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. Samples were labelled and cut when they provided at least 400mm of suitably straight
stem with an estimated under bark diameter of grater than 20mm. Average
under bark diameters ranged from 21mm to 73mm. The position in the tree
where the sample was taken was recorded as either; below 1m, between 1
and 2m or above 2m, when samples were taken from multiple leaders the
leader was recorded. 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, their block, plot, vertical position and leader were
recorded. Bark thickness was recorded and the bark removed using knives
to hand peel the samples, with care taken not to damage the underlying
wood. The number of branches was recorded in three categories; low (less
than 5 branches on the sample), medium (between 5 and 10) and high (more
than 10) as were the size of the average branch on the stem; small
(less then 5mm in diameter), medium (between 5 and 10mm) and large
(grater than 10mm). 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 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 splittin test had
been conducted, each of the two halves were halved again (into quarter
rounds), and reasembeled with the big end in a self alighning jig set in
a vice. Six 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–
Analysis Method
Finite element modeling.
If we take all of the cuddons data and create a longitudinal strian distrbution and load 'a lot' of trees with it and look at the outcome we should get the hypothetical distrobution of strain results if the inter and intra tree distrobutions are the same - ie differences we see in the test are just factors of how the stem was cut on average
if we assume the internal stem varation is the same for each individual, just with different means we can aproximate a standard distrobution for each sample which the growth strain is randomly distributed in the stem from (this is esentually what we calculate as rotational error using sd(Et_RSQS2) - sd(df$RSQS1diff) with our measurement error being sd(df$RSQS1diff) we can then model each individual sample using the mean of all of the tests and the standard devation from the rotational error, and we should see how much the sample really vearies (without measurment error) depending on where we cut.
Then to show the model works, run it where
1: the solutions are then subjected to some random noise, ie once the finishing strain is calulated, add some noise to it form sd(df$RSQS1diff) measurment error this should reproduce our origonal population
2: the initial distrobution of stress within the sample includes measurment error - this should show higher strains than the origonal population and more verability -- i think--
simulate means sampled from popualtion, internal stresses are sampled from population sd. as there is no measurment error in the simulation, the rotational difference is the only source of potentual error. The simulated population should be very similar in mean distrobution as the original. the distobution which describes the differences between centre and rot 90 should be the same as the rotational error calc form the exp data
SO, mean distrobution from the population should be complete assumeing measurment error is uniform, ie the over estimates should cansel the under estimits by the law of large numbers. But in the exp data the difference between cc and rot90 will be from the measurment error (although the global mean distobution is reliable each indiviudal one has an error asocated with it) AND from the rotational error. The simulation being perfect at measurment should have only the rotational error. ie when I calculate distrobution of diff(centre, rot90) the mean should be zero and the sd should be equle to teh experimentally derived one.