How tall is Nutting Hall?

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Blake Floyd
5 years ago
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1 How tall is Nutting Hall?

2 IMAGE DISPLACEMENT on vertical airphotos airphoto (central projection)

3 On a single airphoto topographic-displacement method shadow method On stereo pairs the parallax-height equation instruments / tools

4 On a single airphoto topographic-displacement method shadow method On stereo pairs the parallax-height equation instruments / tools

5 topographic - displacement formula: d *( H h) h o r h o = height of displaced object d = length of displaced object (top to bottom) on photo r = radial distance from nadir (or PP) to top of object on photo (H-h) = flying height above the base of the object * measure d and r on the photo (with an engineer s scale, for example) using the same units (e.g. inches)

6 topographic-displacement method Assumptions 1. PP and nadir at the same position (true vertical airphoto) 2. Flight altitude above the base of the object is known 3. The top and bottom of the object are visible on the photo 4. The degree of object displacement on the photo is great enough as to allow measurement

7 topographic-displacement method H =1,500ft h =100ft d =0.5in r =7.0in How tall is this tree?

8 topographic-displacement method topographic - displacement formula: d *( H h) h o r h o = height of displaced object d = 0.5in H = 1,500ft r = 7.0in h = 100ft 0.5in *(1500 ft 100 ft) h o 100 ft 7. 0in

9 topographic-displacement method d *( H h) h o r r A = 59.5mm d A = 4.5mm (H-h) = 914m r B = 127mm d B = 9.5mm TANK _ A 4.5mm*(914m) 59.5mm 69m TANK _ B 9.5mm*(914m) 68m 127mm

10 RELIEF DISPLACEMENT on a single airphoto d *( H h) ho * r h o d r ( H h) displacement (d ) varies directly with object height (h o ) e.g.: all factors equal, a 100f tree is displaced twice as much on a photo as a 50f tree

11 RELIEF DISPLACEMENT on a single airphoto d *( H h) ho * r h o d r ( H h) displacement (d ) varies directly with distance of the object from nadir (r ) e.g.: a 100f tree 4in from nadir is displaced twice as much on a photo as a 100f tree 2in from nadir there is no displacement at nadir (if r = 0 then d = 0)

12 RELIEF DISPLACEMENT on a single airphoto d *( H h) ho * r h o d r ( H h) displacement (d ) varies inversely with flying height above the datum (H-h ) little displacement on high altitude or space platforms (small scale) larger scale photos better for accurate height measurement

13 On a single airphoto topographic-displacement method shadow method On stereo pairs the parallax-height equation instruments / tools

14 using stereoscopic parallax Relief displacement on photos allows height measurement; if no displacement, no stereoscopic parallax... Parallax: apparent displacement of an object caused by a change in point of observation e.g. same object viewed from each of a stereo pair of photos (stereoscopic parallax)

15 using stereoscopic parallax The parallax-height equation: h o ( H h)* dp P dp b h o = height of displaced object P b = absolute stereoscopic parallax dp = differential parallax (H-h) = flying height above the base of the object * measure P and dp on the photo (e.g., with an engineer s scale, parallax wedge, or parallax bar) using the same units (e.g. inches)

16 using stereoscopic parallax absolute stereoscopic parallax (P b ) sum of the distance of corresponding image objects from their respective nadirs (PPs) to the base of the object always measured parallel to the flight line P b = x 1 + x 2 *a difficult measurement... x 1 x 2 PP 1 PP 2

17 using stereoscopic parallax (when PP1, PP2, and the base of the object are all at approximately the can be substituted for P b in level terrain same elevation) the mean distance between PP and CPP on each photo Average photo base (P ) P = (x 1 + x 2 ) / 2 h o ( H h)* dp P dp x 1 x 2 PP 1 CPP2 CPP PP 1 2

18 using stereoscopic parallax differential parallax (dp ) the difference in the absolute stereoscopic parallax at the top and the base of the object always measured parallel to the flight line dp = (y 1 + y 2 ) - (x 1 + x 2 ) *OR... y 1 y 2 x 1 x 2 PP 1 PP 2

19 using stereoscopic parallax differential parallax (dp ) the difference in the absolute stereoscopic parallax at the top and the base of the object always measured parallel to the flight line dp = (y 1 + y 2 ) - (x 1 + x 2 ) = x - y y x PP 1 PP 2

20 On a single airphoto topographic-displacement method shadow method On stereo pairs the parallax-height equation instruments / tools

21 average photo base (P) use an engineer s scale P = (x 1 + x 2 ) / 2 P = (3.2in + 3.4in) / 2 = 3.3in x 1 x 2 PP 1 PP 2 CPP 2 CPP 1 3.2in 3.4in

22 differential parallax (dp) parallax bar (attached to pocket/lens stereoscope)

23 differential parallax (dp) dp = 13.81mm mm = 3.43mm Stereoscopic parallax of top of object Stereoscopic parallax of bottom of object

24 using stereoscopic parallax The parallax-height equation: h o ( H h)* dp P dp same units! h o = height of displaced object P = average photo base = 3.3in = 84mm dp = differential parallax = 3.4mm (H-h) = flying height above the base of the object = 1,000m

25 using stereoscopic parallax The parallax-height equation: h o ( H h)* dp P dp h (1000m)*3.4mm o 84mm 3. 4 mm 38.9m

26 differential parallax (dp) parallax wedge (transparency)

27 differential parallax (dp) dp = 2.346in in = 0.134in

28 On a single airphoto topographic-displacement method shadow method On stereo pairs the parallax-height equation instruments / tools

29 shadow-length method (see Paine & Kiser, pg ) altitude of the sun on the day of the photo, corrected to Greenwich Mean Time latitude of the photo longitude of the photo and difference in degrees between location of the photo and local noon?

30 proportional shadow method h1 s 1 h s m h2 2.0cm 0.5cm 125m*0.5cm h m 2.0cm h 1 =125m How tall is this tree? s 2 =0.5cm s 1 =2.0cm

Measurement of Direction: Bearing vs. Azimuth

Week 5 Monday Measurement of Direction: Bearing vs. Azimuth Bearing Is an angle of 90 o or less Measured from either North or South in easterly & westerly directions. North 22 o West, South 89 o West,