Distance Measurement Errors (Chapter 6)

We have reviewed at vertical distance measurement and identified errors associated with those. Now
we turn to horizontal distance measurement. There are a number of methods to determine horizontal
distance. In our field school we practiced: ii) pacing, ii) taping and iii) eletronic distance
measurement. Beside these we can determine distance using iv) satellite (i.e. GPS) systems, v) air
photos, iv) remote sensing imaging, and vii) triangulation. These will be discussed at greater length
later in the course. Less common and outdated methods of viii) stadia, ix) subtense bar and x) optical
rangefinder will be briefly mentioned here.

Topic
ENGI 3703 Distance Measurement and Instructor: Prof. Ken Snelgrove
Associated Errors
Surveying and Geomatics Lect 6 - Sept 21/07 Slide 1 of 6
Relative Precision and Accuracy Ratio: Before describing these methods we should define a
measure of precision and accuracy that we can use. Recall that accuracy was defined as
relationship between the measured value and the true value. An accuracy ratio is a measure of
difference between the ‘true’ measurement and the actual measurement normalized by the ‘true’
measurement:

true distance - measured distance error

This is often expressed in a form with a numerator of one and a denominator rounded to the nearest
100 units (e.g. 1/1132 = 1/1100). We will also encounter relative precision (section 10.6) later in the
text. Recall that precision was defined as the degree of refinement with which a measurement is
made. Hence the relative precision would refer to a ratio similar to the accuracy ratio but without
specific knowledge that all systematic errors have been removed from the estimate of truth.

Topic
ENGI 3703 Distance Measurement and Instructor: Prof. Ken Snelgrove
Associated Errors
Surveying and Geomatics Lect 6 - Sept 21/07 Slide 2 of 6
Pacing: (Section 6.3) Pacing may seem a crude form of distance measurement. However, it can be
extremely valuable in many instances high accuracy is not required and in the discovery of mistakes
from other methods with high precision. An average pace is somewhat less than 1 m. However,
many surveyors “train” themselves to take giant steps of 1 m in practice. Knowing ones calibrated
pace length is a useful tool for low accuracy measurement. Accuracy ratio 1/50 to 1/100 for
distances greater than 30 m.

Optical Rangefinders: (Section 6.5 and 4.2 ) Just as you adjust focus a 35 mm camera to manually
improve the clarity of a photograph in older cameras, optical rangefinders use the same principle in
determine distance. The operator adjusts the clarity of the image by changing the distance f1
between the lens and image. The focus length f for give lens (i.e. the value of f1 for an infinitely distant
object, f2=
lens is known. Since the system follows the relation:

1 = 1 + 1
f f1 f2

by keeping a precise
measurement of the distance
f1 in our rangefinder we are
able to determine the the
distance f2 to the object once
the image is in clear focus.
Accuracy ratio 1/50 for
f2 f1 distances less than 50 m.

Topic
ENGI 3703 Distance Measurement and Instructor: Prof. Ken Snelgrove
Associated Errors
Surveying and Geomatics Lect 6 - Sept 21/07 Slide 3 of 6
Stadia: (Section 6.6) Also known as
Tacheometry. Can be easily used with
leveling instruments to determine the
distance of foresight and backsight shots.
The optic of the instrument are set such that
the viewing angle between the top and
bottom cross hairs are constant. The
difference between the top and bottom rod
reading when multiplied by a constant
(typically 100) will provide the geometrically
determined distance to the rod. Accuracy
ratio 1/500 for reasonable leveling procedure
distances.

Topic
ENGI 3703 Distance Measurement and Instructor: Prof. Ken Snelgrove
Associated Errors
Surveying and Geomatics Lect 6 - Sept 21/07 Slide 4 of 6
Subtense Bar: (Section 6.7) is a tripod
mounted bar with targets precisely 2.000 m
apart. The bar is set over a point (B), leveled
and turned so that it is precisely
perpendicular to a one-second minimum
reading theodolite set at point A. The
horizontal angle between the subtense bar
targets is measured using the theodolite to
determine the distance to the bar center and
hence the distance AB. Accuracy ratio
1/3000 for distances of 150m or shorter.
While accurate, this method is seldom used
today.

2.000 m Distance AB = cot
A B 2
where: cot() = 1/tan()

Topic
ENGI 3703 Distance Measurement and Instructor: Prof. Ken Snelgrove
Associated Errors
Surveying and Geomatics Lect 6 - Sept 21/07 Slide 5 of 6
Taping Errors: (Section 6.14-6.16) Taping equipment and methods have been covered in
the field school. However, it is useful to consider taping errors since taping is still used in
practice. These consist of:

1) Incorrect Tape Length Correction

These sources of error tend to be systematic and can be eliminated with careful planning
and technique. Accuracy ratio 1/10,000 can be obtained using taping. To obtain these
accuracies we must use “standardized” equipment with published specifications.

Topic
ENGI 3703 Distance Measurement and Instructor: Prof. Ken Snelgrove
Associated Errors
Surveying and Geomatics Lect 6 - Sept 21/07 Slide 6 of 6