Note centroids are here https://en.wikipedia.org/wiki/List_of_centroids in equation 12 > 13 then devide the 1 by the distance to centroid, 13>14 half the value
The splitting tests are used within breeding programs --ref-- in order to gain a quantitative measure of how much the stem would deform during green sawing. The primary objective of this paper is to present a method (and results from) for estimating how reliable splitting test measurements are when predicting this trait. A cut directly through the pith is a procedure which while not a typicly used cutting staratgy for eucalypt timber production, alows for the largest manifetation of movment during cutting. Having knowledge of how much trust to place in splitting test measurements of individuals is important for tree breeders when they are deciding on selection weights for various traits. 174 samples were measured using the orifonal -ref-- spiltting test, the rapid splitting test --ref-- and a newly proposed test, the "quartering test" and the results from each compared, and used to estimate the reliability of the testing procedure when considered at an abatory angle. 

Method

Samples: The trees used in this study were thinnings of five year old Eucalytus argophloia grown on a moderately steep east facing slope with a rainfall of approximately 700mm per year in Marlborough New Zealand. The 176 samples from 115 individual trees were labelled and cut when they provided at least 400mm of suitably straight stem with an estimated under bark diameter of grater than 20mm. Under bark diameters ranged from 21mm to 73mm with a mean of xxx. The samples were cut from the stems using a chainsaw and were packed into air tight containers with excess water and transported to a cool store where they were stored at 5C until processing, which took place over four weeks, there where no signs (visual or statistical) of sample quality degradation.
Testing procedures: Samples were removed individually from their containers and their to get a unique sample ID recorded. Bark was removed using knives to hand peel the samples, with care taken not to damage the underlying wood. The longest sufficiently straight section of sample which could be obtained from the big end was marked (and the length from the big end recorded), with a maximum length being 50mm short of the small end. The diameter of the big end was recorded as was the small end diameter at the marked point.
Rapid splitting test: The Rapid Splitting test outlined in \cite{Davies_2017} involves splitting with a band saw through the pith from the big end to the marked point. The resulting opening is measured and recorded, from the diameter d, slit length L and opening o, the strain within the sample can be estimated using Equation —. — inc figure—
Splitting Test: The original splitting test, presented by \cite{Chauhan_2010} involves splitting the sample the whole way down the pith (in this case it was achieved by docking the remaining intact end from the above procedure to gain two half rounds), clamping the two halves in the centre and measuring the opening at each end. Here the method is slightly modified due to the (compared to the original paper) low openings to reduce measurement error. In this case, the big end was clamped and the opening was measured at the small end. Note that this is an equivalent geometric measurement and will (theoretically) give the same results. The opening, big end diameter, small end diameter and split length are measured and proceed through Equation — to obtain strain. — inc figure—
Quartered Test: Due to the destructive nature of both splitting test procedures, and inhomogeneity both within and between individuals, repeatability is not directly testable, in the sense; if we cut the sample though the pith at an arbitrary alignment, how close is the result to the (hypothetical) result of a cut through the pith at some other arbitory alignment. In order to test repetability, after the splitting test had been conducted, each of the two halves were halved again (into quarter rounds), and reasembeled with the small end in a self alighning jig set in a vice. Four measurments were taken, providing the spartial relationship between every quarter round. Openings between adjacent quarters were taken to be the average distance between faces. As there are two measurments for each half round test equlivlent, the distances between quarters were averaged. –inc figure–
Under the assumption that the measurement error for each test is equal (testing only the alignment of the splitting tests) a type --- ANOVA can be conducted to estimate the measurement error from the repeated three measurements, equation ----. All three of these tests measure the same strain using slightly different techneques, if there was zero measurment error in the tests there would be no difference between the reported value for each test for each tree. 
ANOVA equation