Lab Write-up for the Orange Group (Charlie)
- 22 February 2011
- N.B. - This write-up is completely fictitious, I did not collect any data or do any of the work described below. It's purely an example of one way to write-up a lab report for this lab. The procedures, error analysis and such are accurate, just the data has been faked.
Greenwich, England is home to the Prime Meridian, the arbitrary line that signifies 0 degree longitude for global navigation. The lab assignment, Where am I?, asks us to determine where a particular location in Greenwich is located using different tools/methods to determine the latitude, longitude, and elevation of that location.
The spot I was assigned was just outside the Starbucks in Greenwich:
For this lab we have to use three different tools/methods to determine the latitude, longitude and elevation. Listed below are the choices I made:
- Latitude - GPS, Google Earth, and estimation
- Longitude - GPS, Google Earth, and estimation
- Elevation - GPS, Google Earth, and estimation
Next the instructions ask us to determine what is due North and due South of that location:
- North - compass and visual observation
- South - compass and visual observation
Lastly the instructions ask us to determine the distance from that spot to the Prime Meridian using two different tools/methods, I used Google Earth and estimation for this quantity.
Equipment and Procedures
- Garmin etrex handheld consumer GPS unit, software version 3.5.0
- Using the GPS involves powering it on, waiting for it to acquire enough satellite signals, noting the margin of error, and then switching the mode to waypoint which displays the latitude, longitude, and altitude. To obtain three readings I slowly spun in a full circle while chanting "umm" and then stopped and waited for the GPS to produce a new reading.
- Google Earth software, version 18.104.22.1682 (beta), running under OSX 10.6.6
- Once Google Earth is launched you can enter the location of interest in the search box and then zoom-in to the appropriate magnification for the task at hand. To obtain three readings I moved the mouse around on the screen and then returned it to the point of interest and re-read the latitude, longitude and altitude from the status bar on the bottom of the screen.
- Estimation using a 48 year old white male American with a background in science and engineering
- For the latitude I found the nearest lamp post and noted the latitude marked on it.
- For the longitude I found the nearest lamp post and noted the longitude marked on it.
- For the altitude I found the nearest lamp post and noted the altitude marked on it.
- For the distance to the prime meridian I calculated my pace by walking the length of the Cutty Sark 3 times, averaging the number of paces, and then dividing the known LOA of 280' by that value. Using this method my pace was determined to be 2.5'. Using a hand-held compass I walked a line due East from the spot to the Prime Meridian keeping track of the number of paces and then multiplied by 2.5' to obtain an estimate of the distance.
- Silva bog standard hand-held compass, circa 1975
- While holding the compass on the outstretched palm of your hand, and using the bubble to ensure that it's level, an accurate reading can be taken if you hold your head directly above the compass and look straight down.
Sources of Error
There are many sources of error when using
Greenwich is also home to the GPS meridian, the 0 degree longitude
Extra Credit: Visualization
Map with circle?
Appendix A: Raw Data
A description of the task at hand and your approach to the work. A description of the spot you are working from. The measurements as listed under Details above, for each of the tools/methods, organized in tabular form. A discussion of the sources of error associated with each of the tools/methods you employed and the likely range into which the correct answer is likely to fall for each of them. The raw data, that is each value read (at minimum 3 values for each data point) for each tool/method you employ for a given measurement. Extra Credit: A basic visualization which utilizes an aerial image with a placemark at the spot, labeled with the coordinates, and visual indications of the "zone of error" for each of the tools/methods you employed.
Description of task and approach
Despite being a completely arbitrary line, the prime meridian holds a great deal of significance for human navigation. During our visit to Greenwich, we used the prime meridian as a reference point for our assigned location. We estimated the latitude, longitude and elevation of the given spot using a GPS, a compass and human estimation. We used footsteps to determine our distance from the Royal Observatory as well as labels on a nearby lamppost.
Description of the spot
For this lab, we were directed to find the corner/intersection of May's Buildings Mews and May's Court. Quickly, we recognized (both through googlemaps and observations of the human eye) that our location was approximately on the same latitude as the Royal Observatory. Our estimate was that we were located 25 m South of the Royal Observatory’s latitude. We first took a description of what was directly North of our location. Standing on May’s Buildings Mews (a brown loose gravel road/driveway) we used a compass to look North and noted a black gate reading “The Grange”, on one side in stone, and “52 Mays Buildings Mews”, on the other side of the gate. Turning around 180° we now took observations of the location directly South of our location. In this direction ran May’s Court North to South. Along this short road were several residential homes identified as “Beaver’s Housing Society”. More directly South of our location was the front yard and the birdfeeder. Looking to the East we identified a lamppost with elevation and longitude markings. We estimated this lamppost to be about 25 meters east of our location, and it proved instrumental in many of our ‘Human Estimations’.
Measurements & Raw data(raw data in bold)
Method 1 [Human Estimation]
royal observatory (51° 28’38.56”) – 25 m = 51.47737777766666° – (25m / 111248.24m) = 51.477153055010373°N
(lengths of degree latitude at 51° = 111248.24m)
Method 2 [GPS]
51° 28.633’ = 51° + (28.633 / 60) = 51.477216666°N
Method 3 [GoogleEarth]
51°28'37.82"N = 51° + ((28 + (37.82 / 60)) / 60) = 51.4771722222°N
Method 1 [Human estimation/lightpole]
0° 0.381’ + 21 m = 0.00635° + (21 m / 70,197.65m) = 0.00664915°W
(length of degree longitude at latitude 51° = 70,197.65m)
Method 2 [GPS]
0° 0.372’ = 0° + (0.372 / 60) = 0.0062°W
Method 3 [GoogleEarth]
0° 0'22.42"W = 0° + ((0 + (22.42 / 60)) / 60) = 0.0062277777°)
Method 1 [Human estimation/lightpole] – 13 m
Method 2 [GPS] – 14 m
Method 3 [GoogleEarth] – 22 m
4) DUE NORTH:
A black gate and driveway for number 52 Mays Buildings Mews (written in stone next to the gate says “The Grange”)
5) DUE SOUTH:
Mays Court…and a housing complex called Beaver’s Housing Society…more specifically the birdfeeder in the front lawn
6) SHORTEST DISTANCE FROM PRIME MERIDIAN:
Method 1 [Human Pace]
184 paces (estimated at .5 m/pace) X 2 = 184 m
Method 2 [GoogleEarth]
Discussions of sources of error
Sources of error made during data collection can be attributed to several factors. In choosing to use Johanna's footsteps to measure distance, we realized that we had no way exact way of ensuring that each footstep was equal to the next. The circumference of Spencer's wheelchair would have been more exact, and originally we found that circumference (using the tiles in the TexMex restaurant) to be two meters. Our first objective was to measure the distance between the spot of our location and the nearest lamppost. That alone was quite a tedious challenge using Spencer's wheelchair as it proved very difficult to follow the exact amount of wheel rotations. The group decided that it would be an inefficient use of time to attempt this method in measuring our distance from the Royal Observatory. Our next solution was to figure out Johanna's pace. Knowing the circumference of Spencer's wheel we compared one rotation to two of Johanna's steps. It took her four steps to go the exact same distance as a whole rotation, therefore it was estimated that one step was equal to 1/2 a meter. Although we are confident in this estimation we cannot be as confident in the consistency of Johanna's steps and therefore the human estimation involved in "Longitude", "Latitude", and "Distance from Prime Meridian" must account for a certain level of error.
Furthermore, when calculating the "Latitude" and "Distance from Prime Meridian" we noticed that we were extremely close, but not exactly, to the same latitude as the Royal Observatory. Using and eyeball estimation we attempted to walk a parallel line to the Prime Meridian from our location to the spot lying on the same latitude as the Royal Observatory (also using a compass to ensure East remained in the same general direction). Again with Johanna's pace this estimate came out as 25m (accounting for possible error in our human estimation on "Latitude" as explained above). From this location (noting the GPS longitude coordinate remained the same as our initial location) we decided an accurate measure of our distance from the Prime Meridian could be found by estimating the distance between us and the Royal Observatory. A number of sources of error occurred in this process. It would be a severe physical challenge to walk from this location directly to the Royal Observatory because of the path leads up the hill, not to mention that a measurement of Johanna's pace up the hill would be an inaccurate measurement of the actual distance since it would include a vast change in elevation. Our solution was to make a human estimation of a halfway point between the two locations, measure the distance between our current location and there, and then double that measurement. Obviously, our estimated halfway point was recorded through no more than the human eye and accounts for some of the possible error. Also, while walking to this point, we ran into a wall, stopped counting the pace while we walked perpendicular to our path until coming to an entrance to the park, where we again continued along our path and pace measurement. This pause in our measurement could also be the cause of some of the inaccuracies.
It is also possible that the degree of error associated with the GPS system and the satellites that it corresponds with is an issue which also may have affected the data points we obtained. When analyzing the results given by 'Google Earth' we looked for 0 degrees longitude and noticed that the spot it directed us to on the map did not appear to run through the Royal Observatory but a significant distance to the East of the Royal Observatory. This peaked our interest and with some basic research on wikipedia we discovered that a GPS will not indicate 0 at the Royal Observatory because GPS' operate according to a "GPS Prime Meridian" that is actually located approximately 100 meters east of the Royal Observatory. This is actually the Prime Meridian used by the International Earth Rotation and Reference Systems Service (identified in this context as the IERS Rference Meridian) specifically because it is the GPS Prime Meridian as identified by the United States Department of Defense. It is the current reference point for WSG84 (World Geodetic System 1984). Ironically, wikipedia identifies 2010 as the year in which WSG84 will no longer be valid after 2010. Anyways, the IRM or GPM is 5.31 arcseconds east of the meridian circle at the latitude of the Royal Observatory (specifically, 102.5 meters). Interestingly enough, this difference is attributed the legacy left behind by the TRANSIT, the first satellite navigational system. The TRANSIT surveyed coordinates in a non-Earth centered ellipsoid, yet has used those coordinates in Earth-centered ellipsoids, accounting for the differences. This helps to explain the source of error presented when using the GPS.
From everything we can tell, GoogleEarth appears to be the most accurate. However, we are not experts in using the program and it too could present inaccuracies. For instance, many of the coordinates it provides depends on the very specific location of the cursor. Try as we might, we cannot say with complete certainty that our cursor was on the exact locations we desired. One question we are left with deals with the elevation GoogleEarth provided. Our "human estimation" was based off of the lamppost nearby which read 13m. We felt our location on the same elevation as this lamppost, and the GPS helped validate that estimate by showing 14m. However, GoogleEarth identified the elevation at our location as 22m, which is a large enough difference to question it as a source of error.
Reviewed - 21 February 2011