286
Chapter 9 Remotely Sensed Images from Above
So the photo scale is 1:4000. One unit measured on the photo is equal to
4000 units in the real world.
A second type of measurement that you can make from the elements
found in an aerial photo is the ability to accurately calculate the height of an
object in the photo simply by examining its shadow in the photo. At first blush,
it seems you’d need to know all sorts of other information—where the photo
was taken, what time of day it was taken, the date on which it was taken—
all variables related to the relative location of the Sun and how the shadows
would be cast. Chances are you wouldn’t be able to easily get your hands on a
lot of this type of information, so you’re probably thinking that there must be
a better way to do this.
You’d be right—photogrammetric measurements give you a much simpler way of determining the heights of objects in a photo from their shadows
without needing all that other data. It relies on three things: (1) knowing the
scale of the photo (which we just figured out); (2) being able to clearly see the
full shadow (from the top of the object) on level ground of all objects whose
heights you want to measure; and (3) already knowing the height of one object with a shadow you can measure. With these things, measuring heights is
a snap.
Let’s take that hypothetical 1:4000 photo from the last example and assume that it’s got a number of large hotels casting shadows on the boardwalk.
You know the height of one building (115 feet) and can measure its shadow
in the photo (from the base to the top) to be 0.10 inches. You can use this
information to calculate the angle of the Sun, which is casting the shadows in
the photo as follows:
tan a ϭ
h
L
In this equation, a is the angle of the Sun, h is the real-world height of the
object, and L is the real-world length of the shadow. From basic trigonometry,
the tangent of a right angle (tan a) is equal to its opposite value (h) divided by
its adjacent value (L). See Figure 9.13 for a diagram of how this works. You already know the height, h (115 feet). The length, L, can be found by taking the
height of the shadow measured in the photo (0.10 inches) and multiplying by
the photo scale (1:4000). It turns out that 0.10 inches on the photo would be
400 inches in the real world, or 33.33 feet. This means if you were to measure
the building’s photo by actually going to the boardwalk, its shadow would be
33.33 feet long. Plugging these numbers into the formula, we find that:
tan a ϭ
115 ft
33.33 ft
and that the tangent of angle a (or “tan a”) is equal to 3.45.
Now, since an aerial photo represents a single snapshot in time, we can
assume that the angle of the Sun is going to remain the same across the photo
for all of the buildings casting shadows. So, the measure for “tan a” will be the
same value when applied to all heights we’re trying to determine. We can use
Chapter 9 Remotely Sensed Images from Above
So the photo scale is 1:4000. One unit measured on the photo is equal to
4000 units in the real world.
A second type of measurement that you can make from the elements
found in an aerial photo is the ability to accurately calculate the height of an
object in the photo simply by examining its shadow in the photo. At first blush,
it seems you’d need to know all sorts of other information—where the photo
was taken, what time of day it was taken, the date on which it was taken—
all variables related to the relative location of the Sun and how the shadows
would be cast. Chances are you wouldn’t be able to easily get your hands on a
lot of this type of information, so you’re probably thinking that there must be
a better way to do this.
You’d be right—photogrammetric measurements give you a much simpler way of determining the heights of objects in a photo from their shadows
without needing all that other data. It relies on three things: (1) knowing the
scale of the photo (which we just figured out); (2) being able to clearly see the
full shadow (from the top of the object) on level ground of all objects whose
heights you want to measure; and (3) already knowing the height of one object with a shadow you can measure. With these things, measuring heights is
a snap.
Let’s take that hypothetical 1:4000 photo from the last example and assume that it’s got a number of large hotels casting shadows on the boardwalk.
You know the height of one building (115 feet) and can measure its shadow
in the photo (from the base to the top) to be 0.10 inches. You can use this
information to calculate the angle of the Sun, which is casting the shadows in
the photo as follows:
tan a ϭ
h
L
In this equation, a is the angle of the Sun, h is the real-world height of the
object, and L is the real-world length of the shadow. From basic trigonometry,
the tangent of a right angle (tan a) is equal to its opposite value (h) divided by
its adjacent value (L). See Figure 9.13 for a diagram of how this works. You already know the height, h (115 feet). The length, L, can be found by taking the
height of the shadow measured in the photo (0.10 inches) and multiplying by
the photo scale (1:4000). It turns out that 0.10 inches on the photo would be
400 inches in the real world, or 33.33 feet. This means if you were to measure
the building’s photo by actually going to the boardwalk, its shadow would be
33.33 feet long. Plugging these numbers into the formula, we find that:
tan a ϭ
115 ft
33.33 ft
and that the tangent of angle a (or “tan a”) is equal to 3.45.
Now, since an aerial photo represents a single snapshot in time, we can
assume that the angle of the Sun is going to remain the same across the photo
for all of the buildings casting shadows. So, the measure for “tan a” will be the
same value when applied to all heights we’re trying to determine. We can use