Scale of a Vertical Aerial Photo (From Paine Chapter 4 With Elements of Arnold Ch. 1)

Scale Classification

Small Scale	1:24,000 and smaller
Medium Scale	1:10,000 to 1:24,000
Large Scale	1:1,000 to 1:10,000
Very Large Scale	1:1,000 and larger

Some useful Scales in Forestry:

1:15,840  1 inch = 20 chains         1:7,920    1 inch = 10 chains

Note: Large scale and Small scale are only relative terms.

For aerial photos or maps of a given area:

• Large scale shows greater detail but a smaller area.
• Small scale shows lesser detail, but a larger area.

Comparing different scales is linear. A given distance on the ground will be twice as long at 1:25K as it will at 1:50K.

Area relationships are squared. Map 1 is four times the area of Map 2 and sixteen times the area of Map 3.

Theory of Scale

Three analytical methods: RF, PSR and equivalent scale

Graphical scale, verbal scale

Representative Fraction (RF)
Ratio of a distance on the photo to the same distance on the ground
Expressed as simple fraction with 1 as numerator

4.2.2 Photo Scale Reciprocal (PSR)
The inverse of RF, also unitless
Take PSR of 24,000. Means the ground distance is 24,000 larger than the map distance (of the same unit)

If the PSR is small it is closer to the actual object size than if the PSR is large

4.2.3 Equivalent Scale
Showing map units as an equivalence in different ground units.
1:24,000 is the same is 1inch = 2,000 feet on the ground

Photo scale relates size or distance on the photo to actual size or distance on the ground. Scale needed to correctly interpret an aerial photo.

4.3 Types of Scale

Average scale – can refer to entire project, single photo, or portion of a photo. Usually not the exact scale of the photos due to various factors

Point scale – photo scale at a point on the ground at a given elevation

4.4 Variation in Scale

Two primary causes of variation over a single photo

1. Tilt
2. Differences in flying height above the ground caused by differences in ground elevation, or topography

Another source of variation between photos in the same mission comes from slight changes in height between exposures.

RF can also be defined as focal length divided by flying height above the terrain. Focal length constant, but flying height above the ground varies as elevation changes.

Higher ground elevations have a larger scale than lower elevations (See Figure 4.2)

Scale changes from point to point over the photo with topography and height of the airplane.

Ridge tops have a larger scale than valleys.

Average scale can vary among photos on the same project and be different than the project average scale.

Focal length of the camera affects photo scale. A cameral using a lens with a longer focal length increases the scale of the photo. (See Figure 4.3)

 Tilt: the scale of a tilted photo changes in a regular manner throughout the photo.

Scale changes across the photo in the direction of the tilt. (See Figure 4.4)

If the scale near the center of the photo is approximately correct:

    The scale is smaller on the side of the photo positive that is tilted upward.

    The scale is large on the side of the photo positive that is tilted downward.

Basic scale equations

See Figure 4.5  Using similar triangles:

f = focal length, H or A-E = flying height above the ground, PD = photo distance, GD = ground distance. f and H have to be in the same units

Photo Scale Determination

Using the camera focal length and flying height equation is easiest

Can be done remotely. If we use the average elevation we get the actual scale. If we use a point elevation we get a point scale

Ways of getting the ground distance

•     Measure the GD directly on the ground
•     Measure the map distance and compute the ground distance using the map scale
•     If we know the ground distance between two points only the photo distance is necessary
•     Use GPS to get grid coordinates and calculate the distance. Which is better UTM or Lat-Long?

Can sometimes use section boundaries if working in an area where the Public Land Survey System is used.

Finding the Scale by Comparison

When the scale of the map or image is unknown or in question. Need another map of known scale to compare.

Locate the same two points on each map or image of a particular earth surface area.

1. If using a vertical airphoto try to select points so that the line between them goes through the Principal Point (PP).
2. Measure the straight-line distances as carefully as possible with an engineer’s scale. Insert the values into the equations.
3. Solve the equation by cross-multiplication. The value solved is the denominator for the unknown RF

Line AB = distance from point A to point B on map of known scale.
Line A’B’ = distance between points A and B on the map or image of unknown scale.
D = denominator of known RF.
X = denominator of unknown RF

4.6.1 Assumptions

All these methods assume a truly vertical photo. No simple way of determining tilt. Must rely on the skill and experience of the pilot.

Assumes error caused by topographic displacement when measuring the photo distance of the baseline is negligible. The error can be minimized by establishing the baseline as close to the nadir as possible and keep both ends of the baseline at approx. the same elevation (See Figure 4.8)

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