet
- T
_{g}= Elevation of a point along the initial tangent.

## Horizontal Alignment

Horizontal alignment in road design and analysis comprises straight sections of road, also known as tangents, which are connected by circular horizontal curves. Typical circular curves are determined by radius and deflection angle. The design and analysis of a horizontal curve require the determination of a minimum radius (using the speed limit), then the curve length, and the objects obstructing the view of the driver.^{}

Based on AASHTO standards, if a horizontal curve has a high speed and a small radius, a high bank or superelevation is required to ensure safety, and if there is an obstructing object around a curve, the engineer must ensure that drivers’ stopping sight distance is far enough to stop to avoid an accident or accelerate to join the traffic.

### Road Design Geometry

**T = Rtan (Δ/2)**

**C = 2Rsin(Δ/2)**

**L = Rπ(Δ/180)**

**M = R[1-cos(Δ/2)]**

**E = R[{1/cos(Δ/2)}-1] **

Where:

- R = Radius
*T*= tangent length*L*= curve length*E*= external distance- BC = Beginning of Curve
- EC = Cnd of Curve
- PC = point of curvature i.e point at which the curve begins)
- PT = point of tangent i.e the point at which the curve ends)
- PI = point of intersection i.ethe point at which the two tangents intersect)
*C*= long chord length i.e straight line between PC and PT*M*= horizontal sightline offset HSO usually known as middle ordinate, – (distance from the sight-obstructing object to the middle of the outside lane)- = coefficient of side friction
*u*= vehicle speed- Δ = deflection angle