Articles

Theoretische berekeningen van systematische fouten bij de bepaling van de oppervlakte van het grondvlak

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Abstract

Theoretical  calculation of the systematic errors made during the determination of the  basal area - To prove his point, the author goes out from  the supposition, that the best approximation for the basal area is an  ellipse. Consequently three parameters are set up to reflect various  characteristics of a given area at any moment. The first parameter (V(t)) is  a measure for the form of the basal area at a moment t and is calculated from  the relation between the large (a) and the small (b) axis of the ellipse. The  use of a second parameter was necessary as the biological growth-centre of  the tree (point M in fig. 3) does not coincide in most cases with the  intersection 0 of the axes of symmetry. The distance between both points (M  and 0), represented by symbol x0(t) is used as a measure for the real stem  dish eccentricity. The third parameter is a measure for the size of the basal  area at a moment t and is called the representative radius (r(c; t)). It is  the radius of a circle with the same surface value as the considered ellipse.      Going out from these three parameters, a formula was worked out up to  basically calculate any r(u; t) in function of the direction u or the angle e  between this radius and the maximum radius (par. 3, form. 5) of any given  stem dish. As the value of x0(t) depends on the dimension of r(c; t), the  concept 'relative eccentricity e(t)' is introduced (cfr. Form. 6) and it  becomes thus possible to give the basic formula a definitive form (cfr. form.  7). By means of this basic formula, it is not only possible to calculate the  descriptive radius at a moment t in function of V(t), e(t) and θ, but a lot  of further deductions can also be made. A first possible application consists  in the calculation of the procentual error Er(u; t) on any radius r(u; t) in  function of V, e and their position regarding to the maximum radius (cfr.  par. 4 1, form. 8).    The evolution of this error in function of the mentionned parameters is  given in fig. 4.     In paragraph 42, the procentual error is calculated from each other on  average of 12 radii, measured at a distance of 300 (form. 8).     This is done in function of the relative eccentricity e and the form of the  basal area. The graphic representation of this calculations is given in fig.  5. In fig. 6 the evolution of the relative distribution SRx (t) on the  mentionned average is given. To calculate this distribution form. 10 was  used.     Paragraph 43 proves that the mentioned procentual errors only need to be  duplicated to know the procentual errors on the calculated surfaces of the  basal area.     Finally, the position of the representative radius has been verified in  function of e, and V and his evolution studied by using the formula 13 and  13' (fig. 7).

How to Cite:

Goossens, R., (1967) “Theoretische berekeningen van systematische fouten bij de bepaling van de oppervlakte van het grondvlak”, Silva Gandavensis 5. doi: https://doi.org/10.21825/sg.v5i0.1016