3. Pointing

Pointing error depends on how accurately the TSI operator can sight (point) at the BS and FS marks. A number of things affect this including

* Parallax
* Cross hair design
* Target width
* Target distance

a. Parallax

The effect and removal of parallax been discussed before. By now the operator should be familiar with its behavior and how to remove it. Even though its affect is random, it's an instrumental error which can be adjusted.

b. Cross hair design

In early telescope-based surveying instruments, cross hairs consisted of spider web stands attached to a reticule ring. In addition to their delicacy, they offered the surveyor only a single sighting option: a solid line, Figure E-2(a). As instrumentation and optics evolved, cross hairs eventually became etched lines on optically flat glass plates. Etching allows for more creative and effective cross hair designs, Figures E-2(b) and 2(c).

  img502a  

(a)

  img502b  

(b)

  img502c  

(c)

Figure E-2
Cross hair Styles

 

A narrow sight mark, such as a plumb bob line, at a longer distance may appear narrower than the vertical solid hair causing some pointing error - the hair obscures the string. Using a split hair design, Figure E-2(c), allows the operator to see both the sight mark and the hair. It is often easier to center the mark between hairs than try to make it coincide with a single one, Figures E-3(a) and (b).

  img503a  

(a)

  img503b  

(b)

Figure E-3
Sighting Plumb Line

 

c. Target width and distance

Although these are separate characteristics they are related because in combination they affect the sight mark's relative size. Figure E-4 shows the same prism pole sighted at two different distances. The closer the pole is, the more difficult to center the cross hair on it.

  img504A  

(a) Distance = x

   img504B  

(b) Distance = 2x

Figure E-4
Pointing Error

 

At shorter distances, a narrower sight mark, such as a plumb line, should be used for more accurate pointing.

How much pointing error could we expect? As an extreme, consider sighting the edge of a target rather than its center, Figure E-5.

 

img505
Figure E-5
Sight Distance and Angular Error

 

Table E-1 shows the error for two different target types at varying distances. The targets are a 0.10 ft diameter prism pole and a 0.03 ft diameter pencil. 

Table E-1
  Prism pole Pencil
  dia = 0.10 ft dia = 0.03 ft
Dist (ft) Accy: 1 in Angle, a Accy: 1 in Angle, a
100 2,000 0°01''43" 6,670 0°00'31"
200 4,000 0°00'52" 13,300 0°00'15"
300 6,000 0°00'34" 20,000 0°00'10"
500 10,000 0°00'21" 33,300 0°00'06"
1000 20,000 0°00'10" 66,700 0°00'03"

 

The accuracy is the distance to the target divided by half the target diameter:  

img506       Eqn (E-1)

 

The angle, a, is computed from:  

img507       Eqn (E-2)

 

At shorter distances, the error could be quite substantial if the target edge was sighted instead of its center. At those short distances, it wouldn't be very likely that the edge would be sighted but centering the cross hair on a larger target does become less accurate.

The beginning surveyor will notice that angle repetition is harder with larger D/R angle spreads in situations when either or both of the sights are short.

d. Minimizing pointing error

Pointing error is a random error so we can't expect to eliminate it entirely, but it can be minimized with careful target selection and use.

To minimize sighting error, Figure E-6:

* At shorter distances, "finer" targets should be used.

* When using a rigid target that is in contact with the ground mark, such as a prism/range pole or pencil, sight as low on the target as possible.

* When using a plumb bob, sight higher up on the line nearer the support. This is where the line swings the least giving the most repeatable pointing.

* For a tribrach mounted target, sight directly at the target.

 

img509   img510    img512  img511
Figure E-6
Proper Sighting

 

What about using the prism glass center where the lines of the individual prisms intersect, Figure E-7? That makes for a nice distinct target, doesn't it?

img515a
Figure E-7
Sighting Prism Glass

 

The vertical line passes through the prism lines' intersection (yellow) and the top mount stud (which coincides with the prism pole center).

If the prism is rotated horizontally, the situation in Figure E-8 is created.

img516a
Figure E-8
Rotated Prism Horizontal Offset

 

Note how the lines' intersection is offset horizontally. Sighting the intersection introduces a systematic error. The top mount stud is still directly above the ground point so it, or a short barber pole attached to it, should be sighted instead.