Surveying II. (BSc) Lecture 5 Budapesti Műszaki és Gazdaságtudományi Egyetem Általános- és...
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Transcript of Surveying II. (BSc) Lecture 5 Budapesti Műszaki és Gazdaságtudományi Egyetem Általános- és...
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