Distance Corrections

1
Distance Corrections

• Chapter 4

2
Introduction

• Types of Corrections
• Incorrect tape Length or Standardization error
• Temperature variations
• Slope
• Sag
• Incorrect tension

3
Incorrect tape length or Standardization error

• Standardization of equipment is a major concern.
  Standardization is the comparison of the
  equipment ex a tape, an electronic distance
  measuring instrument, a theodolite, etc against
  a standard
• In other words, has the equipment been damaged or
  shaken out of adjustment, have repairs or weather
  changes affected it, and so on!!!!
• If so, adjustments need to be made in order to
  compensate for the resulting errors

4
Set a reference

• It is wise to check the equipment periodically
  against a standard
• Ex some surveying offices used to keep one
  standardized tape (an Invar type) that was used
  only for checking the lengths of their other
  tapes

5
For extremely precise work

• Tapes can be mailed to the National Institute of
  Standards and Technology in Gaithersburg,
  Maryland. For a rather large fee, they will
  determine the length of a tape for specific
  tension and support conditions
• A certificate is issued for each tape, giving its
  length to the nearest 0.001 ft at 68F (20C) for
  two conditions
• with the tape supported for its full length and
  subjected to a 12-lb pull
• with the tape supported at its ends only and
  subjected to a 20-lb pull

6
Example 4.1
7
Example 4.2
8
Temperature Variations

• Changes in tape lengths caused by temperature
  variations can be significant even for ordinary
  surveys
• A temperature change of approximately 15F will
  cause a change in length of approximately 0.01 ft
  in a 100-ft tape

9
Temperature Variations

• Example
• If a tape is used at 20F to lay off a distance
  of 1 mile and if the distance is checked the
  following summer with the same tape when the
  temperature is 100F (no temperature correction
  being made), there will be a difference in length
  of 2.75 ft caused by the temperature variation

10
Temperature Variations

• The correction of a tape for temperature changes
  can be expressed with the formula
• Ct 0.0000065(T - Ts)(L)
• In this expression Ct is the change in length of
  the tape due to temperature change, T is the
  estimated temperature of the tape at the time of
  measurement, Ts is the standardized temperature,
  and L is the tape length in feet

11
Relations Celsius / Fahrenheit

• 0C (5/9) (0F 32)
• 0F (9/5) (0C) 32
• IF SI units are being used
• The corrections of the length of a tape is
• Ct 0.000 011 6 (T - Ts) (L)

12
Slope Corrections
13
Slope Corrections

• A tape of length s is stretched along a slope and
  it is desired to determine the horizontal
  distance h that has been measured
• It is easy for tapemen to apply an approximate
  correction formula for most slopes
• The the Pythagorean theorem, is satisfactory for
  most measurements, but for slopes of greater than
  approximately 10 to 15 an exact trigonometric
  expression should be used
• When a 100-ft slope distance is measured, the use
  of this approximate expression will cause an
  error of 0.0013 ft for a 10 slope and a
  0.0064-ft error for a 15 slope

14
Slope Corrections

• Example
• If Slope is greater than 15 , then H s cos A
• H horizontal distance, s is slope distance
  measured, A is grade

15
Sag and Tension Corrections

• Correction in feet for Sag

16
Sag and Tension Corrections

• Correction in feet for Tension