### Aerial Photographs to measure the object height

In this article discuss about displacement
in aerial photograph occurred due to relief or height of object on ground.

Relief/Height/Elevation is the most
significant source of image displacement. When point/object on the photograph
is displaced from its datum position because of its elevation, a displacement
take place so this displacement is called Relief displacement or displacement
due to height of object.

This relief displacement process can
also help to calculate the height of object.

This relief displacement is
explained by below figure. In this Figure, ‘O’ is the camera station. ‘NA' is a
flat plain on which stands a tower ‘AB’ with its base at ‘B’. The image of ‘B’ on the truly vertical
positive photographic plane is ‘b’.

This is the correct planimetric
position (orthogonal) of the image of the tower ‘AB’.

Top ‘A’ is imaged at `a'. The image of ‘A’ is thus displaced from its
correct planimetric position ‘b’, as `A' is vertically above `B', on the
photograph.

This shift of `a' from `b'
represented by distance ‘ba' is called

**relief displacement.**
Let ‘h’ be the height of the tower, ‘H’
the flying height above the datum plane, ‘n’ and ‘N’ is the photo and ground
nadir points (as per the given figure).

na

The
scale of photo along na is
------------

NA’

ba

The
scale of photo along ab is
------------

BA’

Since the photograph is truly
vertical and datum plane is truly horizontal the scale will be constant.

ba na

Hence ------------ =
----------

BA’ NA’

ba BA’

Or -------- =
-------- (1)

na NA’

From similar triangles ONA' and ABA

BA’ h

-------- =
--------

NA’ H

Equation (1) becomes

ab h

-------- =
--------

na H

h

Hence ab =
na* --------

H

If we denote `ab', the displacement
by rd and na, the distance between the nadir point and the image of top of the
object by r then we can write the above equation as

h

RD
= r --------

H

**From this relation one canconclude :**

Relief displacement increases with
increasing value of `r' i.e., it is zero at plumb point and maximum at the
edges of the photograph.

Smaller the height of the object,
smaller is the displacement and vice versa.

If h = o, i.e. for objects in the datum plane there is no displacement.

With increasing value of `H' i.e.
with high flying heights the displacement decreases. The satellite pictures can
thus be considered having very low relief displacement.

While relief displacement
constitutes a source of error in the measurement of horizontal distances on
aerial photographs, it is the characteristics that make it possible to study
overlapping photographs stereoscopically and in the determination of height
differences between objects photographed.

#### Numerical Example-

Q1. The relief displacement for a tower
is 3.01mm and the radial distance from the center of photo to the top of tower
is 66.43mm. If the flying height is 1330m above the base of tower, find the
height of the tower.

Ans. Here in this question given
values are

Relief displacement (RD) = 3.01mm;
radial distance (r) = 66.43mm, flying height (H) = 1330m and height of tower
(h) need to calculate.

So if use the above formula for
relief displacement

h

RD
= r --------

H

First bring all the values to same
measurement units- (in this case converted meter to mm)

SO based on that

h

3.01 = 66.43 ----------

1330000

By solving above

h = 5890.41mm

h = 5.89 meters

so height of tower will be 5.89
meters

with this method height of object on
ground can be calculated using aerial photographs.

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