Scale variations within a single photo are due to changes in ground eleva- 

 tion and the amount of tilt of the image relative to the ground. For an image 

 parallel to the ground, the scale of the photo can be expressed as 



(A-1) 



where f is the focal length of the camera lens and H is the height of the 

 camera above the ground. Since the scale varies for points of different eleva- 

 tion, the scale for a point at an elevation h above the general ground eleva- 

 tion can be written as 



H - h 



(A- 2) 



The problem is compounded when the image is tilted relative to the ground 

 at an angle a. Then equation (A-2) becomes 



y sm g 



H 



(A- 3) 



where y is the radial distance measured on the photo from the nadir or center 

 of the photo to the point of interest. As seen from equation (A-3) , the effect 

 of tilt is to linearly modify the scale in a direction perpendicular to the 

 axis of tilt. The effect of tilt can be minimized through the optimal matching 

 procedure described. With enough information, tilt can be eliminated by recti- 

 fying the photos. According to Tewinkel (1962) about 50 percent of all aerial 

 photos are tilted less than 2° and very few more than 3°. 



A reasonable estimate of the effect of tilt and topographic relief can be 

 determined from equation (A-3). Starting with equation (A-1) and using the 

 known focal length and nominal scale of 



f = 0. 152 meters 

 S = 1:3,600 



a value of H can be determined. 



H = 547.2 meters 



Using the data in reach A as an example, the following average and maximum 

 values of the variables in equation (A-3) were determined. Estimated varia- 

 tions in the elevation of the bluff line within a single photo (h, actual) are 



^avg 



3 meters 



h =5 meters 



max 



Distance from station to nadir (y on photo) 



y, 



avg 



0.0381 meter 

 0.0889 meter 



€9 



