Aerial photogrammetry 02

Scale of Vertical Photograph
Numerical

1. Advance Surveying Aerial Photogrammetry Prof. Rajguru R.S. Civil Engineering Department ([email protected]) Sanjivani College of Engineering, Kopargaon,MH,India

2. Lecture Outline Scale of Vertical Photograph Numerical

3. Scale of Vertical Photograph: Scale in Aerial Photography is the ratio of the distance between two points on an image to the actual distance between the same two points on the ground.  Scale is not uniform and it vary from point to point depending upon the ground profile whether tilt or tip. If the terrain to be photographed is flat, the photographs taken are vertical. If the altitude of the airplane is changed , then scale of photograph is also changed.

4. Scale of Vertical Photograph: O =Exposure Center f =Focal length Ok =Optical axis/camera axis H =Altitude of airplane =Height of pt. A above datum Scale = = From similar triangle, Δ Oka & Δ OKA s = = = Scale at pt. A on ground  

5. Scale of Vertical Photograph: Datum Scale: Scale at datum S = Point Scale: Scale at any point on ground , Scale at pt. p on ground Average S cale: Average ground variation =  

6. Scale of Vertical Photograph: True length of line on ground Let say PQ is the line on ground PQ = = , = & = , = H = Flying Height of airplane = Ground elevation of P & Q above datum = Focal length , & = Ground coordinate of P & Q resp. , = Photograph coordinate of P & Q resp.  

7. Numerical: Ex.1: A line AB 2000m long lying at an elevation of 500m measures 8.65 cm on a vertical photograph for which focal length is 20 cm. Determine the scale of the photograph in an area the average elevation of which is about 800m Solution: Scale = = (1m=100cm & 1m=1000mm) Let find out H first and then scale, = , = , H=5124.027m Scale of Photograph at Avg. elevation of 800m, = = = Therefore , is 1cm =216.20cm  

8. Numerical: Ex.2: Two point A and B which appear in a vertical photograph taken from a camera having focal length of 220mm and from an altitude of 3000m have their elevation as 400m and 600m respectively Their corrected photo coordinate are as under, Determine the length of ground line AB. Solution: Given- H = Flying Height of airplane/altitude =3000m = Ground elevation of A & B above datum = 400m ,600m resp. = Focal length =220mm=0.220m , & = Ground coordinate of A & B resp .= Unknown , = Photograph coordinate of A & B resp .= As per above   Point Photo coordinates (mm) A 23.8 16.4 B -13.6 -29.7 Point Photo coordinates (mm) A 23.8 16.4 B -13.6 -29.7

9. Numerical: First let find out Ground coordinate of A point = = = +281.27 m = = 0.0164 = +193.82 m & Let find out Ground coordinate of B point = = = - 148.37 m = = (-0.0297) = - 324 m & Let find out length of line AB on ground AB = = 672.85 m  

10. Numerical: Ex.3: The ground length of a line AB is known to be 545m & the elevation of A & B are respectively 500m & 300m above m.s.l . On a verical photograph taken with a camera having focal length of 20 cm .The distance ab scaled directly from photograph is 5.112 cm. Calculate flying height above msl . Solution: Given- H = Flying Height of airplane/altitude = Unknown = Ground elevation of A & B above datum = 500m , 300m resp. = Focal length =20 cm = 0.20 m , & = Ground coordinate of A & B resp .= Unknown , = Photograph coordinate of A & B resp .= As per above   Point Photo coordinates (cm) A 2.65 1.36 B -1.92 3.65 Point Photo coordinates (cm ) A 2.65 1.36 B - 1.92 3.65

11. Numerical: First let find out the = , here A & B having different elevation = ( + ) = ( 500 + 300 ) = 400 m = = = 2532.23 m Now find out ground coordinate A & B from = 2532.23 m  

12. Numerical: First let find out Ground coordinate of A point = = = 269.27 m = = 1.36 = + 138.19 m & Let find out Ground coordinate of B point = = ) = - 214.3 m = = 3.64 = 406.3 m & Let find out length of line AB on ground AB = = 552.92 m based on approximate height Actual length of AB given in the problem is 545 m.  

13. Numerical: let find out second approximate height & ground coordinate = Second approximate = 2501.68 m let find out Ground coordinate of A point = = = 265.22m = = 1.36 = + 136.11 m &  

14. Numerical: Let find out Ground coordinate of B point = = ) = - 211.36 m = = 3.64 = 400.7 m & Let find out length of line AB on ground AB = = 545 m This agree with given AB , Hence flying height = 2501.68 m  

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