Principles and reduction of observations and errors in spatial measurement. Techniques of horizontal and vertical angle measurement for precise positioning. Trigonometric heighting and vertical staff tacheometry. Setting out of structures. Design and computation of horizontal and vertical curves.

1. W E E K 4
L E C T U R E 1
Vertical Curves
NETTLEMAN LAND CONSULTANTS, INC.
COPYRIGHT 2014

2. VERTICAL CURVES

3. VERTICAL CURVES

4. Introduction
 Mathematical differences between Vertical and
Horizontal curves
 Parabolic curve = vertical
 Circular curve = horizontal
 A vertical curve is used to provide a smooth transition
between grade lines
 Good vertical curve designs also consider the sight
distances for vehicles
 There are two types of vertical curves, equal and unequal
tangent curves

5. What is a Parabolic Curve?
 Remains a parabola when plotted at exaggerated scale
 Vertical offsets are proportional to square of distance
along a tangent
 Vertical acceleration is constant
 Curve elevation at its midpoint will be halfway from the
elevation at the P.V.I. to the elevation at the midpoint of
a straight line from the P.V.C. to P.V.T.

6. Fundamental Equations (Parabola)
 -
 -
 -
cbxaxorkxy  22
..
axdxdySlope 2/ 
L
gg
a
dx
yd
geRateofChan
2
2
12
2
2



7. Diagram

8. Design Criteria
 Minimize cut and fill
 Balance cut and fill
 Maintain adequate drainage
 To not exceed max. grade
 Provide sufficient sight distance

9. W E E K 7
L E C T U R E 1
Global Positioning Systems I
NETTLEMAN LAND CONSULTANTS, INC.
COPYRIGHT 2014

10. Three Segments
 Control: 5 monitoring stations update satellites
internal orbital model (ephermis) and track the
“health” of each satellite and calibrate clocks
 Space: 31 satellites (six planes with four sv’s each)
orbit 12,550 miles above the earth, making two orbits
per sidereal day
 User: GPS receivers used by the military,
professionals and recreationalists

11. Segments

12. Control

13. Space

14. User

15. Signals
 L1: 1575.42 MHZ (Static GPS)
 C/A: Broadcast 1 MHz Pseudo Random Noise (PRN) pseudo-
random-noise code (SV identifier)
 Nav. Message: info on satellite orbits, clock corrections, and
other system parameters.
 L2: 1227.60 MHz
 P or P(Y): P-Code is a very long (seven days) 10 MHz PRN
code. Y code is embedded into P-code and is encrypted
 Both L1 & L2 (RTK GPS)
 L5: New “band” for precise surveying