Traffic and Highway Engineering
Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Chapter 14, Problem 10P
To determine

The scale of the first vertical aerial photograph and the flying height of both the photographs.

Expert Solution & Answer
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Answer to Problem 10P

   1:19,070_,H1=9835ft,_andH2=12300ft_.

Explanation of Solution

Given information:

Scale of the first photograph S1=1:24,200, focal length of the camera, f=6inches and the average elevation, h=300ft.

Calculation:

Take two control points on a vertical aerial photograph:

Traffic and Highway Engineering, Chapter 14, Problem 10P

Let the length of DE =Xft.

We have been given the value of BC =4.9inch. for one photograph.

For scale two the value of X is found as follows:

   BCDE=ABAD

Substituting the values, we get

   PutABAD=1:24,000andBC=4.9inch =0.41ft

  0.41X=1:24,0000.41X=124,000X=0.41×24,000X=9840ft.

Now, the value of BC =6.2inch.=0.516ft for another photograph.

We have the following formula, for scale first:

   BCDE=ABAD

Substituting the values, we get

   PutBC=6.2inch.=0.516ftandX=9840ft

  0.516X=ABAD0.5169840ft=ABADABAD=19,069.76ABAD=19,070ABAD=119,070=S1

Implying that the scale of the first vertical photograph is 1:19,070

Now, the flying height (H1) of the first photograph using formula

  S1=fH1h

Where, Scale of the first photograph S1=1:24,200, focal length of the camera, f=6inches and the average elevation, h=300ft.

  119,070=0.5ftH1300ftH1300ft=0.5ft×19,070H1300ft=9535ftH1=9535ft+300ftH1=9835ft.

The flying height of the first photograph is, H1=9835ft.

Now, the flying height (H2) of the first photograph using formula

  S2=fH2h

Where, Scale of the first photograph S2=1:24,000, focal length of the camera, f=6inches and the average elevation, h=300ft.

  124,000=0.5ftH2300ftH2300ft=0.5ft×24,000H2300ft=12000ftH2=12000ft+300ftH2=12300ft.

The flying height of the first photograph is, H2=12300ft.

Conclusion:

Therefore,the scale of the first vertical photograph is 1:19,070, the flying height of the first photograph is, H1=9835ft, the flying height of the first photograph is, H2=12300ft.

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