Aerial photogrammetry 03

Relief Displacement in Vertical Photograph

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

2. Lecture Outline Relief Displacement in Vertical Photograph Numerical

3. Relief Displacement in Vertical Photograph: Definition- On an aerial photograph the displacement of image due to variation in relief of terrain is known as relief displacement or height distortion. Let, AB is the object on ground surface (Datum) A =Top point of an object B = Bottom point of an object P = Principal point r a = Radial distance of point a from the principal point p r b = Radial distance of point b from the principal point p Relief displacement = d = r a – r b

4. Relief Displacement : Derivation For Δ ODB & Δ OCA , DB=CA=D, Op=f From Δ opb & Δ ODB , = = D = ……. 1 From Δ opa & Δ OCA , = = D = ……. 2 Equating eq. 1 & 2 = = = H - h h = ( - ) H But ( - ) =d = Relief Dis. , As per def. d=  

5. Relief Displacement : Relief Displacement = d= Where, r a = Radial distance of top point of an object from the principal point p H = Altitude of Airplane w.r.t. ground level h = Height of an Object Conclusion: Taller the object greater the relief displacement. More the radial distance greater the relief displacement Relief displacement decreases when increase in flying height. Relief displacement will be + ve for a point above the datum & vice versa.  

6. Numerical: Ex.1: The Distance of an image of a point 230 m above m.s.l . from the principal point is 34.8 mm. Determine the relief displacement. if the flying height is 1600m (Exam, Gate) Solution: Given: h= Height of object = 230 m r= radial distance =34.8 mm & H = Flying ht. = 1600 m Relief displacement = d= = 5 mm  

7. Numerical: Ex.2: A tower lying on a flat area having an average elevation of 800 m above m.s.l . was photograph with the a camera having focal length of 24 cm. The distance between the top and bottom of tower is measures 0.34 cm on the photograph. A line AB, 200 m long on the ground, measures 12.2 cm on the same photograph. Determine the height of the tower if the distance of the image of the top of the tower is 8.92 cm, from the principal point. (Exam, Gate) Solution: Given: d =relief displacement = 0.34 cm , f= Focal length = 24 cm H = Altitude of camera = Unknown , h = Height of tower = Unknown r= radial distance of top of tower=8.92 cm & AB line ground distance = 200 m & AB line ground map distance = 12.2 cm (relief displacement = d= & )  

8. Numerical: First let find out Height of camera above ground level as a datum ( H ) , , Height of camera above ground level, H = 393.44 m let find out Height of tower ( h ) relief displacement = d= , 0.34 cm = Height of tower , h = 15 m  

9. Numerical: Ex.3: A tower PK, 50m high, appears in a vertical photograph taken at a flight altitude of 2500m above msl . The distance of the image of the top of the tower is 6.35 cm. Compute the displacement of the image of the top of the tower with respect to the image of its bottom. The elevation of bottom of tower is 1250m (Exam, Gate) Solution: Given: d =relief displacement = Unknown H = Altitude of flight above msl = 2500m , h = Height of tower = 50 m r= radial distance of top of tower = 6.35 cm Elevation of bottom of tower is =1250m (relief displacement = d= )  

10. Numerical : First let find out Height of camera /flight above ground level (datum) ( H ) Elevation of bottom of tower is 1250 m H =2500- 1250 = 1250 m relief displacement = d= , = = 0.25 cm   Given = 2500 H    

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