The stadia arc shown in figure 8-7 is the multiplier
stadia arc (the vertical index is at zero); that is, the
observed stadia interval is multiplied by the Hor stadia
arc reading to get the horizontal distance; or the stadia
interval is multiplied by the Vert stadia arc reading to
obtain the vertical distance from the center of the
instrument to the point sighted on the rod This vertical
distance, combined with the HI and the rod reading, will
give the difference in elevation between the instrument
station and the point where the rod is held
The stadia arc, as shown is figure 8-8, is called the
horizontal scale subtraction stadia arc (the vertical
index is at 50). The use of the Beaman stadia arc to
obtain a horizontal distance and difference in elevation
is explained in the following sections.
Horizontal Distance (Subtraction Scale).— The
H scale gives you a percentage that you can apply to an
inclined stadia shot with the alidade to get the
corresponding horizontal distance from the slope
distance. Suppose that with the telescope inclined (that
is, at a vertical angle other than 0°), you read an interval
of 2.45 feet on the stadia rod. The slope distance, then
What is the corresponding horizontal distance? You read
the graduation indicated by the Beaman arc indicator on
the H scale, and find that the reading is 5. This means
that the horizontal distance is 5 percent less than the
slope distance, or
245 feet – (0.05 x 245 feet), or
245 – 12.25 = 232.8 feet.
Difference in Elevation (Vertical Index at
50).— The V scale on the Beaman arc is used to
determine the difference in elevation between the
elevation of the line of sight through the telescope (that
is, the HI) and the elevation of the point you sighted on
the level rod Note that when the telescope is horizontal,
the V scale on the Beaman arc reads 50. This
arrangement makes the use of minus values unnecessary
when you are sighting with the telescope at a negative
vertical angle.
To read the V scale, you take the difference between
50 and whatever you read on the scale and apply this
difference as follows to determine the difference in
elevation.
Suppose that when you made the shot previously
described (where you read 5 on the H scale), the reading
on the V scale was 71. In practice, it is the custom to
shoot the rod at a point that will give you an even reading
on the V scale.
Because the reading was 71, the value you will use
is
71 –50, or 21%.
This means that the difference in elevation between the
HI and the point you sighted on the rod is 21 percent of
the slope distance. The slope distance, in this case, was
245.0 feet; therefore, the difference in elevation is
245.0 x 0.21 = 51.45 feet.
Now that you know how to read stadia and compute
horizontal and vertical distances using stadia, we will
now discuss typical field procedures.
Field Procedures
Figure 8-9 shows two situations that are
encountered in transit-stadia work First, let us discuss
the common situation in which you desire to determine
the difference in elevation between an instrument station
of known elevation and a ground point of unknown
elevation. This situation is shown in figure 8-9, view A.
In this view, the elevation of the instrument station P is
known and it is desired to determine the difference in
elevation between P and the rod station P1. The
horizontal center-line height of the instrument (h.i.)
above point P is equal to PA. As you can see, this h.i. is
different than the HI that you are accustomed to working
with indirect leveling. The rod reading is P1B.
From your studies, you know that the difference in
elevation (DE) between P and P1 can be expressed as
follows:
Therefore, the ground elevation at P1 can be expressed
as follows:
Now let us sight on the rod such that P1B = PA = h.i. In
this case, the situation occurs in which a similar triangle
(PC1P1) is formed at the instrument station P. From
observation of these similar triangles, you can see that
the DE= P1C1 = BC. Therefore, the ground elevation at
P1 can be simply expressed as follows:
This is an important concept to understand when
shooting stadia from a station of known elevation As
8-8
