GPS Chapter

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GPSInvestigation

A GLOBE Learning Investigation

GLOBE 2005 1 GPS


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GLOBE 2005 Welcome - 2 GPS

GPS Investigationat a Glance

ProtocolOnetime Only Measurements:

Time of initial recording and averaged latitude, longitude, andelevation for the following Study Sites:Atmosphere, Hydrology, Land Cover, Soil Characterization, SoilMoisture, and your school which is the center of your GLOBEStudy Site.

Suggested Sequence of GPS Investigation Read the Protocol to learn precisely what is measured and how.

Copy and distribute the Field Guidesto your students.

Prior to using the GPS receiver, identify all of your GLOBE sites that require latitude,longitude, and elevation measurements.

Have the students conduct some test measurements near yourschool, following the GPS Field Guidefound in the Protocolsection. When you and your students are comfortable with theoperation of the receiver go to your GLOBE study sites and,following the GPS Field Guide,take the position measurements ateach site. Report your results back to GLOBE as soon as possibleupon completing the measurements and calculations.

If one or more of your sites are obscured by tree canopy, follow the Offset GPS Activity Field Guideto determine your sites position.

If your students are experiencing difculties with performing the measurementsor are interested in further activities related to global positioning systems, referto and conduct one or more of accompanying activities ( Relative and AbsoluteDirectionsand What is the Right Answer? )


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GLOBE 2005 Welcome - 3 GPS

Table of Contents

IntroductionOverview ................................. ...................................... ... Introduction 1

Satellites ................................. ....................................... ... Introduction 1

GPS Satellites ................................................................... Introduction 1

ProtocolsGPS Measurement Protocol

GPS Protocol Field Guide

Offset GPS Protocol Field Guide

Learning Activities What is the Right Answer?*

Relative and Absolute Directions

Appendix Site Location Data Sheet ..................................... ................. Appendix 2

GPS Investigation Data Sheet .............................................. Appendix 3

Offset GPS Measurements Data Sheet ................................ Appendix 4

Glossary ............................................................................... Appendix 5

* See the full e-guide version of the Teachers Guide available on the GLOBE Web site and CD-ROM.


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GLOBE 2005 Introduction - 1 GPS

P r o t o c o l s

L e a r n i n g A c t i v i t i e s

A p p e n d i x

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I n t r o d u c t i o n

Introduction

Overview

A Global Positioning System (GPS) receiver is ahand-held device that receives data directly fromoverhead satellites. Using a GPS receiver, studentscan determine their location, as measured inlatitude and longitude, almost anywhere in theworld to an accuracy of 10 15 meters. If theyaverage several measurements, typically they candetermine their location to within 10 meters orless. Thus, students can determine the locationof their GLOBE sites with sufcient accuracy toidentify their individual pixel (30 m X 30 m) in

Landsat images. Yes, students can use satellite data. Althoughit was originally designed for military use, GPSis now used primarily in civilian applications.

As a part of GLOBE, students will determinethe latitude, longitude, and elevation of theirschool as well as of their GLOBE study sites. Thisinformation is critical for making GLOBE datauseful for students and scientists around theworld. The visualization of student data as GLOBEmaps would not be possible if the latitude andlongitude of each site where students collecttheir data were not available.

Satellites

An object in orbit around a larger body is calleda satellite. When the Galileo spacecraft reached

Jupiter and slowed down to enter into an orbitaround the planet, it became a satellite of Jupiter.

When we launch a satellite into orbit around Earth,it becomes an articial satellite of Earth just as themoon is a natural satellite of Earth. These articial

satellites in Earths orbit perform a variety of tasksincluding: long-distance telephone, television,and data communication, weather and natural-resource observations, military surveillance, andbasic science measurements.

Our moon is 384,500 km from Earth, and ittakes about one month to complete oneorbit. Because of fuel limitations or a desireto perform close observations, space shuttles

and some observation satellites are only a few

hundred kilometers above Earth. These Low-Earth-Orbit satellites take a minimum of 90minutes to complete one orbit. Communicationssatellites are in orbits 35,792 km above Earth.

At this altitude, these satellites take exactlyone day to circle Earth. This special orbit iscalled Geosynchronous Orbit. A satellite ingeosynchronous orbit always appears to be atthe same place in the sky to a terrestrial observer.Thus, an antenna pointed at a geosynchronoussatellite need not move. Compare this to a spaceshuttle which may pass from horizon to horizonin minutes or our moon which may take a monthto move across the sky.

GPS Satellites

The Global Positioning System consists of a seriesof satellites, ground control stations, and userswith GPS receivers. See Figure GPS-I-1. Thesesatellites are unmanned and are launched byexpendable rockets that place them into orbit.There are 28 GPS satellites in orbit 20,200 km

above Earths surface. At this altitude, the satellitestake about 12 hours to complete one orbit. Thesatellites are spaced in their orbits so that at leastfour are always in view of a terrestrial observerat any point on Earth. A ground-based system of tracking stations monitor the orbits of the satellitesto an accuracy of 1 m, and encodes the satelliteslocation, along with the satellite-generatedtime signal, into the unique identication codetransmitted by each satellite. The satellites transmitencoded signals approximately every 15 seconds.

When received by a hand-held GPS unit, the data

allow the calculation of the latitude, longitude andelevation (or altitude) of the receiver. The radiosignals travel in a straight line from the satelliteto the GPS receiver passing through clouds, lighttree canopies, glass, and plastic, but not throughsolid structures such as buildings and mountains.

When operating, the GPS unit is able to identifyeach satellite as they come into view, and evaluatethe quality of the incoming signals. Modern GPS

G P S


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GLOBE 2005 Introduction - 2 GPS

units may receive signals from up to 12 satellitesat the same time. A minimum of three signalsis required to give the latitude and longitude,

while reception of a minimum of four signals isnecessary to calculate the altitude. Reception of alarger number of signals produces a more accurateresult.

The capabilities of the GPS system rely criticallyon the development of extremely accurateatomic clocks. The most accurate clocks arecapable of neither losing nor gaining morethan 1 second in 20 million years! The timegiven in the GPS receiver is accurate to withinone billionth of a second! The combination of

clocks in the GPS receiver and atomic clocks oneach satellite allow the GPS receiver to recordthe transit time of each radio signal to within 1nanosecond (one billionth of a second). Knowingthe speed of light (about 1 foot per nanosecond)it is possible to use the time delay, betweenthe transmission and reception of the radiosignal, to calculate with extreme accuracy theinstantaneous distance from each satellite tothe GPS receiver. Converting the simultaneoustime delay of signals from three or more satellitesinto distances, it is possible to calculate, by

triangulation, the position (latitude, longitude,and elevation) of the receiver anywhere on thesurface of Earth.

Figure GPS-I-1: A Global Positioning SystemSatellite


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GLOBE 2005 Protocols - 1 GPS

Students should learn the basics of GPS.

Practice making GPS measurements near the school.

Make the GPS measurements at the sites specied.

Submit your GPS data to GLOBE.

P r o t o c o l s


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A p p e n d i x

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learn how many kilometers or meters are in oneten thousandth of a degree of circumference(0.0111 km/0.0001 degrees or approximately 11meters/0.0001 degrees). GPS receivers typicallypresent locations to the nearest 0.0001 degrees,which is approximately 11 meters of latitudeon Earth. Knowing the distance north or southbetween your site and an offset location allows youto determine the difference in their latitudes.

Elevation

All measurements of elevation are made usingmean sea level as a point of reference. For example,Mount Everest has an elevation of 8,850 metersabove mean sea level. Since sea level uctuatesdaily with tides, the mean sea level surface is usedas the reference. The reference surface that passesthrough the global mean sea level and is shapedby Earths gravitational eld is known as the geoid.This surface is not smooth because of the irregulardistribution of Earths gravity eld.

GPS receivers must also use a reference for

determining elevation. Unfortunately, the geoidis very complicated and too large to t in theinternal memory of most GPS receivers. Instead,they contain a simplied shape for a smoothsurface known as the reference ellipsoid. AllGPS elevation measurements are made againstthe reference ellipsoid. See Figure GPS-P-3.

While the geoid and reference ellipsoid mayoverlap in some areas, in others they may differby more than 100 meters. Because of this, the

elevation of your location measured with a GPSreceiver may be signicantly different from theelevation determined by other methods (forexample, topographic maps). The GLOBE serverwill automatically make the geoid correctionto your elevation once you have entered yourGPS measurements for latitude, longitude, andelevation for your site.

Magnetic VariationOn Earth, the magnetic North and South polesdo not line up exactly with the true North andSouth poles (along our planets rotation axis).Earths magnetic north pole is slowly moving and iscurrently located in Canadas Northwest Territoriesabout 11 degrees from the North Pole. Additionally,the magnetic properties of Earths composition

vary slightly among locations. As a result, thereis a unique distortion to Earths magnetic eld atany given place. Typically a small variation of afew degrees must be added or subtracted frommagnetic compass bearings to determine thedirection of true North. This variation is knownas magnetic variationor magnetic declinationand itsvalue depends on your location. Figure GPS-P-4is a world map of magnetic declination. Use thisgure to determine true north at your location. Youmay also use a topographic map to determine themagnetic variation and true North at your location.

You will need to use the true North heading forthe Measuring Wind Direction Field Guidein the

Atmosphere Investigationand for the Offset GPS FieldGuidein this Investigation. Be sure to adjust yourcompass to true North according to the followingdirections.

Figure GPS-P-2: Clear and Blocked Views to a GPS Satellite

Figure GPS-P-3: Geoid and Ellipsoid Surfaces

TopographicElevation is Measuredin Reference to theGeoid.

Geoid

GPS MeasuresElevation in Referenceto the Ellipsoid.

Ellipsoid

EarthsSurface


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W o r l

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Compass: True NorthThe magnetic needle in a compass is attracted by the magnetism of the Earth, and that is why it alwayspoints North. However, there are really two North Poles on the Earth. One is the True North Polewhichis located geographically at the top of the earth (at 90 o North latitude); and the other is the MagneticNorth Pole, an area of highly magnetic rock under central Canada.

Maps and directions are based on True North while the compass needle points to Magnetic North.Magnetic declination is the angle between True North and Magnetic North. Its size and directiondepends on where you are on the Earth. It is necessary to determine the declination to take accuratecompass bearings. Compasses either have a mechanism to set the angle of declination or a scaleto determine declination.Because compasses are attracted to metal objects they will give incorrect readings if the user isclose to, or wearing, metal objects including watches, keys, etc.Three Basic Parts of the Compass

1. The magnetic needle(See A in the Figure GPS-P-5) is attracted by the magnetic North Pole of

the earth. The magnetic end (red) always points to magnetic north.2. The graduated dial (B) is used to set the desired bearing. The bearing is read in degrees

at the sighting arrow (C) at the top of the compass. The dial is graduated in 2 degreeincrements from 0 to 360 degrees. The cardinal directions are at 0 (or 360), 90 degrees, 180degrees and 270 degrees which correspond to North, East, South and West.

3. The base plate (D) has an orienting arrow (E) and a sighting arrow (C). Some models alsohave mirror sights attached. These components are used to line up the magnetic needleand point out the line of travel.

Setting Compass BearingsStep 1:Set the dial (B) to the desired degree reading (the direction in which you want to travel) so that thecorrect compass bearing lines up with the sighting arrow (C).

Step 2: While holding the compass level, turn your bodyuntil the red end of the magnetic needle (A) linesup with the red orienting arrow (E). Put the redin the shed is a useful saying to help studentsremember what to do. The red orienting arrow isconsidered the shed.

Step 3: Your direction or objective will now lie straight

ahead in the direction you are holding thecompass (the direction in which the sighting arrowpoints).

Be sure to choose an object ahead of you in linewith your compass bearing and walk toward it.This allows you to walk without looking downat your compass. Every few paces stop and checkthat you are still traveling in the desired compassdirection.

N

EW

S

C. SightingArrow

E. OrientingArrow

D. BasePlate

B. GraduatedDial

A. MagneticNeedle

Figure GPS-P-5: Compass Example


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Teacher SupportMeasurement Logistics

1. Students must determine the latitude,longitude, and elevation of their school,

and for all other GLOBE study sites.2. Remember, the location and elevation of

each site must be determined only once.3. If you or your school do not own a

GPS receiver and you are borrowingone, you may want to determine all thesites for which you need to take GPSmeasurements. This would allow you tocollect GPS data for all the sites in a shortperiod of time (e.g., a week).

4. Locations of GPS measurements: Some

GLOBE study sites should provide clearviews of the sky and thus good satellitereception (e.g., Atmosphere study site).Others, especially the Land Cover andPhenology sites, may offer poor GPS

Site GPS Measurement Location

School Main entrance Atmosphere study site Instrument shelter locationHydrology study site Surface water sampling locationSoil study sites:

Soil Characterization site Soil prole locationSoil Moisture site Center of the soil moisture star patternSoil Temperature Soil Moisture or Atmosphere site locations

Land Cover sample sites Center of 90 m x 90 m homogeneous areaPhenology Location of the tree, shrub, or one meter square grass area used

for the Green-Up and Green-Down measurements.

Please note that some GPS receivers are not able to display latitude and longitude readings indecimal degrees. If you are using one of these receivers, you should set it to read in degrees anddecimal minutes and then convert the latitude and longitude readings to decimal degrees beforereporting them to GLOBE. To do so, use the formula and follow the example given below:

Converting from Degrees and Decimal Minutes to Decimal Degrees:1 degree = 60 minutesReading in decimal degrees= degrees + decimal minutes/ (60 minutes/degree)

Example:A latitude reading is given as 15 degrees and 39.03 minutes N.

Latitude in decimal degrees= 15 degrees + 39.03 minutes / (60 minutes/degree) =15 degrees + 0.6505 degrees = 15.6505 degrees

reception due to heavy canopy cover. Theschool location is to be determined at thefront or main entrance to the school, thusbuilding may block satellite reception tosome extent. In these cases use the OffsetGPS Protocol Field Guide.

Student PreparationThe Learning Activities in this Investigationprovide additional exercises to help studentsunderstand the measurements of time, relativeand absolute position, and angles, all the basicelements incorporated in the GPS measurement.

Helpful HintsBefore you use a GPS to receiver make sure that itis set to display the following units:

Time as Universal Time (UT) Elevation in meters Latitude and longitude in decimal degrees

If it does not, follow the manufacturers directionsor users manual to make these adjustments.


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GPS ProtocolField Guide

Task

Measure the latitude, longitude, and elevation of your school or a GLOBE study site.

What You Need GPS receiver GPS Data Sheet

Watch Pen or pencil

In the Field 1. Take the GPS receiver to the exact location you would like to determine latitude, longitude,

and elevation.2. Turn on the receiver, making sure that you are holding it vertical and you are not blocking

the antennas view of the sky. In most receivers the antenna is internal and is located at thetop of the receiver.

3. After an introduction message, the receiver will start to search for satellites. Some receiversmay display the previous latitude, longitude, and elevation values while it is locking ontosatellite signals.

4. Wait for the receiver to indicate that at least four satellites have been acquired and that agood measurement is available. In most receivers, this is indicated by the appearance of a3-D message.

5. At one minute intervals and without moving the receiver more than one meter, make verecordings on a copy of the GPS Investigation Data Sheetof all digits and symbols for thefollowing displayed values:a. Latitudeb. Longitudec. Elevationd. Timee. Number of satellitesf. 2-D or 3-D status icons

6. Turn off the receiver.7. Average all ve latitudes, longitudes, and elevations.

8. Conrm for yourself that your results make sense. You should be able to get a roughestimate of your latitude and longitude by looking at a globe or local map.

9. Copy and submit all GPS readings as your site location to the GLOBE Student Data Archive.

10. Follow this protocol at each site that you need to determine latitude, longitude, and elevation.


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Offset GPS ProtocolField Guide

Task

Measure the latitude and longitude of your school or a GLOBE study site when a GPS receiver is unableto make an accurate measurement.

What You Need GPS receiver Watch

Magnetic compass Pencil or pen

Tape measure Offset GPS Measurements Data Sheet

In the Field 1. Determine the direction of true North at your location using Figure GPS-P-4.

2. Go to your desired site and mark it with a ag or other obvious marker.

3. Follow the GPS Field Guideto conrm that good GPS reception is not possible.

4. Use the compass to determine true North.

5. Move either North or South to reach the nearest open area in which you can successfullyfollow the GPS Field Guide. This is your offset location.

6. Follow the GPS Field Guideand record your latitude and longitude. Mark this as the offset

location.7. Record whether the offset location is North or South of your site.

8. Measure the distance between the offset location and your site in meters and record it onthe Offset GPS Data Work Sheet.

9. Divide this distance by 110,000 meters per degree to determine the latitude difference (inten thousandths of a degree) between the offset location and your site.

10. Depending on the direction of your offset location:

If you moved to the north of your site, subtract this value from the latitude of the offsetlocation to determine the latitude of your site.

If moved to the south of your site, add this value to the latitude of the offset location todetermine the latitude of your site.

11. The longitude of your site is the same as that of the offset location.

12. Determine the elevation of your site by using a topographic map.


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A p p e n d i x

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Frequently Asked Questions1. How long does it take for a GPS receiver todetermine latitude, longitude, and elevation?

The GPS receiver may require anywhere from

several seconds to several minutes to acquire asufcient number of satellites after it has beenactivated. This depends on the availability of GPS satellites overhead at the time of yourmeasurement, on the presence of obstructions,and on the energy level of your receiversbatteries. If it takes more than ve minutes toget a satellite lock, change your batteries andtry again.

2. The receiver is not displaying latitude orlongitude. Why?

The receiver has many functions available onvarious display screens besides the Location screen that usually appears rst when the unitis powered up. Please read the manual andfamiliarize yourself with these other functionsof your GPS receiver.

3. The receiver displays InsufcientSatellites, Poor Signal Reception, orsimilar message. What should we do?

Do not record data if any such messages appear.

When the receiver has a good view of the sky,waiting or moving slightly will usually causethese messages to disappear. Standing closeto the receiver or a group of people hoveringaround the receiver may block the receiversview to the satellites and may cause intermittentsignal losses which will prompt the messages toappear. Stand back or hold the receiver high. Inthick foliage or heavy canopy, the receiver maybe unable to lock to the requisite four satellites.Because the satellites move in the sky, tryingagain at a later time may provide better results.If problems persist due to obstructions, followthe Offset GPS Field Guide.


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GLOBE 2005 Learning Activities - 1 GPS

L e a r n i n g

A c t i v i t i e s

! ?

What is the Right Answer?* Through a series of activities, students will learn that thereare no right answers to some questions. A GPS receiver isoptional.

Relative and Absolute Directions A set of activities to introduce students to latitude, longitude,coordinates and relative and absolute directions. A GPSreceiver is not needed.

* See the full e-guide version of the Teachers Guide available on the GLOBE Website and CD-ROM.


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GLOBE 2005 What is the Right Answer? Learning Activity - 1 GPS

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! ?What is the Right Answer?

PurposeTo introduce students to the concept thatsometimes there is no one right answer to aquestion or measurement

Overview Students learn to be careful when searching fora right answer to questions such as What timeis it? by comparing multiple measurementsof the time-of-day. Students gain an intuitiveunderstanding of the characteristics of imperfectmeasurements. Using different clocks, studentssimultaneously record the displayed times. Theresulting time measurements are convertedfrom minutes and seconds to seconds. Thesemeasurements are plotted to illustrate themathematical techniques of averages anddeviations from an average.

Student OutcomesLearn how to measure time.Understand the accuracy of a

measurement.

Science ConceptsLevels of measurement incorporate degrees

of accuracy.There are mathematical techniques

for characterizing the accuracy of ameasurement.

Science Inquiry Abilities Identify answerable questions.Design and conduct scientic

investigations.

Use appropriate mathematics to analyzedata.

Develop descriptions and explanationsusing evidence.

Time Approximately one class period

Level Elementary- do only the clock comparisonstep

Middle and Secondary- do the full activity

Materials and Tools At least one clock per student, any type,

which shows seconds, will sufce

Paper and a writing tool for eachstudent to record times

Copies of the GPS Investigation TimeMeasurements Work Sheetand plotforms for each student

Optional but desirable:Calculator with addition, subtraction,

multiplication and division functionsGPS receiver (Used as a source of

standard time. Access to a GPSreceiver is not essential. If available,

use it as a highly accurate clock.)PreparationProvide at least 10 clocks for use by the class.The students can use school clocks or bringin clocks from home.

PrerequisitesBeginning levels- ability to read time on aclock

Intermediate and advanced levels-plotting and graphing skills


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because you can read the second hand to aboutone second. An analog clock with only hour andminute hands has a resolution of only about oneminute unless you consistently can determine thelocation of the minute hand between individualminute markers.However, the clock that can be read to a resolutionof 1 second can deviate from some standard timesource from a fraction of a second up through a fewhours. The ability of a clock to maintain correcttime is called its accuracy. Therefore, if you havea clock that gains 10 minutes every day, you stillmay be able to read it to a resolution of a singlesecond, but it is accurate to only 10 minutes perday. Some say that this clock has an error of 10minutes per day.

Clocks are machines that display a count of something that changes as time passes. Earlyclocks determined time by counting fallingdrops of water or grains of sand. These werenot particularly accurate because size of waterdroplets or an amount of sand falling is hard

to control. Later clocks counted the swingsof pendulums, the vibrations of tuning forks,mechanical oscillations in electrically stimulatedcrystals, and atomic resonances. Each of thesesubsequent clocks is more accurate than itspredecessor, and all depend on the increasedstability and repeatability of an underlyingcyclical physical process. See Figure GPS-RA-1.

Background GPS measurements will be made by a large varietyof instruments scattered over large geographicregions and long periods of time. Efforts havebeen made to recommend instruments of sufcientaccuracy and resolution to suit the underlyingscientic goals. However, there will be variationsbetween the measurement values because of thediversity of instrument conditions and studentresearchers.

What Is the Right Answer? When people make measurements, they usuallywish to know something about the quality of theiracquired values. Typically someone asks, How faram I from the right answer? or Did I get the rightanswer? This assumes that there is a right answeragainst which to compare the measured value.

Sometimes there is a right answer. However,when scientists begin measuring a quantity,especially if it is the for rst time, there maynot be a standard against which to compareones results. If you have the only instrumentfor making a particular measurement and youhave no reason to doubt the values that youare recording, then it is reasonable to consideryourself to be the standard.

A problem comes when there exist eithermultiple measurement instruments or someoneclaims to be able to produce the right or betterresults. It has been said, Someone with twowatches does not know the time. In this case,you, the scientist, have to decide how to handlepotentially different measurement values or howto choose which measurements and standardsto use.

Resolution and Accuracy Using ClocksThe number of digits or the smallest unit of timethat can be read reliably by a person observing aclock is called the instruments resolution. Thusa digital clock that displays 12:30:21 (meaning12 hours, 30 minutes, and 21 seconds) has aresolution of about one second because the clockuser can read the clock to the nearest second. Ananalog clock (which has hour, minute, and secondhands) also has a resolution of about one second

Figure GPS-RA-1: A collection of clocks, all withdifferent accuracies and resolutions.


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For all clocks to display the same time, ideallyeach clock would have to be set to the sametime simultaneously and experience the sameenvironmental and mechanical conditions.This rarely happens. Clocks typically are set atdifferent times from different references, havingdifferent accuracies, with different constructions,and experience different environments. A givencollection of clocks will tend to offer a collectionof slightly varying time values. This variationin measurement values will be true of mostinstruments for the temperature, distance, andother measurements of the GLOBE Program(thermometers, tape measures, etc.).

In the case of deciding when to feed a pet, anerror of a few minutes from day to day may be

insignificant. However, a Global PositioningSystem location measurement depends onthe clocks onboard the satellites being highlyaccurate. An error of a single microsecond(1/1,000,000 second) may cause the displayedGPS location to be in error by more than 300meters. The desired resolution and accuracydepend on you (the user) and your understandingof your application.

Time Standards

Until the advent of the American railroads inthe late 1800s, there were few widely acceptedstandards for time. Each population center hadits own clocks that were usually referred to localsolar noon when the sun peaks in the sky orsome other celestial event. However, once onemoves through 15 degrees of longitude or about1600 kilometers along the equator, the time of local noon has changed by an hour. To facilitateconsistent scheduling across continent-sizedareas of our planet, time zones were created andimplemented. The railroads needed and presented

a common time reference frame.Today all time zones are referenced to alongitude of 0 degrees that goes throughGreenwich, England. Greenwich houses oneof the great astronomical observatories. It wasestablished for standardization of time for Britishnaval navigation. Thus, the time in Greenwich,England, is used as a standard and is calledGreenwich Mean Time (GMT), Universal Time

(UT), or sometimes Zulu time. (Zulu refers tozero or the 0 degree longitude.) In the GLOBEGPS Protocolyou will use the Universal Time (UT)designation for your measurements.

The Navy and the National Institute of Standardsand Technology (NIST) within the United Statesand telephone companies maintain standardtimes using highly accurate atomic clocksthat count the vibrations of a variety of atomsunder well-dened conditions. The U.S. radiostation with the call letters WWV continuouslybroadcasts the time of day in English on theshort-wave radio frequencies of 5, 10, 15, 20,and 25 MHz from Boulder, Colorado. Thesefrequencies themselves are locked to atomictime standards. The Canadian government

provides a similar service in both English andFrench with their short-wave radio station CHUon 7.335 and 14.670 MHz. Many such servicesexist globally.

The Global Positioning SystemThe Global Positioning System has a series of satellites that broadcast timing signals from highly-accurate onboard atomic clocks. Therefore, a GPSreceiver can determine its time to an accuracycomparable to that of the clocks on the satellite.

The GPS receiver can even remove the delaydue to travel time between the satellite and theterrestrial receiver because the receiver knowsboth the satellites and its own locations. Thus,GPS receivers have become the best alternative tohaving your own atomic clock.

TelecommunicationsComputer communication depends on timemeasurements that must be substantially moreaccurate than the rate at which the data ows. If one is using a 14.4k bit/second modem to transferdata via the Internet, a new information bit may bepresented to the modem every 1/14,400 secondsor 70 microseconds. Thus, the clocks in thecomputer hardware must have sufcient resolutionto separate each individual 70 microsecond sliceof time and must be sufciently accurate betweenthe transmitting and receiving computers clocksso as not to become unsynchronized by more thana fraction of the 70 microseconds. These needs are


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met easily by the use of quartz crystals that can bemade to vibrate mechanically at chosen values of between 10 thousand and 100 million times persecond. The vibrations are electronically countedby a digital circuit to determine the amount of time which has passed.

What To Do and How To Do It Step 1. Get the ClocksLocate at least ten (and preferably more) operatingclocks that display time to a resolution of onesecond. Assign a student to each clock, and declareone student to be the master timekeeper. In aclassroom situation where many students mayhave wrist watches with one second resolutions,these clocks will sufce. Wall clocks displaying

seconds in a variety of different rooms are alsoadequate. Each student should be prepared torecord a time and be able to see or hear the mastertimekeeper.

Step 2. Take the MeasurementsCentrally locate the master timekeeper. At 30minutes and zero seconds after the hour, thisstudent is going to indicate to the other studentsto record their clocks displayed time values tothe nearest second. Perhaps ten seconds beforethe designated time, the master time keeper may

begin counting down aloud to prepare the otherstudents.

Although any particular time will work, choosing30 minutes into the hour increases the chancesthat during the measurements no clocks willadvance to the next hour and thus complicatelater arithmetic processing.

Advanced students:Have the students performthe computations and graphing.

Other students: The teacher performs the

computations and graphing outside of classfor later presentation and discussion. Whileyounger students may not understand thearithmetic, they do understand how the shapeof the histogram plot appears for various clockaccuracies.

Step 3. What time was it? For details, see the sample GPS Investigation TimeMeasurements Work Sheetand instructions.

Determine the average of all time-of-day

measurements.To determine the average time of day when thedata were recorded:

Determine the number of seconds past the hourfor each participants recorded time.

Add these seconds values to produce a sum.

Divide by the number of participants to producethe average time.

Convert this back to minutes and seconds andrecord.

Step 4. Are our clocks any good? Determine Deviation from the Average.For each participant, compute the difference of each participants time value from the average.Do not keep the sign. All results are positive.

Add these together to produce a sum. Divide thissum by the number of participants to producethe average deviation. The average deviation isa measure of how far each measurement is fromthe average time

Plot differences from the average of our recordedtimes. See Occurrences Versus Differences WorkSheet.

Each bin is 10 seconds wide and is 10 secondsfrom the average number of seconds. Recordthe average number of seconds in the centerbox. Place an X in the appropriate bin for eachparticipants number of seconds into the hour.This type of plot is called a histogram.

How would the plot be different if we had a moreor less accurate collection of clocks?


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Further InvestigationIf you have access to a GPS receiver, use its timeto set a clock that can be used as the masterclock for the measurements. The GPS receiversdisplayed time will probably be the most accuratetime available.

If we have higher quality clocks, how will ourcomputed average deviation change?

Students with access to spreadsheet computerprograms may wish to automate the arithmeticcomputations found on the work sheet.

Advanced students may wish to investigate thestatistical concepts of standard deviation andvariance.

Student Assessment Quantitative

Ask students how the histogram plot would bedifferent if they had a better or worse collection of clocks. Better: Xs grouped closer together. Worse:further apart. Could they record clock values?Could they understand the arithmetic? Shouldany of the data be rejected? If a data sample isobviously inappropriate, such as from a stoppedclock, yes!

QualitativeThe student should be able to describe situationsin which it is and is not reasonable to demanda right answer. The student should be able tolist examples of measurements that they makein their lives and should contrast between theavailable and desirable resolutions and accuraciesfor these measurements. The student shouldtake responsibility for determining the accuracyand resolution necessary for the measurementsrequired by an investigation.


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Instructions

Record Times

Computations

Determine the number of seconds past the hour for each participants recorded time.(Total Seconds = Minutes x 60 + Seconds)

Determine the average time.

(Average time = Sum of seconds / Number of participants) Compute the difference of each participants time value from the average.

(Difference = Seconds into the Hour - Average Seconds)(Do not keep the sign All results are positive numbers)

Determine the averages of the differences.

Plot HistogramRecord the average number of seconds in the center box.Each bin is 10 seconds away from the average and 10 seconds wide.Determine the time for each bin by adding or subtracting from the average.For each number of seconds into the hour, place an X in the nearest bin.

(The number of Xs should be the same as the number of par ticipants.)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

GPS Investigation Time Measurements Work Sheet

Seconds

Participant Recorded past the Difference Average ofNumber times Hour Average from Average Differences(Hr Min Sec) (Seconds) (Seconds) (Seconds) (Seconds)

12 30 012 29 5412 30 112 30 1512 31 112 30 2512 30 312 30 712 29 22

12 30 1

Ten StudentsParticipated

180017941801181518611825180318071762

18011806.9

AverageNumber ofSecondsinto the

Hour

Sumdivided bynumber of

Participants

6.912.95.98.1

54.118.13.90.1

44.9

5.916.08

AverageDeviation

DifferenceSum

divided bynumber of

Participants

10 = No. of Participants


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Instructions

Record Times

Computations

Determine the number of seconds into the hour for each participants recorded time.(Total Seconds = Minutes x 60 + Seconds)

Determine the average time.(Average time = Sum of seconds / Number of participants)

Compute the difference of each participants time value from the average.(Difference = Seconds into the Hour - Average Seconds)(Do not keep the sign All results are positive numbers)

Determine the averages of the differences.

Plot HistogramRecord the average number of seconds in the center box.Each bin is 10 seconds away from the average and 10 seconds wide.Determine the time for each bin by adding or subtracting from the average.For each number of seconds into the hour, place an X in the nearest bin.

(The number of Xs should be the same as the number of par ticipants.)

1

2

3

4

5

6

7

8

9

1011

12

13

14

15

16

17

18

19

20

SecondsParticipant Recorded into the Difference Average of

Number times Hour Average from Average Differences(Hr Min Sec) (Seconds) (Seconds) (Seconds) (Seconds)

AverageNumber ofSecondsinto the

Hour

Sumdivided bynumber of

Participants

AverageDeviation

DifferenceSum

divided bynumber of

Participants

10 = No. of Participants = Sum = Difference Sum

Average Time(Minutes) (Seconds)

GPS Investigation Time Measurements Work Sheet

Your Name: Jordan Malik Todays Date: April 14, 2001


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G P S

I n v e s

t i g a

t i o n

O c c u r r e n c e s

V e r s u s

D i f f e r e n c e s

W o r

k S h e e t

P l o

t 1 : H i s t o g r a m

o f N u m

b e r o

f O c c u r r e n c e s v e r s u s


F i g u r e G P S - R A - 3 : A n E x a m p l e

O c c u r r e n c e s V e r s u s D i f f e r e n c e s W o r k S h e e t

2 0 0 1


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G P S

I n v e s

t i g a

t i o n

O c c u r r e n c e s

V e r s u s


W o r k

S h e e

t

P l o

t 1 : H i s t o g r a m

o f N u m

b e r o

f O c c u r r e n c e s v e r s u s



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GLOBE 2005 Relative and Absolute Directions Learning Activity - 1 GPS

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Relative and AbsoluteDirections

TimeFrom one to ve class periods depending onwhich steps you choose to do

Level All levels with some exceptions noted

Materials and ToolsPaper and pencilGraph paperMagnetic compasses

Drawing compasses (for drawing circles)GlobesMetric rulers and meter sticksBar magnet

PreparationNone

PrerequisitesBeginning levels:Students should be at theappropriate developmental level to be able tolearn about the use of latitude and longitude tond a location.Intermediate and advanced levels:Basicunderstanding of degrees, angles andcoordinate systems.

! ?

PurposeLearning about latitude and longitudeDeveloping math skills

Overview Students begin by asking the simple question:Where Am I? Then they learn

about the magnetic Earth and the use of compasses and angles. Students also

learn about the difference between relativeand absolute locations.

Throughout this activity, students practiceusing a variety of math skills.

Student OutcomesLearn how to locate a position.

Science ConceptsLatitude and longitude determine location.

A compass may be used the Earthsmagnetic eld to give direction.

Physical ScienceThe position of an object can be

described by locating it relative toanother object.

GeographyLocation is used to display information on

maps.

Science Inquiry AbilitiesUse a magnetic compass to accurately

determine angular direction.Identify answerable questions.

Design and conduct scienticinvestigations.

Develop descriptions and explanationsusing evidence.

Communicate procedures andexplanations.


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Background The GLOBE program uses GPS receivers todetermine the latitude and longitude of GLOBEstudy sites. However, the ideas of latitude andlongitude, coordinates attached to absolutereference systems, or angles from north maybe new to many students. This set of activitiesintroduces these concepts.

When you ask students, Where are you?, theymay respond, At home or At school. Theanswers are in their own local reference frame.If you use a magnetic compass to determinethe direction to a tree that is north of you, youwill probably conclude that the tree is to yournorth. However, if you move east or west by anysubstantial amount and use the same compassto determine your direction to the same tree,you will nd the tree to be to your northeastor your northwest. Neither the tree nor Earthsmagnetic poles have moved, but your compassindicates a different direction to the tree. Thereis something absolute about the positions of the tree and the poles, but there is somethingrelative about your measurement technique.The starting point moved.

If we impose a gridded coordinate system uponour geographic area of interest or the entireworld and number the various lines on the grid,we now have a reference frame in which we canuniquely determine any location independentof the relationship between your locationand that of another individual. Latitude andlongitude are the names of the values for thecoordinate system in which we shall be workingfor geographic determination of locations withthe Global Positioning System.

What To Do and How To Do It

Step 1. Relative Positions: Where am I? (For all levels)Have students ask themselves the question,Where am I? and have them list words or drawa rough picture of where they are. Lead a classdiscussion on what denes where are we?

Encourage questions and time for reection onwhere a person is and how one might explainwhere anyone was. Good questions for students

to ask are: How can you describe your locationto another student: in your classroom? in anotherclassroom? in another school in town? in anothertown? in another country? Did students describetheir location using relative or absolute references?Emphasize their reference frames.

Step 2. Attempting to Impose a ReferenceFrame: The Magnetic Earth (For all levels)Our planet projects a gigantic magnetic eld as if

it contained a large bar magnet. See Figure GPS-RE-1. Another magnet (like a magnetized needle)will be attracted to our planets magnetic poles.

A magnetic compass contains a magnet whichcan spin freely and be observed. Thus, magneticcompasses are useful navigational instrumentsbecause they allow one to see the direction of Earths magnetic eld, which almost lines up withEarths north and south poles.

Figure GPS-RE-1: The Earth as a Giant Magnet

Figure GPS-RE-2: Suspended Bar Magnet


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Suspend a bar magnet on a string away fromlarge metal objects and allow the magnet to stopany rotation or spin. Attach the string to the endsof the magnet as shown in Figure GPS-RE-2.

Ask students what will happen. The magnetwill eventually stop spinning so that its polesare aligned with north and south directions.Students can test the north-south directionby comparing the magnet with a magneticcompass.

To use the compass, hold the compass on yourngers of your outstretched hand and arm. Holdthe compass at relative to the ground so thatthe needle can move freely, and keep it awayfrom all metal objects. Position yourself so thatyou can look across the compass through northwhile waiting for the needle to stop moving. Donot place the compass near the magnet; it willlessen the effectiveness of the compass.

Step 3. Introductory Compass Angles(For beginning levels)On a blank sheet of paper, record the followingobservations, using a magnetic compass fordirection.

Record your specic location (e.g., on thebig rock outside our classroom window)and the date.

List all things that are directly to yournorth (use the compass to nd yourdirection), east, south, and west, thenwrite a descriptive paragraph on eachdirection.

Tip. Be specific about what is seen and thedirection it is from you. Also record onlypermanent objects. In areas where there aremany things that look similar, try to pick outspecic differences.

Remember that good scientists are specic in theirdescriptions and their drawings. They compareand contrast in their observations. Exampleswould include the following descriptions at twodifferent schools. See Figures GPS-RE-3, GPS-RE-4a and 4b.

1. The red-brown brick building with thegreen window frames is due west. To thenorth of that building is the factory with

the tall smoke stack.2. The area to the east has a single oak treewith a fence extending away from theobserver.

Ask questions about the observations toencourage students to compare and contrast.

Figures GPS-RE-4a and GPS-RE-4b: View from a school site facing west, view from a school site facing east

Figure GPS-RE-3: A panoramic view


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N W S E N

Step 4. Intermediate and Advanced Compass Angles (For intermediate and advanced levels)

You can divide a circle around you into 360degrees. This is also written as 360. See the GPSLearning Activity Working with Angles.Navigationaldirections from some location are given as anglesaround such a circle, with north at the startingplace, or 0. East is 90. south is 180; and westis 270.

Angular Directions from North Your hand can be used to measure directionalangles effectively. As illustrated in Figure GPS-RE-5, if you extend your arm, make a st, and thenextend your thumb, the width of your hand (withthumb extended) is about 15 (you may needto extend the little nger as well). That meansthat six of your hands with extended thumbswould t between north and east. (Each st withextended thumb equals 15, because there are90 between north and east, and 90 dividedby six sts is 15 for each st.) Figure GPS-RE-5:Using your hand to measure 15

Because the angular relationships of eachindividuals hand will differ slightly, you may nd

that you have to extend your nger slightly so thatsix sts t into 90 degrees. You may need to try tomeasure six sts between north and east severaltimes before you consistently get the same numberof sts on repeated trials. Hold your hand assteadily as possible. Focus on what is at the tip of your thumb, and then move your hand so that theback of your hand is now where your thumb tipwas. Because you always take your hand with you,remember how you extended your arm and hand

so that you can make future angle measurements.Practice positioning your hand and thumb so thatyou get a consistent number of hands betweennorth and east or north and west. Now record whatyou see at the end of each hand width. After youfeel condent with your measurements go on to thepanorama observations below.

Step 5. Panorama Observations (For all levels)Take a sheet of paper and fold it in half lengthwise.Cut along the fold, so that you have two long halvesof the paper. Tape two of the ends together andmark the four directions on the paper, as indicatedin Figure GPS-RE-6, so that north is on the twofar ends and south is in the middle. Record allobservations as drawings on the long narrow stripof paper.

Now that you have had experience with themagnetic compass and with the compassdirections, position yourself in the same spotas you did for the compass activity. Draw apanoramic view of what the landscape looks likeall around you by making multiple individualdrawings for each of the four north, south, east,and west directions. Students can mark all theother directions that fall in between (southsoutheast, northwest by north), by measuring theangles with their sts.Step 6. Telling Time with the SunTo extend this step further, use your st to measuretime. Because the sun moves 15 per hour throughthe sky, one can estimate the time in hours untilsunset by measuring the number of hand-widthsfrom the sun to the western horizon. Knowing yourlocal time of sunset, you can then work backwardand estimate your local time without a clock!

Figure GPS-RE-5: Using your hand to measure 15

Figure GPS-RE-6: Preparing the strip for drawing a panorama


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Step 7. Are the North, South, East, and West Directions Relative or Absolute? (For all levels)Go outdoors and mark a point about two metersabove the ground (for example, crossed strips of tape on a school window), so that you can havethe students stand along an east-west line southof the mark. Have the students form a line withthe person on the far east due south of the mark.The students should be spaced at arms length.See Figure GPS-RE-7.

In Figure GPS-RE-8, the boxes represent individualstudents. With compass in hand, the rst studenttakes a bearing on the mark and finds thatthe direction is north and the angle is 0. Thestudents will then record 0 in the box, marked1. Have each student, in numerical order, makean angle measurement between north andthe mark. Because all results will be betweennorth and east for the scenario illustrated, allmeasurement results should be between 0(north) and 90 (east).

Why did each student get a slightly differentmeasurement? Were they all not looking at thesame point? Their compass angles are relative totheir individual and different locations.

Step 8. Compass Directions Are Relative toYour Location (For all levels)For practical purposes, Earths north and southmagnetic poles are xed close to our planetsnorth and south spin axes. In the absence of other magnets, a magnetic compass needle alignsitself with Earths magnetic eld. Thus, its needlewill point to Earths magnetic poles. (The Earthsmagnetic poles will not move much during ourlifetimes.)

Earths magnetic poles appear xed. However, an

observer on the equator will claim the directionto the north as being along a line tangent to theequator. Another observer who is half way fromthe equator to the north pole will also claimthat the direction north is a line tangent to theglobe at his location. However, these two linesare not parallel. See Figure GPS-RE-9. Therefore,they are not pointing in the same direction. Geta globe and try this for a variety of differentlocations around the world. You can see thatthe direction you call north depends on yourlocation. Therefore, north, south, east, and west

are relative directions. These directions are anglemeasurements in the direction of the magneticnorth pole relative to the location from whichthe measurement is taken.

Figure GPS-RE-7: Students lined facing a mark tothe North

Figure GPS-RE-8: Overhead diagram of studentsfacing a particular mark

Figure GPS-RE-9: The direction North as perceived at different points on Earth


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Further background: Directions are not necessarilyunique. What problems does this cause? Navigationbetween arbitrary locations requires a known pointas a xed reference. Giving directions to listenerswho are located at different positions means thatthey must agree to some point in common beforedirections can be given. Unique starting and endingpoints (like trade routes), provide an absolute orxed reference frame such as a coordinate systemplaced on a map. Latitude and longitude providea similar reference frame for our spherical planet.Use the drawing and map in Figure GPS-RE-10to help students understand relative and absolutedirections and positions. A full page version of Figure GPS-RE-10 is included at the end of thisLearning Activity for you to make duplicates forstudent use. Describe how to go from your schoolto your house. Then describe how to go fromanother school to another house. Then ask, what isthe difference? A riddle about absolute directions:Someone builds a house. All of the outside wallsof the house face south. A bear walks up to thehouse. What color is the bear? (Answer: White - if all sides of the house face south, then the housemust be at the North Pole. The only bears in the

Arctic Circle are polar bears.)

Step 9. Describing a Location (for all levels) We wish to introduce absolute reference frames fordescribing locations. Students will expand uponpast activities to answer the question Where amI? or Where is something? and will learn thatthey must specify the where with sufcientclarity so they can communicate their positionunambiguously to someone else. We ask studentsto provide directions relative to some agreed-uponreference or some coordinate system instead of relative to themselves. Cartesian coordinates (x,yaxes in geometry and algebra) and latitude andlongitude on the globe provide such a system.

Place two students back to back, each withchecker boards, so that each cannot see theothers board. Give them two checkers (tokens)and have one place the tokens anywhere uponthe board. Without imposing further rules, havethat student describe to the other student whereto place the token, so that each token is in thesame position on each board. Repeat the processbeginning with the second student. Lead adiscussion on the communication between thetwo students. How did the students choose tocommunicate the locations of their tokens? Whatdetermined the clarity and difficulty of theircommunications?

Figure GPS-RE-11: Describing checker locations

YOURSCHOOL

ANOTHERSCHOOL

ANOTHERHOUSE

YOURHOUSE

North0

180

South

East

90

West

270

North0

180

South

East90

West270

Figure GPS-RE-10: Directions from home to school aredifferent for everyone


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Step 10. Numerically Describing a Location(for intermediate and advanced levels)Label a piece of graph paper or a drawn grid asshown in Figure GPS-RE-12, Have students ndpositions communicated as follows: (1,2), wherethe rst number describes the distance to moveto the right from zero on the horizontal axis andthe second number describes the distance to moveup along the vertical axis.

Then, have students draw a simple picture fromthe following lines between the given sets of

positions. See Figure GPS-RE-13.(4,1) to (4,4) (4,1) to (5,2) (5,2) to (5,5)

(1,4) to (1,1) (1,1) to (4,1) (1,4) to (4,4)

(1,4) to (2,5) (2,5) to (5,5) (4,4) to (5,5)

Discuss what information is needed to communicatepoints and drawings. For example, each linerequired information about a starting point andan end point.On a new piece of gridded paper, go to position(7,4), and draw an arc with a drawing compassthat has a radius of two units. With position (1,1)as the center, draw an arc with a radius of ve unitsthat intersects the rst arc. Finally, draw a third arc,with a radius of ve units and which has a centerat (8.0). Where do they intersect? How many arcsare needed to determine a point.

Suppose that the Cartesian coordinates in TableGPS-RE-1 were mapping a portion of ocean andthat the side of each square was the distance it

Signal travel time

Ship Location milliseconds

Alexandria (0,0) 4.0

Corsica (1,5) 2.0

Hsuchou (6,3) 3.5Figure GPS-RE-13: The resulting simple

Figure GPS-RE-12: Label a sheet of graph paper

Figure GPS-RE-14: Cartesian coordinates dening

Table GPS-RE-1: Ship location and time for Bainbridges signal to travel to each ship


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YOURSCHOOL

ANOTHERSCHOOL

ANOTHERHOUSE

YOURHOUSE

North0

180

South

East90

West270

North0

18 0

South

East90

West270

GPS InvestigationSchool Site Location Map Graphic


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GLOBE 2005 Appendix - 1 GPS

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Site Location Data Sheet

GPS Investigation Data Sheet

Offset GPS Measurements Data Sheet

Glossary


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GPS InvestigationSite Location Data Sheet

You will need at least one copy of this GLOBE GPS Data Sheet per GLOBE site. After making your

eld GPS measurements and averaging the position data, note your results on one of the GPS DataSubmission Sheets, then submit your data to GLOBE. You can do this by accessing the GPS data entrypage under the main GLOBE page (http://www.globe.gov) on the World Wide Web. You will besubmitting the determined average location for each of your sites (Atmosphere, Land Cover, Biology,Hydrology, Soil Characterization, and Soil Moisture Study Sites and your school). The data submittedshould be rounded to the nearest 0.01 minutes as displayed on your GPS receiver.

Type of Site(Atmosphere, Hydrology, etc.)

Site Description(25 characters or less)

Averaged Latitude(Whole Degrees, Decimal Minutes N/S)

Averaged Longitude(Whole Degrees, Decimal Minutes E/W)

Time of 1st ObservationHours: Minutes: Seconds in UT

Type of Receiver Magellan Trailblazer XL & UNAVCO number

or

Manufacturer model number and serial number


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GPS InvestigationData Recorded By: Date Recorded: Year Month: Day:Circle Site type: School Atmosphere HydrologySoil Land Cover PhenologyOtherSite Name: School Name:

School Address:

Do not begin recording data until your GPS receiver has locked in. Wait at least one minute between recording each observation.Record the following data from the appropriate screens on your GPS unit.

OBS Latitude Longitude Elevation Time # Sats Messages

Decimal Degrees (N/S) Decimal Degrees (E/W) Meters H:M:S UTC Satellites Circle if Shown

1 2D 3D

2 2D 3D

3 2D 3D

4 2D 3D

5 2D 3D


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Offset GPS MeasurementsData Sheet

Data Recorded By: Date Recorded: Year Month: Day:Circle Site type: School Atmosphere Hydrology

Soil Land Cover PhenologyOther Site Name: School Name:School Address:

Offset GPS MeasurementsMeasured Latitude: degrees N or S (circle one)

Measured Longitude: degrees W or E (circle one)Direction from GLOBE site to offset location: N or S (circle one)

Distance from GLOBE site to offset location: meters

ComputationsChange in Latitude = Distance:_________meters = ________degrees

GLOBE Sites Latitude:If offset location is further from Equator than the study site:

GLOBE site latitude = (Measured Latitude) - (Change in latitude) = degrees N or S(circle one)

If offset location is closer to the Equator than the study site:

GLOBE site latitude = (Measured Latitude) + (Change in latitude) = degrees N or S(circle one)

GLOBE sites longitude: W or E (circle one) Same as Measured Longitude at the Offset location

GLOBE sites elevation: From a local topographic map using your sites latitude and longitude

110,000 meters/degree


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Glossary

AccuracyThe difference between the indicatedmeasurement value and the true value

AverageA technique for using one number todescribe a group of numbers. An average(or mean) value is computed by summinga set of values and divided the sum bythe number of values summed.

EquinoxOne of the two times of year when thesun appears directly over Earths equatoroccurring typically on 21 March (vernalequinox) and 23 September (autumnalequinox). On these days, the times of daylight and night will be equal.

GeoidThe irregular surface that follows theglobal mean sea level and is shaped byEarths gravitational eld

Global Positioning System (GPS)The Global Positioning System is anavigation system that includes 24satellites orbiting 20,200 kilometers

above the Earth. Using timemeasurements of GPS satellite signals,the receivers can pinpoint our latitude,longitude, and elevation.

HistogramA frequency distribution plot indicatinghow often a particular number appears ina group of numbers

LatitudeThe angle measurement in degrees of a planet north and south of its equator.Beginning at the Earths equator (0),latitude is measured in degrees, with thepoles being 90 north and south.

Longitude

The angle measurement in degreeseast and west around a planets spinaxis. On Earth, the Prime Meridian is thenorth-south line through the town of Greenwich, England. This is 0 longitude,and the International Date Line is 180from the Prime Meridian.

Magnetic CompassA hand-held instrument displayingthe angular orientation of a pivotinglightweight magnet. Because Earthbehaves like a giant magnet, the magnetin the compass will point toward Earthsmagnetic poles which generally indicatesnorth and south.

Magnetic VariationAlso called Magnetic Declination, thisis the angle between the magnetic andgeographic (spin axis) poles specicto a locality. It is expressed in degreeseast or west to indicate the directionto true north from magnetic north.Earths magnetic north pole is slowly

moving and presently located inCanadas North West Territories about11 degrees away from our North Pole.

Additionally, magnetic propertiesof Earths composition vary slightlybetween locations contributing a uniquedistortion to Earths magnetic eld atany given site. Values may be found onnavigation charts.

MeridianThis is a circumference around the Earthssurface which passes through both polesand the equator. These form curves of constant longitude between any two poles.


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NavigationThe science and technology of determining course, position, anddistance traveled.

Offset SiteThis is a site directly north or southof a site where we are able to make asuccessful GPS measurement.

Positions (or Locations) AbsoluteMeasured from an agreed upon xed

location.RelativeMeasured from some arbitrary point such as

your location.Plumb bob

A vertical line formed by a stringsupporting a weight. The weights usedto be made of lead and a former andLatin derived chemical name for leadwas plumbum from which comes theEnglish word plumber.

PrecisionThe measure of the repeatability of anobservation, that is if a measurement isrepeated multiple times, how much willthe individual measured values vary from

the average of all the measurements.Reference Ellipsoid

A smooth surface that approximatesmean sea level. It is used by GPS receiversas the reference surface in their elevationmeasurements.

ResolutionThe smallest change which can bedisplayedby an instrument

SatelliteAny celestial body that orbits anotherlarger body

SolsticeOne of the two times of the year whenthe overhead sun appears furthest fromEarths equator occurring typically on 21

June and 22 December. These will be thelongest and shortest days of the year if your location is respectively closer to orfurther from the overhead sun.

Sun angleThis is the angle between horizontal(the ground) and our sun. Sometimesthis angle is called an elevation oraltitude angle.

TrigonometryThe mathematical study of triangles,trigonometric functions, and their

applications. Trigonometric techniquesallow us to relate angle values to thelengths of various sides of a triangle.

Zenith angleFor our sun angle measurement, thisis the angle between vertical (straightup) and our sun. In navigation, this issometimes called a zenith distance. Onthe days of the spring or fall equinoxes,this angle will be our latitude. The zenithis the point directly overhead whereverwe are. The sum of the sun angle and thezenith angle is 90.


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Circular Units, Distances, and RelationshipsDegree ()

A circle may be divided into 360 (or 400Grads or about two times Pi ( Radians).Small fractions of a degree may beindicated either as decimal fractions(25.2525) or using whole degrees,minutes, and seconds 25 15' 9").

Minute (arc minute, ')One degree may be divided into 60minutes. Therefore, there are 360 x 60 =21,600 arc minutes (21.600') in a circle.

Second (arc second, ")One minute may be divided into 60seconds. Therefore, there are 60 x 60

= 3600 arc seconds in one degree or1,296,000 arc seconds (1,296,000") in acircle.

RadianAn angle measurement unit equal to theangle subtended at the center of a circleby an arc equal in length to the radius of the circle. A full circle contains two timesPi radians or 360. One radian is about57.3. For example: 25. 15' 9" = 25.2525= about 0.4407 radians. Pi is an irrationalnumber (cannot be described as a ratio of two whole numbers and thus requires aninnite number of decimal digits) with avalue of about 3.141592653590. Pi hasbeen computed to millions of digits butthe accuracy of the value listed here wouldinduce errors of less than a meter whenworking with distances the size of oursolar system.

Time Reference FramesLocal Solar Noon

The time-of-day when the sun angle isgreatest at your location. This time isspecic to your location and varies byabout a half-hour throughout the year.

Mean TimeFormerly called Civil Time, this is thetime-of-day value typically displayedon our clocks. It is dened to cause theyearly average location of the sun to bethe same and near overhead at noonin your time zone. Each time zone isdifferent by one hour from adjacenttime zones and is dened to be 15 of longitude with a few minor exceptions

determined by governments to suit localneeds or geography. Your mean may berelated to Universal Time by determiningyour distance from Earths 0 longitudeeither in 15 increments or numbers of time zones. Universal and Mean Timemay be contrasted to Sidereal Time(used by astronomers and sometimescalled star time) which is dened to bringdistant celestial bodies to the same pointin the sky after exactly one Earth rotationaround its sun. A sidereal day is about 4minutes shorter than a day as indicatedusing mean time.

Universal TimeAlso known as UT, Zulu, or GMT(Greenwich Mean Time), this is the time-of-day for a 24 hour day dened to causethe yearly average location of the sun to beoverhead at noon when observed at Earthszero degree longitude.


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Consequences of the 23.5 tilt of Earths spin axis from the plane of Earths solar orbit Arctic and Antarctic Circles

Also called North and South Polar Circles,these are the extremes in latitude (66.5North and South) from Earths poleswhere total darkness or sunlight may beexperienced in local respective winters orsummers.

Tropics of Cancer and CapricornThese are the extremes in latitude (23.5North and South respectively) from Earthsequator between which the sun may bedirectly overhead at some time during theyear.

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