BASIC TERMS OF ROAD GEOMETRY

Contour line = a line, which connects terrain points of the same elevation

Contour line interval (equidistance) = elevation difference between contour lines

Line of maximum slope = a line, which indicates the course of the slope (it is always perpendicular to the contour line)

Centre line = spatial line which defines horizontal and vertical alignment of the road

Horizontal alignment = top-view projection of spatial line to the horizontal plane defining the shape of the road in plan

Vertical alignment = side-view projection of spatial line in developed surface of vertical projection planes defining the shape of the road in profile

DESIGN OF ROAD CENTRE LINE

CHOICE OF THE HORIZONTAL CURVE RADUIS „R“

Road category (in the assignment) to determine the layout (a, v, c, e) according to fig. 0010 and fig. 0020:

Fig. 0010 (layout of two-lane roads)

Fig. 0020 (layout components of two-lane roads)

Assigned:

V [km/h] .... design speed (part of category road class)

Gmax [%] .... maximum longitudinal gradient (for the whole route)

Gradients (longitudinal, crossfall) – forms of expression (fig. 0030):

Fig. 0030 (methods of mathematical expressions of gradients)

a) form „G [%]“:

longitudinal gradient

crossfall – road surface, hard and soft shoulder

L

H100G

100

GLH

mLH

b) form „1:n“:

crossfall – fill and cut slopes of earth construction

To determine the minimum radius „RMIN“ of horizontal curve:

S

V0,3R

2

MIN

V [km/h] .... design speed (part of category road class)

S [%] ......... crossfall in a curve (superelevation) choose in a way it complies with:

6% 2,5% ;S

DETERMINATION AND CALCULATION OF SETTING OUT ELEMENTS OF CLOTHOID TRANSITION CURVE

Transition curve (clothoid) = mathematical curve with a linear increase of curvature (or rather of radius): part of clothoid is used for transition of radius value in the

interval R; (fig. 0040)

Fig. 0040 (setting out elements of clothoid transition curve)

road superelevation and line widening in a curve are developed on the length of transition curve or shorter

transition curve does not have to be used if:

horizontal curve radius R 800 m and also

R 0,375V2

curve offset p 0,25 m

Choosing type of superelevation:

around the centre line approximate estimate of the

transition curve length is L' V (used in the exercise)

around the channel line approximate estimate of the

transition curve length is L' 1,5 V

Draft of tangent polygon:

calculation of central angle of the curve „“ (according to fig. 0050) or simply measure the angle in CAD file

Fig. 0050 (determination of the curve central angle „“)

measure accurately API, PIB, CD, CPI!

calculate the angle „“:

CPI

CDarctgI

it is important to leave a sufficient reserve for transition curves as they will be inserted as follows:

50% of the transition curve in tangent (straight)

50% of the transition curve in curve

Choose the radius of horizontal curve „R“ according to the principles and assumptions:

R RMIN

R > 250 m no need to perform lane widening „W“ in the horizontal curve

Chosen value of „R“ must occur in the table of clothoid transition curves fig. 0060

Determine the minimum crossfall of the curve „Smin“:

R

V0,3S

2

min

[Smin] = %; [V] = km/h; [R] = m

Verify the condition: SSmin

The crossfall of road surface in straight section (the crossfall of “normal crown“) is 2,5 %

Basic setting out elements:

Determine clothoid parameter „A“ using the table fig. 0060:

km/hVm;L´V;L´

Estimate the clothoid parameter „A´“:

R´L´A

Determine the clothoid parameter „A“ from a line of the table fig. 0060 with corresponding value of horizontal curve radius „R“ and at the same time:

´AA

Fig. 0060 (setting out elements of clothoid transition curve)

Write down of the fig. 0060 the chosen value „R“, „A“ and the following setting out elements – L [m], p [m], K [m], X [m], Y [m], θs [g]

All data (except „ θs “) write down in „m“ to 2 decimal places, write down „ θs “ in grads to 5 decimal places

Pay attention to calculations on calculators / in MS Excel

convert „ θs “ from grads to degrees

360° = 400g 0,9° = 1g

Other setting out elements

tangent distance: 2

ItgpRTs

KTT s

length of circular part of the curve:

0θ2II sc

for [c] = °: 180

πIRarcIRL

ccc

for [c] = g: 200

πIRarcIRL

ccc

total length of the horizontal curve with transition curves:

sc L2LL all values (except „c“) write down in „m“ to 2 decimal

places, write down „c“ in degrees to 5 decimal places

DRAFTING OF ROAD CENTRE LINE The centre line is constructed either using a ruler and a curve bow or some Computer Aided Design (CAD) software. It is based on the knowledge of 7 points of the horizontal alignment (A; TS; SC; PI; CS; ST; B)

Process of drafting: (all dimensions are symmetric on both tangents – process according to fig. 0070 resp. fig. 0080)

dimension „T“ points TS and ST

dimension „X“ and dimension „Y“ points SC and CS

Fig. 0081 (setting out elements of horizontal curve with symmetric transition curves)

Fig. 0082 (setting out elements of horizontal curve with symmetric transition curves)

Calculation of chainage of 6 key points ([km]; 5 decimal places!!!):

A = 0, 000 00

TS = API – T

SC = TS + Ls

CS = SC + Lc

ST = CS + Ls

B = ST + BPI – T

DRAFTING INTO THE PLAN Draw all in red into the plan after approval !!! – according to fig. 0090 centre line (dot dashed line) points A, TS, SC, CS, ST, B (including chainage) chainage each 100 m – measure the location from the

nearest point with already calculated chainage table of the curve parameters top of the curve – point PI (Point of Intersection)

Fig. 0090 (example of the plan drawing)