Featured Surveying Discussions - Land Surveyors United - Global Surveying Community2024-03-28T23:08:20Zhttps://landsurveyorsunited.com/hubs/survey-earth-in-a-day/forum/feed/featuredCoordinate Systems and Triangulationhttps://landsurveyorsunited.com/hubs/survey-earth-in-a-day/forum/coordinate-systems-and-triangulation2012-04-09T01:34:55.000Z2012-04-09T01:34:55.000Z⚡Survenator⌁https://landsurveyorsunited.com/surveyors/Survenator<div><p>The rotational motion of the earth spinning on its axis provides two natural points, the poles, upon which to base coordinate systems. These systems are networks of intersecting lines (graticules) inscribed upon the globe to permit the precise location of surface features. They are a method of organizing the concepts of direction and distance so that a comprehensive system of relationships can be established. Two types of systems are in general usage for reference mapping: a geographical coordinate system which uses lines of longitude and latitude to fix positions, and a rectangular coordinate system, such as the Universal Transverse Mercator (UTM) Grid System, which uses eastings and northings as the locational technique. Navigation charts, in contrast to their terrestrial partner, the topographic map, may be overlaid with another geo-referencing system, the Loran-C network lattice.</p>
<p><span class="font-size-4"><strong>The principle of triangulation Figure 1</strong></span></p>
<p><span class="font-size-4"><strong><a target="_self" href="{{#staticFileLink}}1200644915,original{{/staticFileLink}}"><img class="align-full" src="{{#staticFileLink}}1200644915,original{{/staticFileLink}}" width="600" /></a></strong></span></p>
<p><span class="font-size-4"><strong>A great and a small circle Figure 2</strong></span></p>
<p><span class="font-size-4"><strong><a target="_self" href="{{#staticFileLink}}1200644959,original{{/staticFileLink}}"><img class="align-full" src="{{#staticFileLink}}1200644959,original{{/staticFileLink}}" width="600" /></a></strong></span></p>
<p>The terminology associated with coordinate systems includes the following:</p>
<p>i) <strong>Great circle</strong>: A plane passing through the centre of the earth cutting the surface in a great circle (Figure 4.2), e.g., all meridians and the equator. An arc of a great circle is the shortest distance between two points on the earth's surface;</p>
<p>ii) <strong>Small circle</strong>: A plane passing through the earth, other than through the centre (Figure 4.2), e.g., parallels of latitude;</p>
<p>iii) <strong>Poles</strong>: Terminii (north and south) of the earth's axis;</p>
<p>iv) <strong>Meridians</strong> (lines of longitude): A set of north-south lines connecting the poles. Each meridian is half a circle. Two opposite meridians make a great circle (Figure 4.3);</p>
<p>v) <strong>Equator</strong>: The only great circle perpendicular to the earth's axis, and dividing the earth into northern and southern hemispheres;</p>
<p>vi) <strong>Parallels</strong> (lines of latitude): A set of east-west lines running parallel to the equator (Figure 4.3);</p>
<p>vii) <strong>Latitude</strong>: The angle (north and south) subtended by two imaginary straight lines, one extending from a given place inwards to the earth's centre, and the other from the earth's centre to the equator (Figure 4.4);</p>
<p>viii) <strong>Longitude</strong>: The angle (east or west of the prime meridian) subtended by two imaginary straight lines, one extending inwards to the earth's axis, and the other from the earth's axis to the prime meridian (PM), i.e. the meridian chosen for 0° which passes through Greenwich, U.K. (Figures 4.4 and 4.5). Going east from the PM, the meridians are numbered up to 180° East (the eastern hemisphere). Going west from the PM, the meridians are numbered up to 180° West (the western hemisphere) (Figure 4.4). Because the meridians converge at the poles, the 1° longitude interval decreases from 111 kilometres at the equator to 56 kilometres at 60° North or South and zero kilometres at the poles (Table 4.1);</p>
<p>ix) <strong>Graticule</strong>: A network of lines representing parallels and meridians on paper, i.e. geographic coordinates which are defined in degrees, minutes and seconds;</p>
<p>x) <strong>Grid</strong>: Two sets of parallel lines crossing at right angles to form squares, i.e. grid coordinates.</p>
<p><span class="font-size-5"><strong>(a) Meridians; (b) parallels.  FIGURE 3</strong></span></p>
<p><span class="font-size-5"><strong><a target="_self" href="{{#staticFileLink}}1200644972,original{{/staticFileLink}}"><img class="align-full" src="{{#staticFileLink}}1200644972,original{{/staticFileLink}}" width="600" /></a><br /></strong></span></p>
<p><span class="font-size-4"><strong>The geographic grid of parallels and meridians. Point A has a latitude of 50 North and a longitude of 75 West.</strong></span></p>
<p><span class="font-size-4"><strong><a target="_self" href="{{#staticFileLink}}1200645075,original{{/staticFileLink}}"><img class="align-full" src="{{#staticFileLink}}1200645075,original{{/staticFileLink}}" width="600" /></a><br /></strong></span></p>
<p><span class="font-size-4"><strong> </strong></span></p>
<table cellspacing="0" width="100%">
<caption><br />
TABLE 4.1<br />
<br />
THE LENGTH OF 1° INTERVALS OF SELECTED LATITUDES AND LONGITUDES<br /></caption>
<tbody>
<tr>
<th style="border-top: thin solid black;"></th>
<th style="border-top: thin solid black;" colspan="2">LENGTH OF 1° OF LATITUDE</th>
<th style="border-top: thin solid black;" colspan="2">LENGTH OF 1° F LONGITUDE</th>
</tr>
<tr>
<th>Latitude (Degrees)</th>
<th>Statute Miles</th>
<th>Kilometres</th>
<th>Statute Miles</th>
<th>Kilometres</th>
</tr>
<tr>
<td style="border-top: thin solid black;" align="center">  0</td>
<td style="border-top: thin solid black;" align="center">68.704</td>
<td style="border-top: thin solid black;" align="center">110.569</td>
<td style="border-top: thin solid black;" align="center">69.172</td>
<td style="border-top: thin solid black;" align="center">111.322</td>
</tr>
<tr>
<td align="center">  5</td>
<td align="center">68.710</td>
<td align="center">110.578</td>
<td align="center">68.911</td>
<td align="center">110.902</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">68.725</td>
<td align="center">110.603</td>
<td align="center">68.129</td>
<td align="center">109.643</td>
</tr>
<tr>
<td align="center">15</td>
<td align="center">68.751</td>
<td align="center">110.644</td>
<td align="center">66.830</td>
<td align="center">107.553</td>
</tr>
<tr>
<td align="center">20</td>
<td align="center">68.786</td>
<td align="center">110.701</td>
<td align="center">65.026</td>
<td align="center">104.650</td>
</tr>
<tr>
<td align="center">25</td>
<td align="center">68.829</td>
<td align="center">110.770</td>
<td align="center">62.729</td>
<td align="center">100.953</td>
</tr>
<tr>
<td align="center">30</td>
<td align="center">68.879</td>
<td align="center">110.850</td>
<td align="center">59.956</td>
<td align="center">  96.490</td>
</tr>
<tr>
<td align="center">35</td>
<td align="center">68.935</td>
<td align="center">110.941</td>
<td align="center">56.725</td>
<td align="center">  91.290</td>
</tr>
<tr>
<td align="center">40</td>
<td align="center">68.993</td>
<td align="center">111.034</td>
<td align="center">53.063</td>
<td align="center">  85.397</td>
</tr>
<tr>
<td align="center">45</td>
<td align="center">69.054</td>
<td align="center">111.132</td>
<td align="center">48.995</td>
<td align="center">  78.850</td>
</tr>
<tr>
<td align="center">50</td>
<td align="center">69.115</td>
<td align="center">111.230</td>
<td align="center">44.552</td>
<td align="center">  71.700</td>
</tr>
<tr>
<td align="center">55</td>
<td align="center">69.175</td>
<td align="center">111.327</td>
<td align="center">39.766</td>
<td align="center">  63.997</td>
</tr>
<tr>
<td align="center">60</td>
<td align="center">69.230</td>
<td align="center">111.415</td>
<td align="center">34.674</td>
<td align="center">  55.803</td>
</tr>
<tr>
<td align="center">65</td>
<td align="center">69.281</td>
<td align="center">111.497</td>
<td align="center">29.315</td>
<td align="center">  47.178</td>
</tr>
<tr>
<td align="center">70</td>
<td align="center">69.324</td>
<td align="center">111.567</td>
<td align="center">23.729</td>
<td align="center">  38.188</td>
</tr>
<tr>
<td align="center">75</td>
<td align="center">69.360</td>
<td align="center">111.625</td>
<td align="center">17.960</td>
<td align="center">  28.904</td>
</tr>
<tr>
<td align="center">80</td>
<td align="center">69.386</td>
<td align="center">111.666</td>
<td align="center">12.051</td>
<td align="center">  19.394</td>
</tr>
<tr>
<td align="center">85</td>
<td align="center">69.402</td>
<td align="center">111.692</td>
<td align="center">  6.049</td>
<td align="center">   9.735</td>
</tr>
<tr>
<td style="border-bottom: thin solid black;" align="center">90</td>
<td style="border-bottom: thin solid black;" align="center">69.407</td>
<td style="border-bottom: thin solid black;" align="center">111.700</td>
<td style="border-bottom: thin solid black;" align="center">  0.000</td>
<td style="border-bottom: thin solid black;" align="center">   0.000</td>
</tr>
</tbody>
</table>
<p><span class="font-size-5"><strong>Geographical coordinate system</strong></span></p>
<p>The geographical coordinate system was developed from concepts originated by Greek philosophers before the Christian era. It is the primary system used for basic locational reckoning, such as navigation and surveying. The system is basically one of spherical coordinates, the meridians and parallels being neither straight nor equally spaced. It is useful for mapping large areas and the measurement of distances and directions in angular measure of degrees, minutes and seconds. A rectangular coordinate system which is far simpler in construction and usage may be superimposed on the geographical coordinate system.</p>
<p><span class="font-size-5"><strong>Rectangular coordinate system</strong></span></p>
<p>The Universal Transverse Mercator (UTM) Grid System is an international system which provides rectangular grid zones for the globe between latitude 80° South and 80° North. Poleward of 80°, the Universal Polar Stereographic Grid System is used. These systems are named after the map projections on which they are based. The UTM Grid System consists of 60 grid zones, each 6° of longitude in width (Figure 4.6). The origin (0°) of the grid zone is the intersection of the central meridian and the equator, both straight lines. The grid is a network of 1,000 metre, 10,000 metre or 100,000 metre squares, each identified by the grid coordinates of its lower left hand corner. In stating grid coordinates, the number of metres east or eastings (right) is given first, followed by the number of metres north or northings (up). The procedure for reading UTM grid coordinates is explained in Figure 4.7. In order to have all eastings increase towards the right across the entire zone, the central meridian is given the arbitrary value of 500,000 metres east. The equator is given the value of 0 metres north as the reference line for northings increasing up to the 80th parallel north. For the southern hemisphere, the equator is given the arbitrary northing of 10 million metres north, so that northings begin with their lowest value at 80° South latitude and increase northward to attain that figure at the equator. The Universal Transverse Mercator Grid System has now been widely adopted for topographic maps, referencing of satellite imagery, natural resource data bases and similar applications which require precise positioning.</p>
</div>150 year old surveyorhttps://landsurveyorsunited.com/hubs/survey-earth-in-a-day/forum/150-year-old-surveyor2014-06-04T14:04:38.000Z2014-06-04T14:04:38.000ZJ W Veatchhttps://landsurveyorsunited.com/surveyors/JWVeatch<div><p> John Veatch has had a lot of experience as a land surveyor. Unfortunately the John Veatches of the world have a pension for being decades ahead of their time. </p><p> </p><p>The first John Veatch came to St. Mary’s County Maryland even before this country was one. The land surveyor John Veatch came from a preacher’s family, growing up in Indiana and Kentucky. His father was also a member of the Indiana legislature. In 1835 he presented himself to Jorge Antonio Nixon, land commissioner for the Galveston Bay area; and requested a land grant that he was entitled to as a colonist. He picked his land by splitting his certificate, placing part in Jefferson County southeast of the ravine of Tevis because of the “mineral water” there. As we now know his “mineral water” was the oil discovered in the Sour Lake and Spindletop Dome oilfields some fifty years after Veatch left. This is to this day some of the most valuable land in Texas. Veatch spent several years around Bevil and Town Bluff where he practiced surveying. He was elected as a delegate from the municipality of Bevil to the Consultation of 1835 and secured additional land through his surveying practice. “In Oct. 1835, John McGaffey and Dr. John Veatch dragged measurement chains and survey instruments across the McGaffey league (4,426 acres) and McGaffey labor (177 acres), mostly through marsh land”. By 1850 he had moved to San Antonio and amassed $15,000 in real estate.</p><p> </p><p>So the name Veatch has been around for some time. And of course many of you know the name Black & Veatch, the 10th largest consulting firm in the world </p><p>I am one of the latest versions of the John Veatch's and I am also a professional land surveyor. As for me I have watched with some personal interest the land surveying profession wrestle, as has most professions, with the emerging digital revolution. For most of past several decades land surveyors have been scaling the mountain of the new technologies and as they approach the summit they are just now beginning to recognize that I have been up there waiting for them for about 20 years. </p><p> </p><p>I invented and patented a land surveying process and to this day I marvel how resistant my profession has remained to the advances in data collecting technology. Now I know surveyors have a long history of mountain men in our ranks going all the way back G. Washington and I know we don’t drag around 100 foot long steel tapes anymore. That was back in the day when I started surveying. However, land surveyors, and other professional, don’t really seem to be very concerned about the rate that technologies have been invading the information sanctuaries that were once exclusively ours.</p><p> </p><p>.</p><p> </p><p> </p><p>When I first introduced my satellite surveys to other surveyors I was disappointed but not shocked by their lack of interest. In fact one of my business associate and friend, who was the owner of one largest land surveying firms in the area, said to me “Can’t you wait to start all this stuff until I retire?” But the real crunch came when a past member of the state land surveyor’s licensing board, and a competitor, tried to get the state Professional Licensing Board to outlaw my new surveys.</p><p> </p><p></p><p> </p><p>In some ways it is remarkable that the land surveying profession is so far behind the times. Particularly when you consider the fact that land surveyors were one of the first to employ computers in their business. One of the companies I bought early on was a data processing outfit that was housed in my D.C. offices. Those guys would sit all day at terminals creating punch tapes that were then hauled up to Baltimore and run through a computer that drove a pool table sized plotter to create ink on mylar subdivision plats. When I was a VP of Greenhorne & O’Mara, our nations 23 largest architectural & engineering firm, we had a large room for our mainframe that was connected to the terminals in the computing department where Lloyd Jones and the boys were developing surveying routines. The truly sad part of this story is for more than ½ a century land surveying companies all across this land have been creating very accurate coordinate geometry files of survey information in digital form and once the job was completed those files were trashed. That is one of the reasons I suspect that the boundary coordinates for most of the 127 million parcels of land in this country will have to be recomputed.</p><p> </p><p> I saw my first ortho-rectified aerial image (google earth) while on a visit to one of my strategic partners mapping facility in Northern Ireland. In that instant I knew land surveying was going to change in ways that, back then, was hard to imagine. So I got together with a couple of techno-savvy business associates and we formed a company we called VARGIS.com. Our business plan was to bring this new digital mapping to the market place by creating and licensing digital ortho-maps. We had some success creating and licensing about $40 million dollars worth of data to federal, state, and local government agencies as well as utility companies such as Bell South and PAC Bell. Needless to say once people started to understand the utility of our digital maps we got a lot of attention. It was one such fellow was constantly in my office who took some of our data to use for a demo in front of a group of Realtors in Californa. Now as the story was told to me, sitting in the audience was one of the founders of Google. And as they say the rest is the stuff that history is made of. Goolge Earth was born, 90 days later Google had 40 million new customers for their web browser. VARGIS was plugging away trying to make a few bucks sell or licensing our digital maps and Google made billions giving them away.</p><p> </p><p> Keep in mind that back when I was involved with VARGIS, AOL ruled the internet world and at that time it cost us about $5,000 a square mile to produce the mapping data. Yesterday I was given a price of $60K to map 120 sq. miles at ½ pixels. That’s $500 a sq. mile and the datasets will include 6,665,472,000 coordinate points. The fact is an onboard aerial digital camera and lidar can collect more point data in 1/250 of a second than a bus load of land surveyors could collect in a month.</p><p> </p><p></p><p> </p><p> </p><p> </p><p>THE FUTURE IS NOW</p><p> </p><p>The new point of beginning for all future land surveys is orbiting the earth at 5,000 miles an hour 12 ½ thousand miles up in the stratosphere and has been there for a very long time. That’s correct and I suppose I owe my fellow professional land surveyors an apology for my participation in the changes we have been going through the last 20 years (see the POB cover above). The fact of the matter is the PLS’s of this country have had our exclusive provenances invaded by all maner of non-surveyor professionals and others. In the state of Florida it is not “Professional Land Surveyors” it’s “Land Surveyors & Mappers” just how the aerial mapping guys of the world got included in professional land surveying by my state’s professional board is still a big question to me. Now even professional engineers are allowed to sign off on elevation certificates. However what’s coming next will change the profession for ever.</p><p> </p><p>As GIS becomes more user friendly the applications will surely follow. This is not good news for land surveyors. To be sure computer technology has made the tedious simple and the digital revolution has made the storage and retrieval of a universe of information a mouse click away. Even so when it comes to Digital Mapping in the USA what you think you see may not necessarily be what you get. This is particularly true of property lines drawn on public and private online image maps. I am referring here to the proliferation of geographic information systems in every burg and hamlet in the USA. In a misguided attempt to show property lines on government & private systems the locale GIS managers have resorted to all kinds of low tech approaches. The result has been the dissemination of misinformation that the uninformed would justifiably assume to represent the actual legal delineation of property lines. What appears to be missing in any discussions in the Digital Mapping World is the recognition of the fact that lines on a map, or in our new virtual world, do not necessarily represent those same lines in the real world. Even if the person or persons creating these lines uses real world coordinates and connects the dots they create, unless those coordinates & connecting lines were created as a result of a real world professional land surveyor’s standard of care the lines connecting those dots cannot possible represent actual property lines that are legally required.</p><p> </p><p></p><p> </p><p></p><p> </p><p></p><p> </p><p>You will note that the Lee County property line data shows the property lines running through the house (not likely even in Florida)</p><p> </p><p>As for now professional land surveyors have been kept alive by things subsurface. Not minerals or oil or stuff like that but 1/2” iron rods set just below the surface so Joe Homeowner will not sue the guy who put it there because Joe Homeowner won’t hit it with lawnmower. That said there is a phenomenal unintended residual value to this type of subsurface surveying to all the PLS’s of the world who deal in real property surveys. The fact is these iron rods or pipe represent “property rights” above and below the surface when they are used to mark the corners of real estate. Because they are invisible to all of this hi-tech Lidar and other new field data collecting devices “FEET ON THE GROUND” will be the only way to recover and collect the data related to <i>Real Property Corners</i> as well as collect the site and specific point data required by FEMA, and other public and private insurance providers.</p><p> </p><p></p><p> </p><p> </p><p> Maybe GIS really does mean “Get It Surveyed”</p><p> </p><p> Historically parcel level geographic information has been the realm of the professional land surveyor. Yet because of the utility of GIS, amateurs have taken over the process of deciding just what and how land parcel data will be represented on the internet. Even now it is very late in the game for surveyors to attempt to put a stake in the ground (pardon the pun) and claim what is legally and should rightfully be theirs. So how do we get back in the game? My suggestion would be to gather the resources and build a “Real Property GIS” using the new Lidar Mapping Headset I am developing. We are about to once again redesign the land surveying profession however this time we have a specific purpose that that will take thousands of property owners out of a FEMA flood zone and save them a billion or 2 in insurance payments and my Lidar device is the key to the process. The survey points required by FEMA are invisible to all of this hi-tech Lidar and other new field data collecting devices that can collect data at 1000 XYZ coordinates a second and are keeping field data collecting PLS’s sitting at their desk wondering what the hell has happen. And this is the very reason the airborne drones, cars, trucks and all manner of mechanized field data collection systems will not (for now) replace “Feet On The Ground”.</p><p> </p><p> </p><p>AND NOW COMES OUR GOGGLE 2 EARTH GLASSES</p><p> </p><p></p><p> </p><p>No more field crews</p><p></p><p> </p><p>I have been directly involved in GIS mapping for over 20 years. I have developed an application for my patented image based land title surveying technology that will take FEMA flood mapping to a much higher level of accuracy and detail. 2 decades ago aerial mapping firms started using lidar to augment ground control now mobile lidar is collecting data points at a rate of 1000/sec that have XYZ accurate to the centimeter range. However for real property field data collection these systems have limitations that render them useless. They are limited in range because their sensors cannot collect data blocked by tree cover, street only access and other features that limit their ability to identify points that are critical for determining property rights and feature elevations that Government agencies require. </p><p> </p><p></p><p> </p><p> At this point we are dealing with concepts. That said it is clear that all the technology needed to produce a marketable system already exist. What is needed now is system integration and manufacturing. If you and or your company would be interested in pursuing this extraordinary business opportunity please con tact me at:</p><p>email jwv@satellitesurveys.com</p><p>mobile phone: 239 282 9170 </p><p> </p></div>Geographic Midpoint Calculatorhttps://landsurveyorsunited.com/hubs/survey-earth-in-a-day/forum/geographic-midpoint-calculator2012-05-22T17:21:03.000Z2012-05-22T17:21:03.000ZSurveyEarthinaDayhttps://landsurveyorsunited.com/surveyors/SurveyEarthinaDay<div><h1>Geographic Midpoint Calculator</h1>
<p>Finds the exact point that lies halfway between two or more places. Find your personal center of gravity--the geographical average location for all of the places you have lived in. See the results on a Google Map.  <a href="http://www.geomidpoint.com/#using">Using the calculator</a>  <a href="http://www.geomidpoint.com/faq.html">FAQ</a></p>
<p><a target="_blank" href="http://www.geomidpoint.com/"><img class="align-full" src="{{#staticFileLink}}1200644850,original{{/staticFileLink}}" width="750" /></a></p>
<h2>Find your halfway point</h2>
<p>Here are a few of the many possible uses for the calculator:</p>
<ul>
<li>Find your personal center of gravity. Select all cities or addresses where you have lived, then view those places on a map along with a marker pointing at your exact average location.</li>
<li>Find the midpoint of a flight between two cities. For example, the point that lies halfway between Chicago and Los Angeles is located 22 miles (35 km) southwest of Limon, Colorado.</li>
<li>Trip planning--find a central hub for places you are going to visit.</li>
<li>Find a center location for a convention or family reunion that will be fair and equitable for those who are traveling.</li>
<li>Find a central place for a new business or facility that will serve surrounding population centers.</li>
<li>Midpoint locations can be visited using GPS devices. Please read these <a href="http://www.geomidpoint.com/guidelines.html">GPS guidelines</a> before you start your trip.</li>
</ul>
<p><a name="using" id="using"></a></p>
<h2>Using the midpoint calculator</h2>
<p>Add each of your addresses or other locations to the map. See <a href="http://www.geomidpoint.com/help.html">Help</a> for detailed instructions. Use the 'Address' option to enter your addresses or other locations one by one. 'Multiple input' lets you copy and paste a list of addresses from a spreadsheet or other program.</p>
<h3>Address formats</h3>
<p>350 Fifth Ave, New York, NY<br />
10 Downing St, London, UK<br />
Atlanta, GA<br />
Sydney, Australia</p>
<p>Locations can also be specified by latitude and longitude using one of the <a href="http://www.geomidpoint.com/latlon.html">allowed formats</a>.</p>
<h3>Weight by time and other weight</h3>
<p>You can use 'Weight by time' to weight your places for the personal center of gravity calculation. Enter the amount of time you have spent in each place. If you leave the years, months, and days boxes blank then all of your places will be weighted equally for the calculation. As an alternative, you can use 'Other weight' to enter population or other weighting factors for each location.</p>
<h3>Calculation methods</h3>
<p>Three different <a href="http://www.geomidpoint.com/calculation.html">calculation methods</a> are available for calculating the midpoint, each of which is useful in different situations. There are <a href="http://www.geomidpoint.com/methods.html">reasons for choosing</a> one method over another.</p>
<h2>How the calculator works</h2>
<p>The calculator calculates the geographic midpoint based on the assumption of a spherical earth. The geographic midpoint for any two points on the earth's surface is located halfway along the great circle route which is the shortest route that runs between both points, and would be like stretching a string between the two points on a world globe then finding the middle of the string. The geographic midpoint for three or more points on the earth's surface is the center of gravity (center of mass or average location) for all of the points.</p>
<p>To help visualize the concept of center of gravity, imagine that a small weight is positioned at the location of various cities on a world globe. Now imagine that the globe is allowed to rotate freely until the most heavily weighted part of the globe is pulled by gravity until it is facing downward. The lowest (and heaviest) part of the globe is the center of gravity and the geographic midpoint for all of the weighted cities. See <a href="http://www.geomidpoint.com/calculation.html">Calculation methods</a> for a detailed description.</p>
<h2>Map projections</h2>
<p>A lot of distortion occurs when the earth is projected onto a flat surface, for instance, a map using the Mercator Projection. Because of this distortion, if you plot two points on a flat map along with the corresponding calculated midpoint, you will find that the midpoint is often far out of alignment with the two points. This can be easily illustrated by an example. If you place a ruler on a flat wall map between Phoenix, Arizona and Kabul, Afghanistan, the midpoint for the two cities will appear to be in the Atlantic Ocean a few hundred miles off the tip of Portugal. However, the Geographic Midpoint Calculator gives the true midpoint coordinates of latitude 88.9300 North longitude 171.1427 West, which is 72 miles (116 km) from the North Pole. You can verify this by stretching a string between the two cities on a world globe.</p>
<p>In general, a true midpoint in the Northern Hemisphere will be farther north than you might expect it to be when viewed on a flat map, and conversely, a true midpoint in the Southern Hemisphere will be farther south than you might expect it to be. For cities that are close together this apparent difference between a spherical earth and a flat map is only slight, but the difference can be great for cities with a lot of longitude separation, such as cities on different continents. Also, there tends to be more distortion in the polar regions than near the equator. So if your calculated midpoint is farther north than you expect it to be, this is the explanation. Usually, if you take a look at a world globe it will begin to make sense.</p>
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