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Flying height from photo and map scale

Short answer

Find ground distance: 6 cm × 50,000 = 3000 m. Photo scale = 0.20 m / 3000 m = 1:15,000. Flying height above datum H = f/scale + h = 0.24 × 15,000 + 350 = 3950 m.

A line PQ measures 20 cm on an aerial photograph taken with an aerial camera having focal length 24 cm. The same line measures 6 cm on a map drawn to a scale of 1:50000. Calculate the flying height of the aircraft if the average altitude of ground is 350 m.

The photo scale is found from a map distance, and then the flying height from S=f/(H−h)S = f/(H-h).

Step 1: Ground length of PQ

Map scale 1:50 000, so PQ on the ground:

PQground=6 cm×50 000=300 000 cm=3000 mPQ_{ground} = 6\ \text{cm}\times 50\,000 = 300\,000\ \text{cm} = 3000\ \text{m}

Step 2: Photo scale

S=photo distanceground distance=0.20 m3000 m=115 000S = \frac{\text{photo distance}}{\text{ground distance}} = \frac{0.20\ \text{m}}{3000\ \text{m}} = \frac{1}{15\,000}

Step 3: Flying height

S=fH−h ⇒ H−h=f×15 000=0.24×15 000=3600 mS = \frac{f}{H-h}\ \Rightarrow\ H - h = f\times 15\,000 = 0.24\times 15\,000 = 3600\ \text{m} H=3600+350=3950 mH = 3600 + 350 = 3950\ \text{m}

Answer: The photo scale is 1:15 000 and the flying height of the aircraft is 3950 m above datum (3600 m above the average ground).

✓ Answer checked by Claude Opus 5.5 (high effort)

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