Shadows

Homework Materials

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Homework Content

Equations and Assumptions

Assume the focal length ‘f’ to be 6 inches or 152 millimeters.

Scaling Relationships

\[\begin{split}\frac{d}{D} &= \frac{1}{\textrm {scale factor}} = \frac{f}{H}\end{split}\]\[\begin{split}d &= \textrm {map distance} \\ D &= \textrm {ground distance} \\ f &= \textrm {camera focal length} \\ H &= \textrm {flying height} \\\end{split}\]\[\begin{split}\frac{H}{L} &= tan(Sun Angle)\end{split}\]\[\begin{split}H &= \textrm {height of the object} \\ L &= \textrm {length of shadow} \\\end{split}\]

Problems

Show all your work clearly with all units and in detail, leading up to the answer:

  1. If an object in a photo has a known height of 100m and casts a shadow that is 37m...what is the sun angle?

  2. If the sun angle is 37 degrees and the height of the object is 100m what should the length of the shadow be?

  3. Using Google Maps find the latitude and longitude and the shadow length of the following:

    1. Burj Khalifa
    2. Freedom Tower
    3. Washington Monument

  4. Find the published height of each structure.

  5. Determine the sun angle of the Google Maps aerial photo for each structure.

  6. Using the latitude and longitude of each structure and the sun angle calculator at: http://www.susdesign.com/sunangle/

Find the sun angle at each location on:

  1. December 31st, 2015 at noon local time.
  2. July 4th, 2016 at noon local time.
  3. July 4th, 2016 at 4pm local time.

7) Using the provided panchromatic Landsat 8 image locate the Burj Khalifa (hint: you can use the go to x, y tool in ArcMap to quickly locate it). One you have located the structure attempt to measure the shadow length. Look in the Landsat metadata file associated with the image to determine the time the image was collected. Use the sun angle calculator site to determine the sun angle at the time of the image. Is the length of the shadow you measured what we expect it to be? Why or why not?

  1. Review http://www.gislounge.com/shadows-angles-measuring-object-heights-satellite-imagery/

Metadata

Title:Shadows
CreationDate:01/31/2016
SoftwareUsed:None
SoftwareVersion:None