STANDARD FORMULAS FOR COVERAGE AND ENDLAP

The standard formula for scale is [(H-h)/f] = PSR

Where
• H is altitude above sea level (MSL)
• h is ground elevation
• (H-h then becomes altitude above ground (AGL))
• f is focal length of the camera in feet (6” is .5’, 12” is 1’, 8.25” is .6875’)

PSR stands for Photo Scale Reciprocal and is a single number way to represent scale.

This formula can be reworked to get the information desired. The PSR number is sometimes more understandable if it is thought of in its other format as a representative fraction such as 1:36000. This means that one unit on the negative will be 36000 units on the ground. We don’t usually measure distances on the ground in inches, so we can break down the 36000 into a more useful foot unit by dividing by 12 (12 inches per 1 foot). This then becomes one unit on the negative (1”) equals 36000/12 units on the ground or 1”=3000’. To determine how high we have to fly to get this scale with various focal length cameras, we can plug in the information (assume an h of 0 feet):

To determine how much area we cover on the ground, take the 1”=feet scale and multiply by 9 (because our negatives are 9”x9” in size). This will give the full negative coverage, using the above example data, 1”=3,000’ take 9 x 3000 for a raw negative coverage of 27,000’ x 27,000’. In reality, we do not consider the entire negative to be usable because we may miss the center point slightly, the flight altitude may be off a bit, and we want to stay away from the edges for quality and fiducial marks. A reasonable usable area is 7 or 8 inches on the negative depending on several quality and job related factors.

SCALING PHOTOGRAPHS

If you need to determine the scale of an existing image, you will need a map of known scale and some sort of measuring device. Find at least two points that can be identified on both the photo and map. Measure the distance between each of them. To determine the distance between the points on the map, multiply the measured distance by the scale of the map. For example a USGS quad map is a 1:24,000 scale map, or 1”=2,000’. If the distance between your points is 2.5”, multiply 2.5 x 2000 for a distance of 5,000’. Next, divide this map distance by the inches measured between the same two points on the photo or negative. For example if the points measure 3.8 inches on the photo the scale of the photo will be 5,000 / 3.8 or 1”=1315’. This process is very useful as a basis for determining enlargement factors, coverage areas for new photography or actual flying height if fed back into the first formula.

DETERMINING ENDLAP AND EXPOSURE COUNTS

A normal task of flight planning is to determine how many exposures will be taken on a particular flight line. This process uses many of the previously mentioned measurements. The initial step is to determine how long the flight is, usually in feet. Then we need to determine how far we will travel between photographs. For this we need to know the scale and specified endlap. A very typical endlap is 60% for stereo coverage. This means the 60% of one frame will be in common with the frames before and after it. By simple subtraction, this means that we will travel 40% of the frame area between exposures. 40% of a 9” negative is 3.6” (.4 x 9 = 3.6). If our scale is 1” = 3,000’ as in our earlier examples, we will travel 2.6 x 3000’ or 10,800’ between exposures (forward advance). If our measured flight line is 35,000 feet long, we can divide by 10,800 for a raw number of 3.24. This is a realistic situation in that it is not a whole number. We always will round up (to 4) and add one exposure for the start to make this a 5 exposure line. We will cover slightly more distance than required, but this is preferable to cutting the line short and missing part of the project. Good flight planners will try to design the lines to be the correct length for the specified endlap.

Actual endlap percentages or distances between photo centers can be determined in similar fashions using the above processes. Just remember that a standard aerial negative is 9” long and the forward advance between frames is the difference of 100% minus endlap.

SECTION COVERAGE

Many forestry and city customers want sections to be in a photo without cutting off edges as a stereo flight is being done. A minimum endlap can be determined to assure full-block coverage as follows:

The advance from endlap must be less than the difference between the coverage on the film and the block size. For example, if a full section (5280’ x 5280’) needs to be covered using 8.5 inches of a 1”=1000’ negative, the maximum forward advance can be 8500’ – 5280’ = 3220’. Translated to endlap percentage, this is 3220 / 9000 = 36.8% forward advance, or 63.2% endlap (minimum). Usually this results in a specification for 65% endlap.

A more modern way to accomplish the same task is to flight plan the exact center of the photos from the start and generate a point file of these photo centers. The flight crew will then use triggering software to create a photo over each pre-planned point. This takes out some potential errors from relying on endlap, as terrain or camera operator error can drift the actual endlap significantly on a long line.

Our staff of flight planners and camera operators can help with these calculations or explain why some of them are important. Just give us a call or email.