Stadia Surveying Techniques

• The document explores methods of distance measurement in surveying.

Pacing

• Pacing involves counting steps or strides to cover a distance.
• A pace is the length of a single step, measured from heel to heel or toe to toe.
• It's valuable in surveying for determining distances by counting steps, if step length is known.
• Pacing is a quick method for cross-checking measurements from other techniques.
• It's useful for estimating distances when high precision isn't needed.
• Accurately pacing requires knowing one's personal stride length, the "pace factor."
• Two methods exist for calibrating pace: calculating average step length and adjusting stride to a set length like 1 meter.

Example Pacing Calculation

• A surveyor paces a 45-m course (AB) on level ground to find their pace factor.
• The number of paces for each trial is recorded.
• Calculations include finding the surveyor's pace factor.
• An example situation shows how calculating the length of an unknown distance (CD) using pacing.
• Example: 771, 770, 768, 770, 772, and 769 paces are taken.
• Relative precision of measurements are determined, where relevant.
• Example: Assuming the taped length of line CD is 667.0 m.

Odometers and Measuring Wheels

• Distances can be roughly measured by rolling a wheel along a line and counting revolutions.
• An odometer attaches to a wheel and counts revolutions, then converts this to distance using the wheel's circumference.
• Odometers are useful for preliminary surveys when pacing takes too long.
• They're also used for initial route-location surveys and quick checks.
• A measuring wheel is a similar device, where a wheel is mounted on a rod and pushed by a user.
• Measuring wheels are frequently used for curved lines.
• Some odometers can attach to vehicles and operate at speeds of several miles per hour.

Tachymetry

• Tachymetry or tacheometry means "swift measurements," from Greek words takus (swift) and metron (measurement).
• It includes measurements with subtense bars or by stadia.
• Extremely fast electronic distance-measuring devices aren't typically listed in this category.

Subtense Bar (Obsolete)

• Seldom used now, this method was occasionally used for rural property surveys using a subtense bar.
• The subtense bar is now replaced by electronic distance-measuring devices.
• In Europe, the method involved a 2 m horizontal bar with sighting marks, mounted on a tripod.
• The tripod was centered and leveled over one end of the line and oriented perpendicular to the line.
• A theodolite at the other end of the line sighted the subtense bar using theodolite.
• The theodolite aligns the bar perpendicularly by observing the sighting mark and measuring the angle subtended by the marks.
• Distance (D) from the theodolite to the subtense bar is computed using an equation to derive the measurements from the angle.

Stadia

• Developed by James Watt in 1771, the stadia method is more common than the subtense bar in the US.
• The word "stadia" comes from the Greek word "stadium", a foot race track.
• Many transits, theodolites, and leveling telescopes have three horizontal cross hairs.
• The top/bottom hairs are called stadia hairs.
• The surveyor reads where the stadia hairs intersect a scaled rod.
• The rod intercept is the difference between the two readings.
• Stadia measurement uses a telescope with stadia hairs and a graduated stadia rod.
• Stadia hairs are equally spaced relative to the horizontal cross hair.
• Hair spacing is designed so that at 100 meters, the intercept on a vertical rod is about 1 meter.

Stadia (continued)

• The stadia principle can estimate heights of objects.
• Hold a ruler upright at arm's length, align its top with the top of the object, and move a thumb to coincide with the base.
• Pacing determines the distance to the object's base.
• Stadia measurement involves observing the locations of stadia hairs on a rod held vertically.
• The distance from the telescope to the rod is found using proportional relationships in similar triangles, using D = Ks + C.
• C is the stadia constant, i.e. the distance from the instrument center to the principal focus.
• C iis usually equal to zero for internal focusing telescopes.
• K is the stadia interval factor of the instrument.

Stadia - Example Calculation

• Example Problem 1: A stadia rod at point B is sighted from point A.
• The upper and lower hair readings (1.300 m and 0.900 m) and stadia interval factor (K = 100) are given.
• Given: instrument constant (C = 0), the length of line AB is calculated.
• Example Problem 2: Stadia rod held, using instrument set up.
• Upper and lower hair readings are given, as is the stadia interval factor (K), and instrument constant (C).

Taping or Chaining

• Surveyors used ropes, lines, or cords treated with wax and calibrated in ancient units for centuries.
• These are obsolete, although calibrated wires may be used.
• Until recently, the 100-ft steel ribbon tape was the common measuring device.
• "Chaining" is a carryover term from when Gunter's chain was introduced.
• Edmund Gunter invented the surveyor's chain in the 17th century.
• His chain came in 33 ft, 66 ft, and 100 ft lengths in 17th century, and 66-ft was the most common

Summary of Distance Measuring Methods

• Table 3-1 summarizes various distance measuring methods.
• The table also shows precision levels, and appropriate use cases per method.

Measuring Tape - Materials

• Measuring tapes vary in length, material, and weight.
• They are graduated with etched, stamped, or printed marks.
• Steel tapes were recently used when high precision was required.
• Electronic distance measurement is replacing this now due to improvements in the former's accuracy and convenience.
• Steel tapes are still OK for short distances of just a few hundreds of feet or less.
• Lightweight steel tapes with nylon coating are most common.
• Nylon coated tapes MUST be kept straight to avoid weak spots during tightening.
• Wet tapes should be wiped dry dry AND with an oily cloth.
• Heavy steel tapes maintain length when continuously supported to a tension (10-12 lbs) and temperature (68F).

Measuring Tape - Fiberglass and Accessories

• Fiberglass tapes use thousands of glass fibers coated with polyvinyl chloride.
• These are less expensive, more durable, and found in common lengths like 50-ft and 100-ft.
• Strong and flexible fiberglass tapes resist length changes due to temperature and moisture.
• These are safe near electrical equipment.
• When tension forces of 5 lbs or less are applied, tension corrections are likely not needed.
• But, they may be needed for values greater than 5 lbs.
• Accessories include Flags or lining rods, used as signals/markers.
• Flags are circular, hexagonal, or octagonal, with one end pointed.
• Taping pins are used for marking tape ends or intermediate points when taping.
• Taping pins are painted for visibility, carried on a wire loop.
• Plumb bobs were formerly made of brass to avoid compass interference.
• They weigh 6-18 oz with replaceable points and a string attachment.

Accessories

• The following lists different accessories used in taping work.
• Hand levels help surveyors hold tapes horizontally for accurate measurements.
• Hand levels may roughly determine elevation via a metal sighting tube and bubble.
• Spring balances measure tape stretch from tightening.
• Increase in length determined with a formula.
• For average, the tension applied can be sufficiently estimated.
• Very precise requires a spring balance or tension handle.
• Clamping handles used with leather thongs or spring balances for tensioning tapes.
• Specialized clamps with scissors-type grips are available for partial lengths.

Taping Over Ground

• Steel tapes should be supported along their full length on level ground or pavement.
• This is often impossible.
• On smooth ground with little underbrush, the tape can rest on the ground.
• A taping party has a head tapeman and a rear tapeman.
• The head tapeman leaves a taping pin with the rear tapeman to count the number of tape lengths.
• The head tapeman walks toward the end of the line with the zero end of the tape.
• When the head tapeman reaches the end of the tape length, the rear tapeman stops him.
• The rear tapeman holds the tape at the starting point and aligns the head tapeman using a range pole as a guide.
• It is necessary to ensure that the tape is tight.
• Can be achieved by wrapping a leather tong at the end or using a clamp.
• The head tapeman sticks the taping pin in the ground and right angles to align the tape.

Taping Over Ground on Level Ground.

• After rear tapeman aligns and has the 50-m mark, then they call "all right."
• The tapeman can scratch, a taping pin, a lumber crayon, or keel on pavement to mark points.

Taping Along Sloping Ground

• Three methods are available for when there are sloping grounds
  • The tape is held horizontally with plumb bobs.
  • The slope is held along the tape measure, then a correction is implemented to account for horizontal differences.
  • The sloping distance is taped, a vertical angle is measured for the slopes, which is later computed. referred to as dynamic taping.

Taping Over Level Ground

• When taping downhill, the rear tapeman should connect the zero end on the ground and the front uses a plumb bob.
• When taping uphill, the rear connects with the plumb bob, whilst the front keeps the end on the ground.
• Taping downhill is easier as you can hold the end of the tape on the ground.
• If the ground is uneven, both tapemen require plumb bobs with the tape high.
• Hand levels can also be used.
• You can determine elevations to adjust heights by using other surveyors body as reference.

Taping Over Level Ground

• Breaking tape or breaking chain refers to the process of measuring in sections.
• Counting the number of ft taped is represented in the rear tapeman pin collection.
• These measurements will tell how good the slope errors are.