User:Taxelson/PISY sap wood estimation
In the case when no bark edge is preserved in a trunk, we use to try estimating the number of the missing rings according to what number of sapwood rings are usually found in the actual species and area. If we are dealing with wood from historical construction it may not be a good idea just to compare with sap wood frequencies in resent trees. Before the era of modern forestry, "mature" trees - i.e old trees with an decreased increment growth, often affected by fire, were preferred. Therefore I have done a small study samples from 65 trees used in timber buildings i Dalarna, Sweden with the outermost ring from AD 1236 to AD 1834.[1] The number of sapwood rings varied between 31-116, which is rather disappointing indeed! This is a lot worse than the often used statistics saying between 40-80 sap wood rings.
Looking a bit closer to the distribution by dividing into classes, I found it adequate to take the square root of the number of sap wood rings to make the distribution more symmetrical. Doing so I get the mean of 8.23 and a standard deviation, STD=1.2. Using ±2σ (95% confidence) will than give 34-113 sapwood rings (5.84^2 to 10.62^2) - still a span of 79 years of uncertainty if less than 34 sapwood rings are preserved in the sample!
May there be any measurable aspect of the sample with a strong correlation towards the number of sapwood rings? I did measure the total width of the last 32 heartwood rings (sum of ring width measurements on dry samples) and found a correlation towards the number of sapwood rings corr=-0.52. (using less than 32 rings gives lower correlation - measuring more rings are not tested) So, yes, the total width of the youngest 32 heartwood rings seems useful for estimating the number of sapwood. So next step is plotting the relation between "heart32" and "sap n". Using the diagram function of Calc (Open Office), I found the most linear pattern when using the square root of the number of sapwood rings and natural logarithm (ln) of the "heart32"-measure. The linear regression suggested the function y=11.48-1.7x, and as y=sqrt(sap_n) and x=ln(heart32) we do find the relation between "sap_n" and "heart32" being that the number of expected sapwood rings are (11.48-1.7*ln(heart32) )^2. Using this function (optimized: (11.48-1.15*ln(heart32) )^2) the difference between the expected number of sapwood rings and the real number gives STD=16.48) .
- ↑ The very outermost ring is not present in all samples but possible to estimate accurate in comparison to other logs from the same construction. Only when there are no reasons to suspect any timespan of more than a year between the felling of the timber for a building, it is included.