115AL Extra Credit Problems (see Lab 2 for reference) * Due on or before the day of the midterm

Put only answers on this page (in the appropriate units), attach separate page(s) with your work; this includes which formula(s) you used, the math and how you did your unit conversions etc. but it does not have the be perfectly neat, only legible      *no work = no credit

Heights of Displaced Objects

where,
D is the length of the displaced image in inches;
R is the radial distance from the nadir to the top of the displaced image; and,
H is the altitude above the base of the object.

2. The Great Box of Cheeps, having a base measuring 560 feet along each side, is the largest known structure of its type.  Assume the Great Box is photographed with a mapping camera having a 10 inch focal length.  If the length of the base measures 0.9 inches on the photograph, what is the scale of the print?  If the length of the displaced box image is 0.1 in. and the distance from the middle of the top of the box to nadir (principal point) is 1.8 inches, what is the height of the box? (hint: you have to use 2 formulas to solve this)
 

_________ ft
                                                                                                                                            ________ m


 3. On a photograph of California's "smog belt," the distance from the nadir to the top of a 500 foot cellular broadcast tower is measured as 3.8 inches.  If the  photograph was taken from an altitude of 4,800 feet, how much would you expect the image to be displaced on the photograph?
 

________mm
              _________cm


 4. The top of the somebody's building, a 1500 ft structure, appears 2.3 inches from the nadir of a photograph and the displaced image is exactly .375 inchs long.  From what height above Manhattan was the photograph taken?
 

_________ ft
     _____ m

 
 
 
 
 
 
 
 
 
 

Parallax Method

where,
A = height of aircraft above ground datum;
P = absolute parallax at base of object being  measured (average photo base length)
dP = differential parallax.

Important: If object heights are to be determined in feet or meters, the height of the photographing aircraft (H) must also be in feet or meters.  Once the exact photo scale has been ascertained, the flight altitude can be found by multiplying the RF denominator by camera focal length.  Absolute stereoscopic parallax (P) and differential parallax (dP) must be expressed in the same units; ordinarily these units will be hundredths of millimeters or thousandths of inches.

1. Estimate the height of a tower. Assume the aircraft is flying at 8,000 feet.
- you measure dP to be 2.5 mm
- photo base (p) is 87 mm

 __________m
__________ft


 2. Determine the depth of Meteor Crater by measurement of differential parallax.  Assume flight line is parallel to bottom edge of prints (H = 16,000 feet;  P = 2.75 inches).
- you measure dP to be 0.3 cm

 __________m
___________ft
Shadow Method
Height of object  = shadow length * Tan a
where, "a" is the sun angle at that date and time.

1. Determine the height of the tower using the formula given above.  Assume another building in the same photograph is 80' tall and is casting a shadow of 120' (ground distance, of course), and that the photo scale is 1:14000. You measure the shadow as 7 mm long.

A. Fill in the known object height and the shadow length measurement in the "shadow method" algorithm.  Solve for tan a.  Remember the tangent of an angle applies to opposite over adjacent side.

B. After tan a is calculated, determine the height of the tower by measuring the shadow of the photo.  Convert the photo distance to ground distance and using the shadow method formula.
 

___________ ft
                                                                                          __________ m