Forest Mensuration. Brack and Wood

Comparison instruments

• Calipers (point of measurement must be accessible)
• Diameter or girth tape (point of measurement must be accessible)
• Wheeler penta-prism (optical measurement instrument)
• Spiegel Relaskop (optical measurement instrument)
• Telerelaskop (similar to the Spiegel Relaskop but with 8 times viewfinder magnification).

Comparisons

Object or tree-based errors

1. If the tree has a circular cross-section, then there is no error with either approach.
2. For a non-circular cross-section, the girth tape overestimates sectional area (for a given perimeter, a circle has the greatest area). Normally, this bias is small.
3. One measurement of diameter may give errors (large or small, positive or negative), for a non-circular cross-section. The size and magnitude of this error depends on where arms of the caliper are placed or which axis is sampled.
4. For an elliptical cross-section, caliper instruments give a better estimate of sectional area (g) than girth tape if the major and minor (i.e. longest and shortest) axes are measured and area is determined by calculating:
   g = PI x A x B / 4
   where A and B denote the length of the major and minor axes and PI is about 3.14159.
   The estimate is only slightly better than that achieved by using a tape, and then, only if the diameters are the true major and minor axes. If they are not, the error may be larger, and positive or negative.
   • In practice, several procedures are available when using calipers, depending on the outline of the cross-section:
     • maximum and minimum diameters, or
     • maximum diameter and that at right angles to it
     • any two diameters at right angles. This is the most common procedure unless precision and bias is particularly important and the trees are markedly eliptical.
   • Mostly the diameter recorded is accepted as being equal to the arithmetic average, i.e. (A + B)/2.
   • If a section is close to elliptical, the true diameter is given by the geometric mean:
     Geometric mean = SQRT (A x B)

Measuring diameter at accessible locations

• Precision: The girth tape is more precise than the calipers. Reading the PI scale on a girth tape allows a much finer resolution of measurement.
• Bias: Apart from the object errors described above, well maintained tapes and calipers are unbiased per se. However, cloth and fibreglass tapes can stretch and the sliding arm of a caliper can be damaged and not perpendicular to the scale when read. These problems will introduce a bias.
• Ease of correct use:
  • Need to maintain correct pressure (caliper) and tension (tape) at the moment of measurement. With experience this skill is easily acquired.
  • Need to ensure the correct location of the point of measurement, i.e. placing the instrument at right angles to the stem axis. Incorrect placement introduces an error that is proportional to the angle of displacement (Q) and is always positive:
    Caliper: Measures diameter x Sec (Q)
    This error may occur when measuring each axis.
    Tape: Measures perimeter of an ellipse with major axis (diameter x sec (Q)) and minor axis diameter, i.e. in effect the error occurs on one axis only.
• Practicability: The girth tape is small and light. Calipers are heavier, more cumbersome and can be fatiguing if used for long periods.
• Use on standing trees: Tape and calipers are both easy to use on standing trees. However it is difficult to climb while holding calipers, so they are less useful on locations that are only accessible with ladders or climbing techniques. One measurement by tape is faster than two by caliper (two are essential with the caliper if error in measurement is to be minimised with trees of non-circular shape).
• Use on felled tree: Caliper is easier than tape, especially if only one measurement is needed (i.e. not maximum and minour axes). A single measurement may be acceptable when compiling a frequency table based on diameter or estimating the total cross sectional area of a large number of trees/logs but it is not recommended for individual trees/logs.
• Price: Tape is much cheaper than calipers.
• Custom and history: The choice between tape or caliper may be based on customs more than anything else. For example, reasons that tapes are the most commonly used instrument in Australia include:
  • Inheritance of Hoppus system which was based on girth measurement. The Hoppus system became obsolete in Australia anout 40 years ago.
  • Early interest in large native trees - too large for calipers so had to use tapes.