GPS and Navigation

Subject Topics: Geography, Geometry and Trigonometry

GPS and NavigationHow 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?

Early Greek Contributions to Navigation

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

Department of Defense

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

US Naval Observatory

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

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

Can you find your nearest CORS Location?Click Here to Find Them.

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

Stations Are:

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?

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)

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

What is the difference between satellites using triangulation and trilateration?

Trilateration

Triangulation

acb

GPS and NavigationTriangulation: Where in the World?

Longitude and 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 (").

0° latitude

90° 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.

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

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

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

EXAMPLE: Longitude of 77.023Remember: 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"

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

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

LocationLongitude (degrees)

GPS Units (Longitude) Latitude (degrees)

GPS Units (Latitude)

US Navy Yard 38.889° 77.009° USNA Memorial 38.8723° 76.995° Washington Memorial 38.889° 77.049° US Naval Observatory 38.920° 77.066° National Gallery of Art 38.891° 77.0199°

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 numberdetermined?

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

National Gallery of Art, GPS Position

US Capitol, GPS Position

Shortest Possible Confidence Interval = _______ m

Distance (d)= _______ m

Longest Possible Confidence Interval = _______ m

_____ m_____ m

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 distance confidence interval (Ld): D + 2(WAAS value)= Sd

Confidence intervals are written as: (Sd) ≤ d ≤ (Ld) or d € (Sd , Ld)

Navy Fitness and GPS Challenge Scenario: Location Long. Lat.

Point 1 2nd Street & Independence Ave. SW 38°53'15.17"N 77° 0'12.67"WPoint 2 2nd Street & Constitution Ave. NW 38°53'31.01"N 77° 0'12.61"WMidpoint (W) Midpoint of Mall 2nd St. between

Independence and Constitution Ave. 38°53'23.21"N 77° 0'12.67"WPoint 3 14th Street & Constitution Ave. NW 38°53'31.29"N 77° 1'54.90"WPoint 4 14th Street & Independence Ave. SW 38°53'15.09"N 77° 1'55.03"WMidpoint (E) Midpoint of Mall 14th St. between

Independence and Constitution Ave. 38°53'23.17"N 77° 1'54.90"W

Distance (d) Length (m) Confidence Interval

Point 1 to Point 2 (a) 487 m

Point 2 to Point 3 (b) 2,465 m

Point 3 to Point 4 (a) 490 m

Point 4 to Point 1 (b) 2,462 m

Midpoint W to Midpoint E 2,464 m

Confidence Intervals (What was your WAAS Value Again?)

a

b

c

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?

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?

• 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.

Wrap Up:

Cartographer

Tracking Marine traffic(click on the image to visit this site)

Plotting a Course and Velocity Made Good (VMG)

Boat SpeedXTE

VMG Rhumb Line

Ground Track

DestinationStart Point

•provide any advantage to speed and reaching your destination!

NAVIGATION TERMINOLOGY DEFINITION

•Knot (kt)

•Speed Over Ground (SOG)

•Course Over Group (COG)

•Rhumb Line

•Velocity Made Good (VMG)

•Course Offset

•Cross Track Error (XTE)

Angle % 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 85 .4% 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

10 1.5% 2 2.5 3 3.6 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.115 3.5% 2.1 2.6 3.1 3.6 4.1 4.7 5.2 5.7 6.2 6.7 7.2 7.8 8.320 6.4% 2.1 2.7 3.2 3.7 4.3 4.8 5.3 5.9 6.4 6.9 7.4 8 8.525 10.3% 2.2 2.8 3.3 3.9 4.4 5 5.5 6.1 6.6 7.2 7.7 8.3 8.830 15.5% 2.3 2.9 3.5 4 4.6 5.2 5.8 6.4 6.9 7.5 8.1 8.7 9.235 22.1% 2.4 3.1 3.7 4.3 4.9 5.5 6.1 6.7 7.3 7.9 8.5 9.2 9.840 30.5% 2.6 3.3 3.9 4.6 5.2 5.9 6.5 7.2 7.8 8.5 9.1 9.8 10.445 41.4% 2.8 3.5 4.2 4.9 5.7 6.4 7.1 7.8 8.5 9.2 9.9 10.6 50 55.6% 3.1 3.9 4.7 5.4 6.2 7 7.8 8.6 9.2 10.1 10.9 55 74.3% 3.5 4.4 5.2 6.1 7 7.8 8.7 9.6 10.5 60 100% 4 5 6 7 8 9 10 65 136.6% 4.7 5.9 7.1 8.3 9.5 10.6 70 192.4% 5.8 7.3 8.8 10.2

VELOCITY MADE GOOD TABLE

Rhumb Line Rhumb Line

C= Course offsetX= Angle between magnetic north and the Rhumb lineY= Course over ground angle (COG)

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= (X-Y) C= (Y-X)

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).

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

Click here to visit the Naval Postgraduate School Arctic Modeling Effort

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.

ARCTIC ICE NAVIGATION CHALLENGE

• 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?

Wrap Up: