Assorted Brain Teasers by Kundan Pangtey - HTML preview

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TEASER - 12

DEGREE OF DISTANCE

A  contour  map,  by  definition,  is  a  map  of  a  surface  showing undulations with the help of  lines joining equal  elevation,  also called topographic map.

On  a  regional  scale,  the  ratio  of  a  unit  distance  on  a  contour map at any point to that on ground is always same.

(a)          True

(b)          Falls

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THE EXPLANATION:

A  map  or  any  drawing  made  on  a  flat  sheet  of  paper  are  2D transformation of 3D objects. Even the image formed on our retina (eye) is in 2D format. The 3D perception in our brain is caused due to  2D  image  received  from  two  different  eyes  set  at  an  angle  with respect to center of an object.

During earlier days relief on a map used to be shown with the help of variations  of  light  and  shade  to  give  effect  of  3D  objects  in  2D images.  As  the  use  of  shading  became  systematized  the  contour lines,  visually  representing  different  elevations  of  land  came  into general  use.  Contour  map  is  a  graphical  conventional  method  for showing  changes in height  or  depth on a 2D map with the help of lines that connect points of equal elevation called contour lines.

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CONTOUR MAP WITH VARIABLE SHADING

The  pattern  of  contour  lines  can  depict  landforms.  Areas  of  tightly spaced  contour  lines  describe  steep  changes  in  elevation  and sparse  contours  depict  flat  areas.   The  Mean  Sea  Level  (MSL)  is generally taken as “base” or datum surface, on which contours are referenced   or   plotted.   With   each   contour   line   representing   a standard distance above or below the base line, one can accurately calculate height or depth simply by counting the lines from the base line.

Theoretically,   the   distance   measured   on   a   contour   map,   in accordance with its scale should match to that on ground. However earth,  being  a spheroid, making  a regional contour  map is a tricky one.

Two things can happen while making contour maps (especially on a regional scale) of earth surface;

i.       The  globe  surface  is  curved  along  two  directions  X  &  Y axis. When flattened or stretched it cracks vertically (when one axis is curved) and also horizontally when both axis are curved.

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RIGID CAKE CURVED AND FLATTENED

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RIGID HEMI-SPHEROID (EARTH) CURVED AND FLATTENED

ii.  The  tall  mountain  (vertical  component:  height  or  depth)  is squashed onto a 2D flat base or datum surface.

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TALL OBJECT  SQUASHED ON A FLAT SURFACE

While making contour maps, the plumb lines (or longitude lines) that converge downward towards center of earth are made parallel with constant distance between longitudes, irrespective of undulations.

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LONGITUDE LINES BECOME PARALLEL ON FLATTENING

The  earth  surface  can  be  likened  to  a  curved  rubber  sheet  over which cones (similar to mountains) are placed. When rubber sheet is flattened  the  distance  between  summits  (S1  –  S2  –  S3)  of  cones progressively decreases where as distance between base (root)  of cones (R1 – R2 – R3) does not change.

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RUBBER SHEET WITH CONES  (CURVED & FLATTENED)

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CONTOURES OF CONES PLOTTED ON RUBBER SHEET

Where as the distance between summits of cone (S1, S2, S3) in a contour map, does not change, irrespective of bending or flattening of  rubber  sheet.  The  contour  map  assumes  that  the  distances between S1 to S2 to S3 is same as that between R1 to R2 to R3.

In a regional contour map, the bigger area of  a mountain, such as Himalaya or Tibetan Plateau, are squeezed on to a smaller area on a  datum  plane,  such  as  Mean  Sea  Level  (MSL).  Conversely,  the depths  of  oceans  are  brought-up  and  stretched.  Therefore  one (single) scale may not be applicable to measure a ratio between a unit distance on map to that on the ground at all points in a regional map.

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CONTOUR MAP OF AN UNDULATING SURFACE (2D)

Although a single scale has been provided for above contour map, the ratio (map to ground) may be different for depths (dark region) and different for high ground (light region).

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RELIEF MAP OF TIBETAN PLATEAU AND INDIAN PLAIN (ONE SCALE MAY NOT BE APPLICABLE)

Similarly  a  single  scale  may  not  be  applicable  for  a  map  or  a photograph of large area depicting Himalayas, Tibetan plateau and Indian  Planes  together.  There  may  be  huge  elevation  difference between them.

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