The Ninth International Conference on Computing in Civil and Building Engineering
April 3-5, 2002, Taipei, Taiwan

FUNCTIONALIZATION OF HIGHWAY ALIGNMENTFOR COMPUTER-BASED DESIGN
K. Makanae1
1Department of Project Design, Miyagi University, Miyagi 981-3298, Japankoji@makalab.org

Abstract
Under the present highway design method, highway alignment is treated as the sequence of segments prescribedby the design speed. However this method is not useful for the advanced computer-based design. This paper
shows the functionalization of highway alignment for computer-based design. Curvature and gradient functions
are defined for a highway alignment. By functionalization of highway alignments, cross fall and widening arecalculated, thus 3 dimensional highway geometric models can be defined automatically.

Introduction
The horizontal trajectory of a traveling automobile is determined by variations of velocity
with time and variations of curvature by maneuvering. The vertical trajectory depends onvariations of velocity and gradient with time. Time, velocity, curvature and gradient, therefore,
need to be represented by coordinates in the design space at a certain point in the design
process. Conventional design methods avoid conversion to space coordinates in the designprocess. They position instead elements of a two-dimensional alignment that are suitable to atime-velocity-curvature or time-velocity-gradient system on a plan or profile in advance(Lorenz, 1971; AASHTO, 1994).
The method proposed in this study is aimed at computerizing highway geometric design bydefining a highway alignment based on functionalization of curvature and gradient that use
distance as a parameter.
Functionalization of highway alignment
On the assumption of an automobile traveling at a constant velocity, a time-velocity-curvaturesystem can be expressed by distance. Time-velocity-curvature and time-velocity-gradientsystems can be regarded to be equivalent to distance-curvature and distance-gradient systems,
respectively. Here, functions with the horizontal distance along a highway alignment as aparameter in each system are defined as the curvature and gradient functions. The curves on
the curvature and gradient diagrams drawn as a result of horizontal and vertical design byexisting design methods.
The method proposed in this study handles these curves as functions that determine highwayalignments and thereby tries to design highway alignments in a process reverse toMakanae

conventional methods. Horizontal and curvature functions can be represented by continuous
piecewise linear functions and can be specified by the list of turning points of curvature andgradient with the distance.
A driver traveling along a continuous highway alignment turns the steering wheelcontinuously. Then curvature function Θ(l ) is becomes also continuous. Θ(l ) may thus beregarded as a continuous piecewise linear function. Θ(l ) at distance l in section n (n = 1, 2,3…) is expressed as shown in Eq.(1). Curvature function Θ(l ) can be defined by given (ln,θ n ) as a boundary condition.
Θ(l ) = ∆θ (l − l ) + Θ(l )nn −1n −1θ − θ n−1
∆θ n = nl n − l n−1(1)where,ln : distance at the end of section n (where l0 = 0)
θ n : curvature at the end of section n ( θ 0 is the initial curvature)∆θ n : rate of change in curvature in section n
For existing design methods, elements of a vertical alignment consist of straight lines andvertical curves. For vertical curves, parabolic curves are generally used. Gradient, which is adifferential of vertical alignment, is then represented by a linear expression. Since verticalgradient is continuous as well as horizontal alignment, gradient function J(l) at distance l insection n ( n = 1, 2,3…) is represented by equation shown in Eq.(2). Thus, gradient function
J(l) can be defined by boundary condition (ln, jn)
 J ( l ) = ∆ j (l − l ) + J ( l )nn −1n −1j − j n −1∆j n = nl n − l n −1(2)where,
jn : gradient at the end of section n ( j0 is the initial gradient)∆j n :rate of change in gradient in section n

Schema of Geometric Design Model

This study uses an undivided two-lane highway without a sidewalk as a basic model. Here,design speed, width of the traffic lane and shoulder, and standard value of crossfall aredefined as the initial values.

MakanaeLayer 3
Expansion
Condition

Layer 1
BasicConditions

Layer 2
DesignConditions

design speed

max.crossfall
sight distancemax. rate ofchange ingradientmin. length oftransition curve

Layer 6
Expansion

3D coordinates ofcenter line

mileage interval
for the expansion
of 3D geometry

max. curvature

max. crossfall

standardlane width

Layer 5
Supplementary
Information

gradient
function J(l)cornering force
coefficient

vehicle type

Layer 4
DesignInformation

length ofcrossfalltransitions

Cuvature function
Θ(l)Super elevationI'(l)3D coordinates ofthe edge of lanes

lane widthWl(l)standard
shoulder widthroad width(one side)W(l)standard
crossfall
design conditions

3D coordinates ofthe edge of shoulders

functions for defining highway geometry

Fig. 1 : Schema of geometric design model

Based on the boundary conditions for curvature and gradient function, 3D coordinates of thehighway alignment can be defined. Crossfall and widths of the lane can be determined by thecurvature functions automatically. Thus, a 3D highway geometric design model can be built
in the design space.
Restrictions are placed on curvature and gradient functions in view of the comfort and safetyof the occupants of the traveling vehicle. The restrictions considered in this study are shown
below:- Maximum curvature- Minimum length of transition curve- Vertical gradient- Length of vertical circular curve

The modeling process of the 3D highway geometry can be classified into 6 layers
schematically (Fig. 1).
-Layer 1 provides the most basic information on the highway to be designed, and defines
such elements as the design velocity, design vehicle, basic lane width, basic
shoulder width and basic cross slope.
Makanae-Layer 2 provides conditions for defining the curvature and gradient functions that define
the alignment.
-Layer 3 shows conditions that define the conditions for expanding curvature and gradientfunctions.
-Layer 4 provides data that define curvature and gradient functions, backbone of thegeometric design defined by the design engineer, which are the boundary
conditions of the functions.
-Layer 5 provides preliminary data for defining a geometric design based on the highwayalignment defined in Layer 4. The data are obtained automatically.
-Layer 6 shows the results of expansion to the design space of the highway geometric
design built based on the data defined in Layers 4 and 5.
Development of Geometric Design System Prototype

A prototype of a highway geometric design system was developed. Under the system, thedesign engineer sets curvature and gradient functions while constantly monitoring thegeometric design expanded on the design space, by repeating a procedure at a high speed forsetting the functions temporarily, expanding them to the design space and drawing analignment. For following the procedure, interactive response by GUI and high-speed
computing are essential.
In order to speed up drawing and computing, an array is defined for each increment indistance to store all the information required for the expansion in the design space. At thesame time as when the curvature and gradient functions are set, re-calculation is carried out
for the information in the array, and an alignment is drawn accordingly.
Fig.2 shows the prototype’s GUI. Curvature and gradient functions are set in two windows at
the bottom of the screen by a mouse. Then, a three-dimensional design model is automatically
expanded based on the predetermined basic design conditions. Graphics showing thehorizontal alignment, perspectives (showing driver's view and bird's-eye view), verticalalignment, crossfall and width increase are updated and drawn simultaneously. In design, theengineer determines boundary conditions for curvature and gradient functions one by one
while constantly monitoring information that is updated with the movement of a cursor by amouse.
The boundary conditions for respective functions are set so as not to deviate from the range
specified by the restrictions. The design engineer can, therefore, carry out design without
being aware of parameters for elements of the alignment such as the radius of a circular curveand clothoid. Also shown as required is the area required for securing combined gradient andsight distance that have not been given as conditions controlling curvature and gradientfunctions.

MakanaeFig.2: GUI of the geometric design system

Benefits of Geometric Design System

The geometric design system using curvature and gradient functions produces the following
benefits.
-Setting only of curvature and gradient functions enables automatic definition of geometric
design and immediately provides three-dimensional data.
-Curvature and gradient functions are simple piecewise linear functions, and enable thedesign engineer to carry out design without considering parameters of clothoids orcircular curves.
-Curvature and gradient functions are always continuous and guarantee the continuity of
the highway alignment.
-Three-dimensional data for geometric design may be used to easily display twodimensional drawings and three-dimensional prospects. Thus, design and evaluation canbe performed simultaneously.
-Transmission of precise design information is possible only with a few data. Data
processing is also easy.
MakanaeConclusion

This study has illustrated that highway geometric design can be determined basically bycurvature and gradient functions with distance l as a variable. It has also been indicated thatbuilding a geometric design model by these functions can increase the efficiency of computerbased design.
By the method shown in this paper, conditions concerning design standards are provided to acomputer as numerical functions with the design velocity, and curvature and gradient asvariables. The design method is totally different from existing methods based on drawing(Beilfuss and Guess, 1990). The design engineer can now obtain an alignment that meets
design standards without being aware of alignment parameters. Wasteful drawing work isreduced, and design efficiency is increased. Since alignment design becomes possible while
monitoring a three-dimensional highway alignment, visual evaluation, or verification of how
the alignment looks to driver's eyes, is now possible. Thus, the quality of design is expected
to increase.
In the field of highway engineering as well as in other fields, product models are now being
developed (OKSTRA, landXML etc.). For defining highway alignments, however, existing
methods based on alignment parameters are still being used. The geometric design model
built by the method proposed in this paper can be expanded in the three-dimensional design
space with fewer data more precisely with the object format being maintained. Complicatedmodels such as intersection models that are made based on the geometric design model can beused as product models.

References
Autodesk(2000): http://www.landxml.org.
Lorenz, H. (1971): TRASSIERUNG UND GESTALTUNG VON STRASSEN UND AUTOBAHNEN,
Bauverlag GmbH, Wiesbaden & Berlin.
OKSTRA(2001): Objektkatalog für das Straßen- und Verkehrswesen, http://www.okstra.de/.
ASSHTO(1994): A Plicy on Geometric Design of Highways and Street, AASHTO.
Beilfuss, C.W. and Guess, R.R.：Development of a Roadway Design/Graphics Interface System, Transportation
Research Board, 1990.

Makanae