Risk Assessment Math; what is the t/ Ratio?

t = 12”R Dia. 24”

t = 3.6”

The diagram above represents a 24” (inside the bark diameter), of a stem or branch, with roughly, a center column of decayed wood, (the diagonal lines). The t (above) is the outside shell of sound non-decayed wood. The diagram indicates that the internal wood decay has consumed roughly 2/3 of the -section.

The t/R ratio is simply the ratio of the sound wood shell thickness (t), without the bark, to the radius of the cross section (R). The above example has a t/R ratio of 30%, or .30 or roughly 1/3 of the radius is sound! Guidelines for evaluating trees for decay! The first published guidelines showed up in the early 1990’. Mattheck, 1994, “The Body Language of Trees; A handbook of Failure Analysis”. Editor’s note; it was really much before this work, federal workers in western states and the even late great MN DNR forest health unit of the 1980’s; “How to Detect Assess and Correct Hazard Trees Recreational Areas”.

Claus Mattheck proposed a .30 to .35 t/R ratio threshold of high risk of stem failure from a central column of decay for full crown trees. He noted that failures begin to accelerate in surveys, as the ratio begins to fall under .25 t/R. This became generally interpreted as a .30 t/R ratio or a 30% Remaining Wall!

In 1999, Fraedrich and Smiley published “Guidelines for Qualifying and Evaluating Wood Decay in Stems and Branches”. They proposed using diameter as an easier way to work with the math. They proposed using 15% or .15 of diameter as a threshold of high risk, for full crown trees. About this math; what you need to know is that as you see above they are both the same! A 30% t/R ratio is equivalent to 15% of diameter! A 15% of diameter is equivalent to a 30% t/R ratio!

Fair warning to you; I think and present in % remaining walls using t/R ratios. Many of my examples I use will be presented in t/R ratios. I will qualify as to % diameter is most all of the examples; however, you will learn a lot more if you are familiar with this easy math.

Diameter / Radius, below .15 (Diameter) shell wall .30 (Radius) shell wall 30”/ 15” 4.5” 4.5” 24”/ 12” 3.6” 3.6” 18”/ 9” 2.7” 2.7”

If I show an example with a 20% t/R ratio there is only a 10% of diameter wall! Standing trees with 20% t/R ratios or 10% of diameter walls can be critical risk of failure in some cases while is other cases they be "relatively safe”! Why is this?

If I show an example with a 10% t/r ratio there is only a 5% of diameter wall! Why is this tree still standing? There are few mature, full crown exposed trees standing with less than say, 7-8% t/R ratios, but there are some. Why?

In 2001, I published the “Evaluating Tree Defects” field guide. It proposed a guideline of using or looking for 1” of sound wood for each 6” of stem or branch diameter. The math is based on a 32% t/R ratio or 16% diameter. It remains an easy way for Arborists estimate quickly the amount of sound wood they would like to find based on measured diameters. Many, many additional publications would follow.

Most recently in 2013 the ISA published the “Tree Risk Assessment Manual” for TRAQ training and qualification. Cited; Dunster, Julian A., . Thomas Smiley, Nelda Matheny, and Sharon Lilly. 2013. Tree Risk Assessment Manual. Champaign, Illinois: International Society of Arboriculture. Under branch and stem decay they recognize these existing formulas and guidelines and why they cannot be used in all cases. “The most common threshold allows for the loss of 2/3 of the diameter of the stem, in the center of a round stem! That is; if the remaining sound wood thickness surrounding an internal cavity is more than 1/6 of the trunk diameter (1/3 of the radius) then the tree is considered not likely to fail under normal weather conditions”. You must learn how to use the risk rating matrix form the new ISA BMP.

While it is now well recognized that these general guidelines do have a place in evaluating the risk of stem or branch failure, relative to decay, they are limited. The guidelines lose relevance for mature trees with large diameter stems. This is all about increases in bearing capacity relative to increasing cross-section, attributes of wind loading, location of the decay, and to some extent material strength. The new ISA BMP and the above new ISA risk assessment manual provide a systematic and structured approach to assessing tree risk. Please note! This is the new “Standard of Care”. Arborists practicing tree risk assessment can be held accountable to the current standard of care. Ed Hayes, Hayes Tree, LLC, Rochester, MN, December 2013.