Aerial Photography and Camera Geometry - Cheat Sheet
Your 30-minute revision companion for photo scale, ground coverage, flight planning, and camera geometry. Master the formulas, nail the common pitfalls, and solve board-style problems with confidence.
Photo Scale — Core Concept
Formulas
Scale = f / H
Meaning
f = focal length (mm); H = flying height ABOVE GROUND (m). Result is scale ratio 1:S where S = H/f.
Watch out
H MUST be above ground level (AGL), NOT above sea level (MSL). Use mean ground elevation for terrain variation.
When to use
Every time you need to relate photo distance to ground distance. This is THE fundamental formula.
Ground distance = Photo distance × S
Meaning
Photo distance (mm); S = scale denominator (e.g., 10,000 for 1:10,000); ground distance in same units as scale denominator scale.
Watch out
Unit conversion is critical. If photo is in mm and S = 10,000, result is in mm — convert to meters (÷1,000).
When to use
Converting measured distances on a photo to real ground distances.
Average Scale = f / H_avg
Meaning
H_avg = mean ground elevation above datum for hilly terrain; f = focal length.
Watch out
Using sea-level flying height instead of terrain-corrected height will give incorrect scale.
When to use
When flying over terrain with significant elevation changes; use average elevation, not min or max.
Common values
Value
152 mm, 210 mm, 300 mm, 500 mm
Symbol
f
Quantity
Standard focal lengths
Value
230 mm × 230 mm (23 cm square)
Symbol
d
Quantity
Standard photo format
Value
1,000–6,000 m AGL
Symbol
H
Quantity
Typical flying height range
Important facts
- Photo scale = f/H; always measure H from ground, not sea level.
- Vertical photo: principal point = nadir (true for near-vertical shots within ±3°).
- Photo format is square: standard 230×230 mm (23 cm) for most metric cameras.
- Scale denominator S = H/f; larger S means smaller scale (less detail, more coverage).
- Same ground distance appears DIFFERENT lengths on different scale photos.
Key definitions
Metric Aerial Camera
Example
Zeiss RMK camera with f = 152 mm is a standard metric camera used in Philippine airborne surveys.
Precision camera with known focal length, calibrated interior orientation, and standard format (typically 230×230 mm square).
Focal Length (f)
Example
A 152 mm focal length creates wider ground coverage; 300 mm creates narrower coverage but larger scale.
Distance from lens principal plane to image plane; standard values: 152 mm, 210 mm, 300 mm.
Principal Point
Example
Located at center of photo for a vertical shot; used as origin for photo coordinate system.
Point where optical axis intersects the photo plane; marked on every aerial photo for reference.
Nadir
Example
For a vertical photo from 1,500 m AGL, nadir is the ground point at (0,0) in the photo frame.
Ground point directly below the camera; coincides with principal point on truly vertical photos.
Flying Height (H)
Example
If plane flies at 2,000 m MSL over terrain at 500 m elevation, H = 1,500 m AGL.
Altitude of aircraft above ground level (AGL), NOT above sea level.
Diagrams to know
- Similar-triangle diagram: camera lens to ground (shows f and H relationship)
- Photo frame with principal point and cardinal directions marked
Ground Coverage and Photo Dimensions
Formulas
Ground side = d × S
Meaning
d = photo format side (m); S = scale denominator. Result in same units as d.
Watch out
Ensure d and result are in same unit system (convert mm to m first if needed).
When to use
Calculate ground coverage in one direction (N–S or E–W).
Ground area = (d × S)²
Meaning
Square photo covers square ground area. Result in m² or hectares.
Watch out
This is AREA, not just ground side. Common error: forgetting to square the side length.
When to use
Find total area covered by one photo for flight planning.
Ground area (hectares) = (d × S)² / 10,000
Meaning
Convert m² to hectares (1 ha = 10,000 m²).
Watch out
Remember 1 ha = 10,000 m², not 1,000 m².
When to use
Express photo coverage in hectares (standard for land surveys in Philippines).
Photo area = d²
Meaning
Photo format area in mm² or m².
Watch out
This is photo (image) area, not ground area.
When to use
For theoretical coverage; rarely asked directly.
Common values
Value
1,150 m × 1,150 m = 132.25 ha
Symbol
Area₅₀₀₀
Quantity
Photo at 1:5,000 scale (standard urban survey)
Value
2,300 m × 2,300 m = 529 ha
Symbol
Area₁₀₀₀₀
Quantity
Photo at 1:10,000 scale (regional survey)
Value
3,450 m × 3,450 m = 1,191 ha
Symbol
Area₁₅₀₀₀
Quantity
Photo at 1:15,000 scale (wide coverage)
Important facts
- Ground side is always photo dimension × scale denominator.
- Ground area grows as SQUARE of scale denominator: doubling S quadruples coverage.
- A single photo at 1:10,000 covers ~500–530 hectares (useful reference for exam).
- Coverage area is INDEPENDENT of focal length (depends only on format and scale).
- 1 hectare = 10,000 m² = 100 m × 100 m (useful for quick conversion).
Key definitions
Ground Coverage
Example
A 230 mm photo at 1:10,000 scale covers 2,300 m × 2,300 m = 529 hectares.
Total ground area imaged by one vertical aerial photo.
Photo Format
Example
Format size determines maximum single-shot coverage; larger format = broader coverage at same scale.
Physical dimensions of the film/sensor; standard metric camera = 230×230 mm square.
Diagrams to know
- Photo frame with dimensions d and ground square with side d×S
- Coverage comparison: same format, different scales (smaller scale = larger coverage)
Flight Planning — Overlap and Air Base
Formulas
Forward overlap = 60% (standard)
Meaning
Successive photos along a flight line overlap 60%; gap = 40% × ground side.
Watch out
60% is standard; some surveys use 55–65%. Smaller overlap = fewer photos, less cost but poorer stereo.
When to use
Calculate spacing between consecutive exposures for stereo coverage.
Air base = Ground side × (1 − Overlap %)
Meaning
Ground distance between consecutive exposure centers; e.g., air base = (d×S) × 0.40 for 60% overlap.
Watch out
If overlap = 60%, the OVERLAP LENGTH is 0.60 × ground side; AIR BASE (gap) is 0.40 × ground side.
When to use
Plan flight spacing to achieve desired overlap.
Sidelap = 30% (standard)
Meaning
Adjacent flight lines overlap 30% to ensure complete stereo coverage across entire survey area.
Watch out
Sidelap prevents gaps between flight lines; use 25–35% depending on terrain and camera drift.
When to use
Calculate spacing between parallel flight lines.
Number of photos (flight line) ≈ Line length / Air base
Meaning
Estimate exposures needed to cover a straight-line distance.
Watch out
Round UP (not down) to ensure complete coverage; add extra photo at start and end.
When to use
Flight plan estimation.
Common values
Value
920 m (for 2,300 m ground side)
Symbol
B₁₀₀₀₀
Quantity
Air base at 1:10,000 (60% overlap)
Value
460 m (for 1,150 m ground side)
Symbol
B₅₀₀₀
Quantity
Air base at 1:5,000 (60% overlap)
Value
60% (range 55–65%)
Symbol
OF
Quantity
Standard forward overlap
Value
30% (range 25–35%)
Symbol
SL
Quantity
Standard sidelap
Important facts
- Standard forward overlap is 60%; gap (air base) = 40% of ground side.
- Standard sidelap is 30%; prevents gaps between adjacent flight lines.
- Stereo requires TWO overlapping photos from different positions.
- Overlap is measured CENTER-TO-CENTER (air base), not edge-to-edge.
- Too little overlap (<50%) = incomplete coverage; too much (>70%) = wasted photos and cost.
- 60% overlap + 30% sidelap is international standard (matches PRC/BNSP requirements).
Key definitions
Forward Overlap
Example
At 60% overlap, if ground side = 2,300 m, then gap = 920 m and air base = 1,380 m.
Percentage of successive photo overlap along a flight line; standard 60% for stereo coverage.
Sidelap
Example
Flight lines spaced to achieve 30% sidelap prevent strips being missed.
Percentage overlap between adjacent parallel flight lines; standard 30% for complete area coverage.
Air Base
Example
For 60% overlap and 2,300 m ground side: air base = 0.40 × 2,300 = 920 m.
Ground distance between centers of consecutive photo exposures (100% − forward overlap % × ground side).
Stereoscopic Coverage
Example
60% forward overlap + 30% sidelap creates stereopairs for the entire survey area.
Overlapping photos imaged from two positions, allowing 3D viewing and height measurement.
Diagrams to know
- Flight line diagram showing forward overlap: consecutive photos with 60% overlap, air base labeled
- Flight block diagram showing parallel flight lines with 30% sidelap; indicate flight direction and tie lines
Photo Interpretation — Coordinates and Geometry
Formulas
Photo distance = Ground distance / S
Meaning
Reverse of ground distance formula: convert known ground distance to photo dimension.
Watch out
Unit consistency: if ground distance is in meters and S is 10,000, photo distance = meters / 10,000 = 0.0001 m = 0.1 mm.
When to use
Predict how a ground feature appears on a photo of known scale.
Magnification = H / (f + ground distance × tan θ)
Meaning
For inclined photos (non-vertical); for vertical photos, this simplifies to Scale = f/H.
Watch out
Vertical photos only: use simple Scale = f/H. Tilted photos require more complex derivation.
When to use
Advanced: tilted photo geometry (not core PRC exam).
Important facts
- Principal point is reference (0, 0) on photo; all measurements made relative to this point.
- Fiducial marks ensure proper photo alignment and orientation.
- For a vertical photo: 1 mm on photo = 1 × S m on ground (at standard scale).
Key definitions
Photo Coordinate System
Example
A point at +50 mm (east) and −75 mm (south) of principal point on a 1:10,000 photo is 500 m east and 750 m south on ground.
2D x–y grid on photo with origin at principal point; measured in mm from center.
Fiducial Marks
Example
Fiducials at ±115 mm from center define the 230×230 mm format boundary.
Four corner marks on photo frame defining photo format boundary; ensure principal point is centered.
Diagrams to know
- Photo frame with fiducial marks, principal point, and x–y coordinate system
- Ground coordinate system and photo-to-ground coordinate transformation diagram
Worked Board-Style Problems
Common values
Value
f = 152 mm, H = 1,520 m → Scale = 1:10,000
Symbol
Ex1
Quantity
Example 1 scale
Value
d = 230 mm, S = 10,000 → ground side = 2,300 m, area = 529 ha
Symbol
Ex2
Quantity
Example 2 ground coverage
Value
Photo distance = 45 mm, S = 10,000 → ground distance = 450 m
Symbol
Ex3
Quantity
Example 3 ground distance
Value
Ground side = 2,300 m, overlap = 60% → air base = 920 m
Symbol
Ex4
Quantity
Example 4 air base
Important facts
- PROBLEM TYPE 1: Given f, H → find scale. Use Scale = f/H directly.
- PROBLEM TYPE 2: Given scale, photo distance → find ground distance. Use Ground = Photo × S.
- PROBLEM TYPE 3: Given format, scale → find ground coverage. Use Ground side = d×S; area = (d×S)².
- PROBLEM TYPE 4: Given ground side, overlap % → find air base. Use Air base = Ground side × (1 − overlap%).
- PROBLEM TYPE 5: Terrain correction. If terrain elevation varies, use average elevation for mean scale.
Diagrams to know
- Sample calculation flowchart: input (f, H, scale) → output (ground side, area, air base)
Must remember
- Formula #1: SCALE = f / H (focal length / flying height above GROUND, not sea level).
- Formula #2: GROUND DISTANCE = PHOTO DISTANCE × SCALE DENOMINATOR (unit conversion critical).
- Formula #3: GROUND SIDE = d × S; GROUND AREA = (d × S)² (area is SQUARED).
- Formula #4: AIR BASE = Ground side × (1 − Forward overlap %) = Ground side × 0.40 (for 60% standard overlap).
- Key fact: H must be ABOVE GROUND LEVEL (AGL), not above sea level (MSL); use mean elevation for terrain.
- Standard overlap: 60% forward overlap along flight line; 30% sidelap between parallel flight lines.
- Photo format: 230 mm × 230 mm square (23 cm); this is your reference for all format calculations.
- Common exam trap: Confusing photo DISTANCE (mm) with ground DISTANCE (m); always convert units explicitly.
- Stereo geometry: Two overlapping photos from different positions create stereoscopic 3D view; 60% overlap ensures stereo pair coverage.
- Quick reference: At 1:10,000 scale with 152 mm focal length, flying height = 1,520 m AGL; ground coverage ≈ 2,300 m × 2,300 m ≈ 529 hectares.
Last minute tips
- UNIT TRAP: Photo dimensions in mm; scale denominator (e.g., 10,000) is unitless. Ground distance = (mm × scale denominator) ÷ 1,000 = meters. Write out units EVERY TIME.
- H IS AGL, NOT MSL: If flying height above sea level is 2,000 m and terrain is 500 m elevation, use H = 1,500 m for scale calculation. Missing this = WRONG ANSWER on every scale problem.
- OVERLAP ≠ AIR BASE: 60% overlap means 40% GAP. Air base = 0.40 × ground side, NOT 0.60 × ground side. This is the #1 board-exam mistake.
- AREA IS SQUARED: Ground area = (d × S)², not just (d × S). Forgetting the square will cost you full marks on ground coverage problems.
- PRC/BNSP standard: Forward overlap 60%, sidelap 30%; these are not negotiable for licensed surveyors in Philippines. Know these as baseline.
Comparison tables
Focal Length vs. Ground Coverage (at constant flying height)
| Focal Length | Scale (H fixed) | Ground Side | Ground Area | Detail Level | |
|---|---|---|---|---|---|
| 152 mm (wide angle) | Larger (1:more) | Wider coverage | Larger | Larger | Lower (less detail) |
| 210 mm (standard) | Medium | Medium | Medium | Medium | Medium detail |
| 300 mm (narrow angle) | Smaller (1:fewer) | Narrower coverage | Smaller | Smaller | Higher (more detail) |
Flying Height vs. Scale (at constant focal length f = 152 mm)
| Flying Height (m AGL) | Scale Denominator S | Ground Side (mm → m) | Overlap Gap (60%) | Use Case |
|---|---|---|---|---|
| 760 | 5,000 | 1,150 m | 460 m | Detailed urban mapping |
| 1,520 | 10,000 | 2,300 m | 920 m | Standard regional survey |
| 2,280 | 15,000 | 3,450 m | 1,380 m | Wide area planning |
| 3,050 | 20,000 | 4,600 m | 1,840 m | Regional reconnaissance |
Overlap % Effect on Air Base and Photo Efficiency
| Forward Overlap % | Gap % (Air Base %) | Photos per km | Efficiency (cost vs. coverage) | Stereo Quality |
|---|---|---|---|---|
| 50% | 50% | ~2.17 | Lower cost | Weak overlap, gaps possible |
| 60% (standard) | 40% | ~2.74 | Balanced | Full stereo, industry standard |
| 70% | 30% | ~3.33 | Higher cost | Excellent stereo, redundant |
Diagrams
Aerial Photography Formula Hierarchy
Mind map showing the hierarchical relationship between photo scale, ground coverage, and flight planning formulas. Branches show core concepts, relationships, coverage calculations, flight parameters, and common pitfalls students encounter.
Photo Scale Calculation & Ground Distance Conversion
Step-by-step flowchart showing the complete process from given camera parameters to final ground distance calculation, highlighting the critical step of ensuring H is above ground level (AGL) and the unit conversion from mm to meters.
Flight Plan Overlap Calculation
Flowchart showing the complete flight plan design process, from ground side calculation through overlap selection to final flight block spacing with forward and lateral coverage.
Photo Scale States for Terrain Variation
State diagram illustrating how photo scale handling changes depending on terrain type, from flat terrain with single scale to hilly terrain requiring average scale calculation.
Standard Overlap & Gap Distribution (60-40 Rule)
Pie chart showing the 60-40 forward overlap standard: 60% of successive photos overlap, creating a 40% gap (air base) between exposure centers along a flight line.