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GPS and Navigation Subject Topics: Geography, Geometry and Trigonometry

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GPS and Navigation

How have humans navigated their world, in the past, and in the present?

What does GPS stand for?

How do you think GPS works? What is involved?

There’s a lot that goes into GPS. Here are some of the organizations involved:

Click on each symbol or banner to go to their websites to learn more.

The home of the discovery of GPS and research operations for the Navy.

Department of Defense

The Nat. Geodetic Survey is responsible for maintaining the National Spatial Reference System and the Continuously Operating Reference Station network.

US Naval Observatory

The US Geodetic Survey Runs the Continuously Operating Reference Station (CORS) network across N. America.

Our Nearest Stations Are:

Can you find your nearest CORS Location?

Click Here to Find Them.

What Satellites are Overhead Right Now?

Click the satellite picture to find out.

- How Do Satellites and GPS units communicate?
- 31 satellites
- Radio Waves (mechanical waves)
- Pseudo Random Code (PRC)
- Atomic clocks and accurate time
- Geodesy (accounting for the uneven features of the Earth’s surface)
- Mathematical equations
- What else?

How long does it take a radio signal from a satellites to reach your GPS unit?

Distance (D)= time it takes the satellite radio wave to travel (T)

x Speed of light (300 km/ms)

or D=T x (300/ km/ms)

What is the difference between satellites using triangulation and trilateration?

c

a

b

Trilateration

Triangulation

GPS and Navigation

Triangulation: Where in the World?

Longitude and Latitude

90° latitude (+)

If you were looking at the top of the Earth, from the North Pole, much like looking down at the face of a clock, fill in the degrees of longitude on the diagram below starting with the prime meridian (0°) at 6 o’clock.

0° latitude

90° latitude (-)

http://oceanservice.noaa.gov/education/lessons/plot_course.html

There are 60 minutes per degree of longitude or latitude, written as ('), and there are 60 seconds per minute (").

Convert degrees of longitude and latitude into precise minutes and seconds:

Decimal x 60 = minutes (') remaining decimal x 60 = seconds (")

EXAMPLE: Longitude of 77.023

Remember: Degrees remain the same

.023 x 60 = 1.38, so 1 becomes the minutes 77°1'

.38 x 60 = 22.7994 becomes the seconds so 77⁰ 1' 22.7994"

Convert degrees of longitude with minutes and seconds back into degrees only:

Degrees + (minutes/60) + (seconds/360)

Click here for the National Geodetic Society Online Converter for degrees into minutes and seconds.

Practice Converting Degrees of Longitude and Latitude into Minutes and Seconds and Then Find and Label the Locations on Student Map 1.

What is the significance of each location?

How are the streets in Washington DC laid out?

How are the streets labeled and numbered?

How is a road number

determined?

What are the quadrants?

Can you find the state circles?

Why would this system be useful for navigation?

When Measuring Distances with GPS What Are Confidence Intervals? WAAS Values?

Distance (d) measured using GPS from point to point

Shortest possible distance confidence interval (Sd):

D - 2(WAAS value)= Sd

Longest possible distance confidence interval (Ld):

D + 2(WAAS value)= Sd

Calculate the confidence interval for the shortest possible distance and longest possible distance from the steps of the US Capitol to the National Gallery of Art. You measured the distance on your GPS to be 800 m, your WAAS is 10 m.

Shortest possible distance confidence interval (Sd):

D - 2(WAAS value)= Sd

Longest Possible Confidence Interval = _______ m

Distance (d)= _______ m

Longest possible distance confidence interval (Ld):

D + 2(WAAS value)= Sd

_____ m

_____ m

Shortest Possible Confidence Interval = _______ m

National Gallery of Art, GPS Position

US Capitol, GPS Position

Confidence intervals are written as:

(Sd) ≤ d ≤ (Ld) or d € (Sd , Ld)

To meet the standards in the Navy’s scenario the Mall must be a rectangle and not a parallelogram, meaning it must have 90° angles at the corners. Check for right angles using the Pythagorean Theorem to find the lengths of the two diagonals:

c2 = a2 + b2 or c=√ a2 + b2

Rectangle or Parallelogram?

b

c

a

But Wait! How do we account for the variability of our data and confidence values when calculating angles?

To account for data variability and range of error you have to use calculus to account for the WAAS value which was 6m total (represented by ∆). The equation would be:

∆a=6 m

∆b=6 m

Calculate for ∆c

∆c = (a x ∆a + b x ∆b)

√ a2 + b2

Why would ∆c be larger than your WAAS value?

Wrap Up:

- Name and explain the role of the different organizations that contribute to the maintenance of GPS satellites, coordinates, accuracy, and accurate time keeping.
- What is the difference between triangulation and trilateration? Explain how they are used by GPS units and satellites.
- What are some factors that might affect successful GPS measurements? Explain.
- When measuring distances between two points, what are confidence values and how do they affect how individuals find their locations?
- Discuss how GPS technology might be useful when creating records of naval navigation, crime scenes, tracking animal populations, or even archaeology.

Tracking Marine traffic

(click on the image to visit this site)

provide any advantage to speed and reaching your destination!

Plotting a Course and Velocity Made Good (VMG)

Ground Track

Boat Speed

XTE

Start Point

Rhumb Line

VMG

Destination

- NAVIGATION TERMINOLOGY DEFINITION
- Knot (kt)
- Speed Over Ground (SOG)
- Course Over Group (COG)
- RhumbLine
- Velocity Made Good (VMG)
- Course Offset
- Cross Track Error (XTE)

N

N

C= (X-Y)

C= (Y-X)

Rhumb Line

Rhumb Line

- Draw and label:
- Course over ground below the rhumb line (COG).
- Angle between your COG and true North (Y).
- Angle between the rhumb line and true North (X).

- Draw and label:
- Course over ground above the rhumb line (COG).
- Angle between your COG and true North (Y).
- Angle between the rhumb line and true North (X).

C= Course offset

X= Angle between magnetic north and the Rhumb line

Y= Course over ground angle (COG)

Click here to view a slideshow about theNaval Research Laboratory Arctic Research Initiative.

Click here to visit the Naval Postgraduate School Arctic Modeling Effort

ARCTIC ICE NAVIGATION CHALLENGE

On the map draw a star at your starting point at the Eastern most entrance of the Northwest Passage. Also label Baffin Bay and the Gulf of Boothia.

Wrap Up:

- Explain how GPS is used to track marine traffic and shipping trade and how this information might be used.
- Explain a rhumb line and course offset angles and how they are used in navigation.
- What is velocity made good?
- Describe how to use GPS to calculate velocity made good and course offset angles.
- How can GPS technology be useful to scientists when studying climate change?

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