Spiegel Relaskop
Forest Measurement and Modelling.

The Spiegel Relaskop, also known as a Relaskop, is a sophisticated instrument that can be used to measure stand basal area and tree height and diameter at any point up a tree bole. In conjunction with other equipment, the Relaskop can be used in the estimation of distance (range) to an object and the number of trees / ha.

The Relaskop has a peep-hole at the rear and a clear window at the front. Three additional windows in the lower half of the instrument allow light to enter and illuminate the scale. A brake button, bottom half at the front of the instrument, allows a weighted wheel within the Relaskop to rotate. When looking through the peephole, a circular field of view is seen. The scales are seen in the bottom half of this field of view and scale readings are taken where the scale touches the line halfway up the field of view.

Height The standard metric Relaskop has three scales for measuring (vertical) height. The appropriate scale will depend on the horizontal distance from the tree.
  • left-most scale - 20 m from the tree.
  • middle-left - 25 m from the tree.
  • middle-right - 30 m from the tree.

If you depress the brake button and look straight up or down, the appropriate distance values can be seen alongside their scales.

Select a point that is 10 to 60 m (horizontal) from the tree of interest. The base and tip (or any other points of interest) must be clearly visible from the selected point. If the tree is leaning, the point where you observe the tree should be at 90 degrees to the plane of the lean. If the lean is severe (i.e. more than 10 degrees from vertical), the point directly beneath the tip of the tree should be located (e.g. using a pumb-bob) and the horizontal distance taken from this point. The actual distance chosen is related to an initial estimate of the tree height:
  • Trees less than 12 m height: Set out 10 m and use the 20 m scale, but divide final estimates by 2.
  • Trees 12 - 18 m: Set out 15 m and use the 30 m scale, but divide final estimates by 2.
  • Trees 18 - 23 m: Set out 20 m and read directly from 20 m scale.
  • Trees 23 - 28 m: Set out 25 m and read directly from 25 m scale.
  • Trees 28 - 35 m: Set out 30 m and read directly from 30 m scale.
  • Trees 35 - 45 m: Set out 40 m and use the 20 m scale, but multiply final estimates by 2.
  • Trees 45 - 55 m: Set out 50 m and use the 25 m scale, but multiply final estimates by 2.
  • Trees greater than 55 m: Set out 60 m and use the 30 m scale, but multiply final estimates by 2.

Once the observation point is found and the appropriate scale selected, sight through the peephole to the base of the tree. Tap the brake button several times until the scale settles then read the height directly from the appropriate scale. If you are looking down towards the base of the tree, this reading is the vertical height that the base of the tree is beneath your eye. Sight to the top of the tree (or other point) and again tap the brake button until the scale settles. The scale is a direct reading of the height above your eye to this new point. Add the two heights together if the base of the tree was below your eye to determine total (vertical) height. If the base of the tree was initially above your eye (i.e. the base if above you on sloping ground) subtract the initial height from the upper height to determine (vertical) height.

Height is determined (and recorded) to the nearest quarter metre (0, 1/4, 1/2, 3/4 m) for trees less than 20 m, or to the nearest half metre (0, 1/2 m) for trees greater than 20 m.

Bole diameter The band labelled with "1" and the four narrow (or quarter) bands along side are used to estimate diameter.

To determine the bole diameter for a known height on the tree:
  1. Depress the brake button and move back until the tree bole appears to cover all of band 1 and the 4 quarter bands, i.e. the left side of the tree is aligned with the left of band 1 and the right side of the tree is aligned with the right side of the right most quarter band.
  2. Measure the horizontal distance (D in m) to the tree (directly beneath the point of interest).
  3. Calculate the bole diameter (d in cm) as:
    d = 4 * D
  4. This method provides a maximum precision for determining diameter with the Relaskop. With experience, a reading within 2.5% of the true diameter is possible (i.e. plus or minus 1 cm for a 40 cm dob).

To measure both height and diameter at one or more points up the stem:
  1. Measure out a horizontal distance (D in m) appropriate for the height of the tree.
  2. Sight to the base of the tree and the point of interest and determine height using the appropriate scales and calculations.
  3. With the brake button depressed, align the right side of the tree with the right side of band 1 and ensure that the left side of the tree falls within the quarter bands. If the left side of the tree goes beyond the quarter bands, you will need to move further away from the tree - you will need to be 5 m away for every 20 cm of diameter. If the left side does not make it to the quarter bands, i.e. it falls within band 1, align the right side of the tree with the left side of band 1.
  4. Estimate the number of quarter bands that are covered by the tree bole (between 0 and 4). Experienced operators can read down to fifths of a quarter band:
    • 1/5 just into the quarter band
    • 2/5 almost half a quarter band
    • 3/5 at least half a quarter band
    • 4/5 almost the whole quarter band
  5. Calculate diameter (d in cm) as:
    d = 2 * D * (b + (q/4))
    where b equals 1 if band 1 is covered and 0 otherwise,
    q denotes the number of quarter bands (read down to one fifth of a quarter band).
  6. The example in the above figure covers band 1, three quarter bands, and one fifth of another quarter band. If the tree is 20 m away, then
    d = 2 * 20 * (1 + (3.2/4))
    d = 2 * 20 * 1.8
    d = 72 cm
  7. The precision (p in %) of this estimate depends on the distance from the tree (D in m) and the estimated diameter (d in cm) :
    p = 10 * D/d
  8. The example above has a precision of:
    p = 10 * 20 / 72
    p = 2.8%
    Thus we would expect the diameter to lie between 72 cm +/- 2 cm.

Note that the above approaches only measure diameter along one axis of the bole. If the bole is elliptical, this measurement will over- or under-estimate the average diameter. The diameter measurement could be repeated at 90 degrees, but this is rarely carried out in practice.

Stand basal area The Relaskop can generate nine basal area factors (BAFs) using bands 1, 2 and combinations of the quarter bands:
Bands BAF (Calculation)
1 quarter 0.0625 (1/16)
2 quarters 0.25 (1/4)
3 quarters 0.5625 (9/16)
Band 1 1.0(1/1)
Band 1 + 1 quarter 1.5625 (25/16)
Band 1 + 2 quarters 2.25(36/16)
Band 1 + 3 quarters 3.0625 (49/16)
Band 1 + 4 quarters
Also called Band 4
Band 2 2.0
Choose the appropriate BAF and combination of bands. Then, standing over the sample point, hold the brake button down and make a sweep of 360 degrees while comparing the tree diameters at breast height with the selected bands. Count the number of trees whose diameter at breast height appears greater (wider) than the selected bands - IN trees. Ensure trees are not hidden behind closer trees by stepping to one side and checking before returning to the sample point. Where trees appear to be the same width as the selected Relaskop bands, or it is not obvious that the tree diameter is larger, measure the distance to the tree and that tree dbh and refer to the borderline calculations. Once the sweep has been completed, multiply the count of IN trees by the appropriate BAF to get stand basal area (m^2/ha).

[relaskop.htm] Revision: 6/1999