FOR220

1
FOR 220 Aerial Photo Interpretation and Forest
Measurements
Lecture 12 Scale of a Vertical Aerial Photograph
Paine, Chapter 4
FOR 220 Aerial Photo Interpretation and Forest
Measurements
2
Scale
Scale
Any quantitative measurement on a photograph
involves the use of scale to convert the
photograph's measurements to the actual ground
measurements
Without knowledge of scale, it is impossible to
relate the distances between 2 points (or the
size of an object) to an actual distance (or
size) on the ground.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
3
Scale
Scale
The ratio of distances between corresponding
points on a photograph (or map) and on the ground.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
4
Scale
Representative Fraction (RF) (Definition 1)
Ratio of the distance on a photograph to the same
distance on the ground, and expressed as a simple
fraction. Example 1 / 15,840 (the photo
distance is 1 / 15,840 times the ground
distance) Units are the same (numerator and
denominator), thus the ratio is unitless
RF usually expressed as a ratio on maps (e.g.
124000)
FOR 220 Aerial Photo Interpretation and Forest
Measurements
5
Scale
Representative Fraction (RF) (Definition 2)
Ratio of the focal length of the camera lens and
the flying height of the aircraft at time of
exposure.
Why are the two formulas for determining RF
equivalent? What geometry concept is involved?
FOR 220 Aerial Photo Interpretation and Forest
Measurements
6
Scale
Photo Scale Reciprocal (PSR) (Definition 1)

• Ratio of the ground distance divided by the
  photograph distance.
• Example 15,840 (the ground distance is 15,840
  times the photo distance)
• The inverse of RF
• Unitless
• The smaller the PSR, the closer you are to the
  actual landscape

FOR 220 Aerial Photo Interpretation and Forest
Measurements
7
Scale
Photo Scale Reciprocal (PSR) (Definition 2)
Ratio of the flying height of the aircraft
divided by the focal length of the camera lens.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
8
Scale
Equivalence

• Ratio of the distance on a photograph to the same
  distance on the ground, and expressed as a ratio.
• Examples
• 4 inches 1 mile
• 1 inch 1000ft.
• Units usually not the same.
• A more logical expression of scale, to some

FOR 220 Aerial Photo Interpretation and Forest
Measurements
9
Scale
Example 1
Given RF 1 31,680 What are the PSR and the
Equivalence scale (in inches per mile)?
FOR 220 Aerial Photo Interpretation and Forest
Measurements
10
Scale
Example 2
EQ is 1 inch 1 mile What are the RF and PSR?
FOR 220 Aerial Photo Interpretation and Forest
Measurements
11
Types of Scale
Average Scale
Average between points, for part of a photograph,
an entire photograph, or several
photographs. Will be different from one
photograph to the next, depending on variation in
topography.
Nominal Scale
The nominal scale is specified in a photo
contract. It is the desired average scale or,
the goal of an air photo mission.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
12
Types of Scale
Point Scale

• Photo scale at a point on the ground at a given
  elevation.
• Every point at a different elevation has a
  different scale.
• Range of point scale in a photograph f (focal
  length of a lens) / min and max flying height
  (variation in elevation within a given photograph)

FOR 220 Aerial Photo Interpretation and Forest
Measurements
13
Variation in Scale
Variation in Scale
As we just mentioned, scale is probably not
constant across a photograph. Within a single
photograph, scale is a function of tilt and
topography. Therefore, RF can be re-defined as
Photo
Lens
FOR 220 Aerial Photo Interpretation and Forest
Measurements
14
Variation in Scale
Variation in Scale
Assuming flat terrain, increasing the focal
length by 2 decreases the PSR by half.
PSR 10,000
PSR 20,000
FOR 220 Aerial Photo Interpretation and Forest
Measurements
15
Variation in Scale
Variation in Scale
Tilt causes variation within a single
photograph. Scales are different on either side
of the tilt.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
16
Basic Scale Equations
Basic Scale Equations (Review)
Relative Fraction
Where (from p. 70, Paine 1981)
FOR 220 Aerial Photo Interpretation and Forest
Measurements
17
Basic Scale Equations
Basic Scale Equations (Review)
Photo Scale Reciprocal
FOR 220 Aerial Photo Interpretation and Forest
Measurements
18
Basic Scale Equations
Average Scale Calculations
Example 1. Average scale between two road
junctions.
Ground distance Measured in the field is 1395 ft.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
19
Basic Scale Equations
Average Scale Calculations (continued)
Example 1. Average scale between two road
junctions.
Photo distance 1.14 inches Ground distance
1395 feet Elevation of point A 526
feet Elevation of point B 584 feet
Measured in field, or from topographic map, etc
Must be expressed in the same units

• All points 555 feet above mean sea level are at
  a PSR of 14,680
• Rounded to the nearest 10 by convention.

FOR 220 Aerial Photo Interpretation and Forest
Measurements
20
Basic Scale Equations
Average Scale Calculations
Example 2. Average scale between two (other)
road junctions.
Flying height above mean sea level (MSL) 8000
feet Average elevation of landscape features
800 feet Focal length of lens 6 inches
Must be expressed in the same units

• All points 800 feet above mean sea level are at
  a PSR of 14,400.

FOR 220 Aerial Photo Interpretation and Forest
Measurements
21
Basic Scale Equations
Average Scale Calculations
Example 3. Using a map and a photograph with
limited information.
FOR 220 Aerial Photo Interpretation and Forest
Measurements
22
Basic Scale Equations
Flying Height Calculations
Example 4. What is the flying height of the
aircraft (H) if the focal length is 6 inches?
PSR 14,650 Average elevation 555 feet ? 6
inches (0.5 ft.)
Hint Solve for A
Remember H A - E
7880 - 555 7325 feet H
FOR 220 Aerial Photo Interpretation and Forest
Measurements
23
What theme is represented by this map? How
do you know?
FOR 220 Aerial Photo Interpretation and Forest
Measurements
24
What are these features and where are they?