DESIGN PROBLEM $2$

A transition curve is required for a dual carriageway road with a design

speed vdesign $=27\mathrm{.}78$ m$/$s$.$ The bearings of the two straights defining the

cuve are bearing $1(25)$and bearing $2(50).$ Assuming absolute minimum

conditions of design for the minimum radius R of the circular curve $($in

reference to the applicable value superelevation e$),$ and a value of C $(0\mathrm{.}60),$ identify the

followings:

$2\mathrm{.}1.$ The transition length, L $(2$ d$.$p$.).$

$2\mathrm{.}2.$ The shift, S $(2$ d$.$p$.).$

$2\mathrm{.}3.$ The length along the tangent required from the intersection point to

the start of the transition, IT$(2$ d$.$p$.).$

$2\mathrm{.}4.$ The form of the cubic parabola and the coordinates of the point at

which the transition becomes the circular arc of radius R$.$

$2\mathrm{.}5.$ Plot the transition curve $($cubic parabola$)$ assuming a proper offset

for the largest x or y coordinate $(2$ d$.$p$.).$

$2\mathrm{.}6.$ To minimise efforts in setting up the highway centreline and increase

sustainability of the project design, what is the optimum value of $$rate of

change of radial acceleration$$ Copt that meets the criterion L $<=$ Lmax with

the least difference and still maintain the radial acceleration with the

range of values recommended by the UK standards $($L $=$ length of the

transition curve; Lmax $=$ maximum length of transition curve recommended

by the UK Standards$)?(2$ d$.$p$.).$

$2\mathrm{.}7.$ Provide values in Tables and plot a unique graph of the variable C

$($x axis$)$ against the variable L $($y axis$)$ including their trends for the

following three conditions $($show at least one sample calculation of L vs

C for each condition below$)$:

a$)$ Same initial design speed vdesign and superelevation e conditions.

b$)$ Same initial design speed vdesign with a superelevation e of $1$ value

step below.

c$)$ Same initial superelevation e with a design speed vdesign of $1$ value

step below.

$($Hint: range of variation of C for plotting the graphs is to be considered

from C $=0\mathrm{.}02$ m$/$s$3$

to C $=0\mathrm{.}60$ m$/$s$3$

$,$ identifying C $=$ Copt at any condition

and using steps of $0\mathrm{.}02$ m$/$s$3$

for C$).$

Critically comment on the results and justify with calculations, where

required, by responding to the following points:

$2\mathrm{.}7\mathrm{.}1.$ Clearly state if the trend of the three curves is analytically coherent

and whether it is increasing$/$decreasing for increasing values of the

variable C$.$ Explain the reason why this happens, by critically linking the

$4$

mutual impact of all the involved design parameters $($C$,$ L$,$ v$,$ e$,$ and R$)$ in

the curves$$ trend.

$2\mathrm{.}7\mathrm{.}2.$ Which condition amongst the three listed at point $2\mathrm{.}7$ provides the

highest values of L$,$ and why?

$2\mathrm{.}7\mathrm{.}3.$ How would you rank the trend of the three curves in terms of which

one is returning the highest value of L$,$ with C being taken constant

across the three conditions?

$2\mathrm{.}7\mathrm{.}4.$ Which parameter amongst v and e affects mostly L $$ in terms of

returning its largest value $-$ for the transition curve? Support your

statement with reference to the curve trends in the graph and the

obtained numerical values.