GELE Photogrammetry & Cartography — Aerial Photography and Camera GeometryExam Answer Templates

Examiner tip

Either the verbal definition OR the formula earns the mark — but writing both in one sentence is safest and takes only 10 seconds.

Model answer

Photo scale is the ratio of a distance measured on the aerial photograph to the corresponding horizontal distance on the ground, given by Scale = f / H, where f is the camera focal length and H is the flying height above the terrain.

Answer structure

• One complete sentence: state the ratio definition AND the formula Scale = f/H [1 mark]

Scoring breakdown

Common mark deductions

• Writing scale as a decimal without the ratio form
• Omitting the formula or defining H as altitude above sea level

Key phrases to include

• ratio
• focal length f
• flying height H above terrain
• Scale = f/H

Examiner tip

The word 'coincide' is the trigger word examiners look for in the second part of this answer.

Model answer

The principal point is the point on the photograph where the optical axis of the camera lens is perpendicular to the photo plane (the foot of the perpendicular from the lens center). On a truly vertical photograph, the principal point coincides with the nadir point.

Answer structure

• Part A: define principal point as foot of optical axis on photo plane [½ mark implied]
• Part B: state it coincides with the nadir on a vertical photo [½ mark implied]

Scoring breakdown

Common mark deductions

• Defining principal point without mentioning the optical axis
• Forgetting to state the coincidence condition for a vertical photo

Key phrases to include

• optical axis
• perpendicular to photo plane
• nadir
• truly vertical photo
• coincide

Examiner tip

Always pair the percentage with its type — '60%' alone earns zero; '60% forward overlap' earns the mark.

Model answer

Standard forward overlap (along the flight strip) = 60%; standard sidelap (between adjacent strips) = 30%.

Answer structure

• State forward overlap = 60% [½ mark]
• State sidelap = 30% [½ mark]

Scoring breakdown

Common mark deductions

• Swapping the values (60% for sidelap, 30% for forward overlap)
• Giving only one value

Key phrases to include

• forward overlap
• 60%
• sidelap
• 30%
• stereo coverage

Examiner tip

The unit-conversion step (152 mm = 0.152 m) is where most errors occur; write it explicitly to secure the setup mark even if you make an arithmetic slip later.

Model answer

Given: f = 152 mm = 0.152 m; H = 1 520 m

Formula: Scale = f / H

Substituting: Scale = 0.152 / 1 520 = 1 / 10 000

∴ Photo scale = 1 : 10 000

Answer structure

• Line 1: List given data with unit conversion (mm → m) [setup mark]
• Line 2: Write the formula Scale = f/H [1 mark]
• Line 3: Substitute and simplify to 1:10 000 [1 mark]

Scoring breakdown

Common mark deductions

• Failing to convert f from mm to m before dividing (getting 1:10 instead of 1:10 000)
• Writing the answer as 0.0001 without the ratio form

Key phrases to include

• Scale = f/H
• unit conversion mm to m
• 1:10 000
• ratio

Examiner tip

Questions that give both aircraft altitude AMSL and terrain elevation are testing whether you know H = altitude − terrain. This single step distinguishes top scorers.

Model answer

Step 1 — Compute flying height above terrain:
H = 2 000 − 200 = 1 800 m

Step 2 — Compute photo scale:
Scale = f/H = 0.152/1 800 = 1/11 842 ≈ 1:11 842

Step 3 — Compute ground side length:
Ground side = d × S = 0.230 m × 11 842 = 2 723.7 m

Step 4 — Compute ground area:
Area = (2 723.7)² = 7 418 533 m² ≈ 741.9 ha

∴ Ground area ≈ 741.9 hectares

Answer structure

• Step 1: H = altitude − terrain elevation [sets up correct H]
• Step 2: Scale = f/H [1 mark for formula and substitution]
• Step 3–4: Ground side = d × S; Area = (dS)² converted to ha [1 mark for correct area]

Scoring breakdown

Common mark deductions

• Using H = 2 000 m instead of 1 800 m (ignoring terrain elevation)
• Forgetting to square the ground side when computing area
• Failing to convert m² to hectares (1 ha = 10 000 m²)

Key phrases to include

• H = altitude − terrain elevation
• Scale = f/H
• ground side = d × S
• Area = (dS)²
• hectares

Examiner tip

Remember: going from photo to ground you MULTIPLY by S; going from ground to photo you DIVIDE by S. Draw a quick arrow to remind yourself during the exam.

Model answer

Given: photo distance = 48 mm; Scale = 1:12 000 (S = 12 000)

Formula: Ground distance = photo distance × S

Substituting: Ground distance = 48 mm × 12 000
= 576 000 mm
= 576 m

∴ Ground distance = 576 m

Answer structure

• Line 1: Identify photo distance and scale denominator [setup]
• Line 2: State formula Ground distance = photo distance × S [1 mark]
• Line 3: Substitute and convert mm to m [1 mark]

Scoring breakdown

Common mark deductions

• Dividing instead of multiplying (photo distance ÷ S)
• Leaving the answer in mm instead of converting to m

Key phrases to include

• ground distance = photo distance × S
• scale denominator
• unit conversion mm to m

Examiner tip

For diagram-based 3-mark questions, allocate: 1 mark for the sketch, 1 mark for labels/definitions, 1 mark for the formula. A well-drawn sketch with proper labels can earn 2 of the 3 marks even if the formula derivation is incomplete.

Model answer

Geometry of a Vertical Aerial Photograph:

For a truly vertical photograph, the optical axis of the camera is directed vertically downward.

Key elements (label each on sketch):

• L = Lens center (perspective center) — located at the aircraft
• O = Principal point — where the optical axis intersects the photo plane; it is the geometric center of the image
• N = Nadir — point on the ground directly beneath L; its image n coincides with O on a vertical photo
• f = Focal length — perpendicular distance from L down to the photo plane (L to O)
• H = Flying height above terrain — vertical distance from the ground datum up to L

Relationship: Scale = f / H (similar-triangle relationship)

[Sketch description: Draw a horizontal photo plane at the bottom; above it, a point L (lens) connected by a vertical line through O (on photo plane) extending down to N (on ground datum). Label LO = f, ground datum to L = H, and mark the photo format width d. Show the similar triangles.]

The similar-triangle proof: For any ground point A at ground distance D from N, its photo image a at photo distance d_a from O satisfies d_a/D = f/H, confirming Scale = f/H.

Answer structure

• Part 1: Neat labeled sketch with at least 4 of the 5 required elements labeled [1 mark]
• Part 2: Brief verbal description of each element with correct definitions [1 mark]
• Part 3: Statement and explanation of the Scale = f/H relationship derived from similar triangles [1 mark]

Scoring breakdown

Common mark deductions

• Sketch present but unlabeled — loses the diagram mark
• Confusing focal length with flying height in the diagram
• Omitting the similar-triangle basis for the scale formula

Key phrases to include

• lens center
• optical axis
• principal point
• nadir
• focal length f
• flying height H
• similar triangles
• Scale = f/H

Examiner tip

When working backwards from area to scale, the square root step is the key — write it explicitly. Examiners award a process mark for √Area = ground side.

Model answer

Given: f = 210 mm = 0.210 m; format d = 230 mm = 0.230 m; Area = 529 ha = 5 290 000 m²

Part (a) — Photo Scale:
Ground side = √Area = √5 290 000 = 2 300 m
Scale denominator S = ground side / photo side = 2 300 / 0.230 = 10 000
∴ Scale = 1 : 10 000

Part (b) — Flying Height:
Formula: Scale = f/H → H = f / Scale = f × S
H = 0.210 × 10 000 = 2 100 m

∴ Scale = 1:10 000; Flying height H = 2 100 m above terrain

Answer structure

• Step 1: Compute ground side from given area (√529 ha converted to m²) [1 mark]
• Step 2: Compute scale denominator S = ground side / photo side [1 mark]
• Step 3: Use H = f × S to find flying height [1 mark]

Scoring breakdown

Common mark deductions

• Forgetting to convert ha to m² before taking the square root
• Substituting f in mm instead of m when computing H

Key phrases to include

• ground side = √Area
• 529 ha = 5 290 000 m²
• S = ground side / photo side
• H = f × S
• 1:10 000

Examiner tip

This is a compare-and-contrast question. Use a parallel structure: define forward overlap → state value → state purpose; then repeat for sidelap. The symmetry of your answer signals a thorough understanding.

Model answer

Forward Overlap (Endlap): This is the overlap between successive photographs along the same flight strip, expressed as a percentage of the photo format. The standard value is approximately 60%.
— Purpose: Ensures that each ground area is covered by at least two consecutive photos from slightly different positions, enabling stereoscopic viewing and parallax measurement for height determination.

Sidelap: This is the overlap between photographs from adjacent parallel flight strips. The standard value is approximately 30%.
— Purpose: Ensures complete, gap-free coverage of the survey area between strips, and provides stereo overlap at the strip boundaries to eliminate coverage gaps due to aircraft crab, drift, or tilt.

In summary: forward overlap provides stereo coverage within each strip; sidelap ensures full areal coverage without gaps between strips.

Answer structure

• Para 1: Define forward overlap (≈60%) and state its purpose (stereo, parallax) [1 mark]
• Para 2: Define sidelap (≈30%) and state its purpose (gap-free coverage between strips) [1 mark]
• Para 3: Concise summary distinguishing the two [1 mark]

Scoring breakdown

Common mark deductions

• Giving the correct percentages but failing to explain WHY each is needed
• Confusing the direction: forward = along strip, sidelap = between strips

Key phrases to include

• forward overlap / endlap
• 60%
• sidelap
• 30%
• stereoscopic viewing
• parallax
• gap-free coverage
• adjacent strips

Examiner tip

Board exam numerical questions at the 2-mark level almost always award 1 mark for the correct formula and 1 mark for the correct answer. Never skip writing the formula.

Model answer

Given: Photo distance = 62 mm; Scale = 1:12 000 → S = 12 000

Formula: Ground distance = photo distance × S

Ground distance = 62 mm × 12 000
= 744 000 mm
= 744 m

∴ True ground length = 744 m

Answer structure

• Line 1: State given data and extract S = 12 000 [setup]
• Line 2: Write formula [1 mark]
• Line 3: Substitute, compute, and convert mm → m [1 mark]

Scoring breakdown

Common mark deductions

• Dividing photo distance by S instead of multiplying
• Leaving answer in mm

Key phrases to include

• Ground distance = photo distance × S
• S = 12 000
• 744 000 mm = 744 m

Examiner tip

For 5-mark numerical questions, the examiners typically award marks at each distinct computational step. Make each step visible on a separate line — do NOT chain all arithmetic in one step or you lose intermediate marks.

Model answer

Given: Scale = 1:10 000 (S = 10 000); d = 230 mm = 0.230 m; forward overlap p = 60%

Part (a) — Ground coverage of one photograph:
Ground side = d × S = 0.230 m × 10 000 = 2 300 m
Ground area = (2 300)² = 5 290 000 m² = 529 ha

Part (b) — Air-base (B):
The air-base is the advance per exposure along the flight direction.
For forward overlap p = 60%, the photo advances by (1 − p) of the ground format:

B = (1 − p) × ground side
B = (1 − 0.60) × 2 300 m
B = 0.40 × 2 300 m
B = 920 m

∴ Ground side = 2 300 m; Area = 529 ha; Air-base B = 920 m

Answer structure

• Step 1: Convert d to metres [setup mark]
• Step 2: Ground side = d × S = 2 300 m [1 mark]
• Step 3: Area = (2 300)² = 529 ha [1 mark]
• Step 4: State the formula B = (1 − p) × ground side [1 mark]
• Step 5: Substitute p = 0.60 and compute B = 920 m [1 mark]
• Final: Clearly boxed answers with units [1 mark — follow-through]

Scoring breakdown

Common mark deductions

• Using p = 60 instead of p = 0.60 (not converting percentage to decimal)
• Computing B = p × ground side instead of (1 − p) × ground side
• Forgetting to convert area from m² to hectares

Key phrases to include

• ground side = d × S
• area = (dS)²
• air-base B
• B = (1 − p) × ground side
• forward overlap p = 0.60
• 529 ha
• 920 m

Examiner tip

The '+1' in photo count is a classic board-exam trap. Think of it like fence posts and gaps: 15 gaps require 16 posts. Examiners are specifically checking whether you know this rule.

Model answer

Given: f = 210 mm = 0.210 m; d = 230 mm = 0.230 m; H = 3 150 m; p = 60%; strip length L = 20 km = 20 000 m

Part (a) — Scale:
Scale = f/H = 0.210 / 3 150 = 1/15 000
∴ Scale = 1:15 000

Part (b) — Ground coverage:
Ground side = d × S = 0.230 × 15 000 = 3 450 m
Area = (3 450)² = 11 902 500 m² ≈ 1 190 ha
∴ Ground area ≈ 1 190 ha

Part (c) — Number of photos:
Air-base B = (1 − p) × ground side = (1 − 0.60) × 3 450 = 0.40 × 3 450 = 1 380 m

Number of intervals = L / B = 20 000 / 1 380 = 14.49 → 15 intervals (round up)
Number of photos = intervals + 1 = 15 + 1 = 16 photos

(Add 1 photo at each end to ensure complete coverage beyond the strip boundary.)

∴ Scale = 1:15 000; Area ≈ 1 190 ha; Number of photos = 16

Answer structure

• Part (a): Scale = f/H → 1:15 000 [1 mark]
• Part (b): Ground side = 3 450 m; Area = 1 190 ha [1 mark]
• Part (c) Step 1: Air-base B = (1−p) × ground side = 1 380 m [1 mark]
• Part (c) Step 2: Intervals = L/B rounded up to 15 [1 mark]
• Part (c) Step 3: Photos = intervals + 1 = 16 [1 mark]

Scoring breakdown

Common mark deductions

• Using n = L/B without adding 1 for the first exposure at the start of the strip
• Not rounding up the number of intervals (using 14 instead of 15 gives incomplete coverage)
• Omitting unit conversion for strip length (km to m)

Key phrases to include

• Scale = f/H = 1:15 000
• ground side = d × S
• B = (1 − p) × ground side
• intervals = L/B
• photos = intervals + 1
• round up

Examiner tip

This is a conceptual 2-marker. The first sentence earns 1 mark if it mentions 'mean terrain elevation'. The second mark requires explaining the variation of scale with elevation — do not skip this.

Model answer

Average scale refers to the representative scale of an aerial photograph taken over terrain with varying elevation, computed by using the mean ground elevation of the survey area.

Formula: Average Scale = f / H_avg
where H_avg = aircraft altitude (AMSL) − mean terrain elevation.

The average scale is used because the actual scale varies across the photo — it is larger (more detailed) over elevated terrain (smaller H) and smaller over low-lying areas (larger H). The mean elevation provides a single representative value for practical mapping.

Answer structure

• Sentence 1: Define average scale using mean terrain elevation [1 mark]
• Sentence 2: State formula H_avg = altitude − mean elevation, and explain why scale varies [1 mark]

Scoring breakdown

Common mark deductions

• Not explaining why scale varies (larger over hills, smaller over valleys)
• Confusing 'average scale' with 'constant scale' — scale is never truly constant over undulating terrain

Key phrases to include

• mean terrain elevation
• H_avg = altitude − mean elevation
• scale varies with relief
• average scale = f/H_avg

Examiner tip

In a 5-part flight-planning question, organize your work with clear labeled sub-parts (a) to (f). The examiner marks each sub-part independently — a wrong answer in part (c) should not cascade if you show the correct formula. Show all formulas before substituting.

Model answer

Given: Area = 15 km × 10 km; f = 152 mm = 0.152 m; d = 230 mm = 0.230 m; Scale = 1:20 000 (S = 20 000); p (forward overlap) = 60%; q (sidelap) = 30%

(a) Flying height above terrain:
H = f × S = 0.152 × 20 000 = 3 040 m

(b) Ground coverage per photograph:
Ground side = d × S = 0.230 × 20 000 = 4 600 m
Area per photo = 4 600² = 21 160 000 m² = 2 116 ha

(c) Air-base (advance per exposure, along-strip direction):
B = (1 − p) × ground side = (1 − 0.60) × 4 600 = 0.40 × 4 600 = 1 840 m

(d) Strip spacing (perpendicular to flight direction):
W = (1 − q) × ground side = (1 − 0.30) × 4 600 = 0.70 × 4 600 = 3 220 m

(e) Number of flight strips:
Assume strips run along the 15 km dimension (east–west); strips spaced across the 10 km width.
Number of intervals across = 10 000 / 3 220 = 3.11 → 4 intervals (round up)
Number of strips = intervals + 1 = 4 + 1 = 5 strips

(f) Total number of photographs:
Photos per strip:
Intervals along strip = 15 000 / 1 840 = 8.15 → 9 intervals (round up)
Photos per strip = 9 + 1 = 10 photos
Total photos = 10 photos/strip × 5 strips = 50 photographs

∴ Summary:
H = 3 040 m | Ground side = 4 600 m | Area = 2 116 ha
Air-base B = 1 840 m | Strip spacing W = 3 220 m
Number of strips = 5 | Total photos = 50

Answer structure

• Part (a): H = f × S = 3 040 m [1 mark]
• Part (b): Ground side = 4 600 m; Area = 2 116 ha [1 mark]
• Part (c) + (d): B = (1−p) × 4 600 = 1 840 m; W = (1−q) × 4 600 = 3 220 m [1 mark]
• Part (e): Strips = (10 000/3 220 rounded up) + 1 = 5 [1 mark]
• Part (f): Photos per strip = (15 000/1 840 rounded up) + 1 = 10; Total = 50 [1 mark]

Scoring breakdown

Common mark deductions

• Forgetting '+1' for both photos per strip and number of strips
• Confusing which dimension is along-strip vs. across-strip when computing total photos
• Using q = 30 instead of q = 0.30 for sidelap

Key phrases to include

• H = f × S
• B = (1−p) × ground side
• W = (1−q) × ground side
• round up to ensure complete coverage
• photos = intervals + 1
• total = photos/strip × strips

Examiner tip

Pitfall questions reward precise engineering language. Use 'H = altitude − terrain elevation' and 'unit conversion (mm to m)' as your exact phrases — these are the mark-triggering terms.

Model answer

Pitfall 1 — Using altitude above MSL instead of height above terrain:
The formula Scale = f/H requires H to be the flying height above the ground surface, not above mean sea level. If the terrain has an elevation h above MSL, then H = aircraft altitude (AMSL) − h. Ignoring terrain elevation overestimates H and underestimates the scale (makes the photo appear smaller-scale than it truly is).
Avoidance: Always compute H = flight altitude − mean terrain elevation before applying Scale = f/H.

Pitfall 2 — Unit mismatch between f and H:
The focal length f is typically given in mm while H is in metres. Substituting without converting (e.g., 152 mm ÷ 1 520 m) gives 0.1 instead of the correct 1/10 000.
Avoidance: Convert f to metres before dividing (f = 152 mm = 0.152 m), then Scale = 0.152/1 520 = 1/10 000.

Answer structure

• Pitfall 1: altitude vs. terrain height — definition of error and avoidance strategy [1 mark]
• Pitfall 2: unit mismatch mm vs. m — definition of error and avoidance strategy [1 mark]

Scoring breakdown

Common mark deductions

• Naming the pitfall but not explaining the avoidance strategy (loses the second half of the mark)
• Repeating the same pitfall twice with different wording

Key phrases to include

• H above terrain not MSL
• H = altitude − terrain elevation
• unit conversion f mm to m
• Scale = f/H

Do

• State the formula if one exists (e.g., Scale = f/H)
• Include the correct SI unit or standard value (e.g., 60% for forward overlap)
• Use the exact technical term (principal point, nadir, forward overlap)
• Write in complete sentence form — not bullet fragments

Don't

• Do NOT write more than 2–3 lines — extra content adds no marks and wastes time
• Do NOT define terms the question did not ask for
• Do NOT leave the formula out thinking the definition alone is enough

Do

• Write the formula on a separate, clearly visible line
• Show unit conversion explicitly (mm to m, m² to ha)
• Use a two-paragraph or two-step structure so each mark is physically separate
• State the final answer clearly with a boxed or underlined value and unit

Don't

• Do NOT skip the formula and jump straight to numbers
• Do NOT omit units on the final answer
• Do NOT write a wall of text — use line breaks to separate marks

Do

• Number or label your parts: Step 1, Step 2, Step 3 or Part (a), Part (b), Part (c)
• Include a labeled diagram for geometry questions — it can earn 1 mark independently
• State formulas symbolically before substituting numbers
• Conclude with a summary sentence restating the final answer

Don't

• Do NOT write one long unbroken paragraph for a 3-mark answer
• Do NOT skip the diagram if the question says 'with a sketch'
• Do NOT use approximate formulas without acknowledging the approximation

Do

• List all given data in a 'Given:' block at the start — this shows organised thinking and prevents mid-solution errors
• Label each step clearly (Step 1, Step 2, etc.) so the examiner can award partial marks easily
• Show the '+1 rule' explicitly for photo count and strip count
• State the rounding decision with justification: '8.15 intervals → round up to 9 for complete coverage'
• Write a final summary box with all answers together

Don't

• Do NOT skip writing 'Given:' and 'Formula:' sections — these earn process marks
• Do NOT chain all arithmetic on one line — lose a step, lose a mark
• Do NOT round DOWN for number of photos or strips — incomplete coverage is an automatic error
• Do NOT forget unit conversions at any step (especially km to m, mm to m, m² to ha)