W E E K 4

L E C T U R E 1

Vertical Curves

NETTLEMAN LAND CONSULTANTS, INC.COPYRIGHT 2014

VERTICAL CURVES

VERTICAL CURVES

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

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.

Fundamental Equations (Parabola)

-

-

-

cbxaxorkxy 22 ..

axdxdySlope 2/

L

gga

dx

ydgeRateofChan

22

12

2

2

Diagram

Design Criteria

Minimize cut and fill

Balance cut and fill

Maintain adequate drainage

To not exceed max. grade

Provide sufficient sight distance

W E E K 7

L E C T U R E 1

Global Positioning Systems I

NETTLEMAN LAND CONSULTANTS, INC.COPYRIGHT 2014

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

Segments

Control

Space

User

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