Surveying II. (BSc)

Lecture 5

Budapesti Műszaki és Gazdaságtudományi EgyetemÁltalános- és Felsőgeodézia Tanszék

Setting out transition curves

Forces acting on a vehicle

mg

sinmg

cosmg

cosmg

sincos mgmg

Straight

sinmgR

vm

2

Forces acting on vehicle

Vehicle in left curve

sincossincos

22

R

vmmgmg

R

vm

sincos2

mgR

vm

Driving in a curve

When R is sufficiently big, then the steering wheel does not need to be rotated too much.

What hapens when R is not so big?

The car is driven along a transition

curve

Transition curve: a curve which changes its curvature

continuously.

Transition curves in practice: F1 racing line

The Clothoid

1 R

1

RLp L

Determination of the parameter

Radius

Speed

Parameter

Setting out the centerline of roadworks – transition curve

straighttransition curveradial curvetransition curvestraight

The geometry of the transition curve

L – length of transition curve (TC)R – radial curve offsetX,Y – coordinates of the endpoint of TC.

X0 – chainage of the center of radial curveTh – ‚long’ tangent lengthTr – ‚short’ tangent length – deflection angle of terminating tangent

RLp

Standard clothoid (p=100)

(source: Nemesdy: Útívkitűző zsebkönyv)

Computation of the length of curves:

1. Length of transition curve: L

2. Length of radial curve:

180

2RIHR

3. Length of the total curve:

RIHLIH 2

Setting out the characteristic points of curve (including transition curve)

Starting point of TC

Terminating point of TC = Starting point of RC

Terminating point of TC = Terminating point of RC

Starting point of TC

Starting point of TC (both)

1. can be computed from WCBs

2. Computation of the tangent length:

2

tan

RRt

tXT 0

3. Starting point can be set out by distance observation

Setting out the terminating point of TC (both)

1. X’ can be computed from the tangent length and the coordinates of theterminating point (table):

XTX 2. The terminating point can be

set out using offset surveys.

Setting out the terminating point – polar setting out (radiation)

1. X’ can be computed from the tangent length:

XTX

2. The setting out data (, r) can be computed using X’ és Y:

X

Y

YXr

arctan

' 22

Setting out the middle of the curve:

1. IK can be computed:

Radiation:

2

180 IK

2. rIK can be computed:

R

RRr

IKIK

sin

Setting out the middle point of the curve

1. x’IK can be computed:

Offset survey:

IKIKIK rx cos

2. yIK can be computed:

IKIKIK ry sin

Setting out the detail points on the curve:

From the staring point:

Standard clothoid (p=100)

(forrás: Nemesdy: Útívkitűző zsebkönyv)

Detail point coordinates (5m interval)

Setting out the detail points of TC - radiation

From the corner point (S):

1. x’ can be computed:

xTx

2. The setting out data (, r) can be computed using X’ and Y:

i

ii

iii

x

y

yxr

arctan

' 22

Setting out characteristic and detail points using grid coordinates:

Let’s compute the grid coordinates of the terminating point:

1. The SiSi-1 WCB is computed from the grid coordinates of the corner points (intersection of the given tangents)

2. The WCB S-AV can be computed:

1iiSSAVS

3. The grid coordinates of AV can be computed using the 1st fundamental task of surveying:

AVSSAV

AVSSAV

rXX

rYY

cos

sin

Machine guidance