UKTC Archive

RE: t/R 0.3 = 30 or 70% Hollowing

Subject: RE: t/R 0.3 = 30 or 70% Hollowing
From: Philip van Wassenaer
Date: Mar 01 2021 20:14:05
And it was also soundly refuted in other articles...

Thanks for sharing this and emphasizing these points. The t/r may work for 
the conifer forests that the data came from but not for all open trees by a 
long shot. And if you look into it carefully, if you have the whole graph of 
the whole dataset you will see that it falls apart with bigger trees, just 
the ones it has been used so many times to fell...

It's actually frightening how many in the global arb community probably still 
doggedly hold on to that handy, simple little equation...

Regrettably...

Philip van Wassenaer, B.SC., MFC
Urban Forest Innovations Inc.
1331 Northaven Drive
Mississauga ON L5G 4E8
Tel:  (905) 274-1022
Cell: (647) 221-3046
Fax: (905) 274-2170


www.urbanforestinnovations.com

-----Original Message-----
From: uktc-request@xxxxxx.tree-care.info <uktc-request@xxxxxx.tree-care.info> 
On Behalf Of Jim Quaife
Sent: March 1, 2021 12:09 PM
To: UK Tree Care <uktc@xxxxxx.tree-care.info>
Subject: RE: t/R 0.3 = 30 or 70% Hollowing

Added to which Claus admitted that his graph with the 30% line was "adapted" 
to make the point Jim

-----Original Message-----
From: uktc-request@xxxxxx.tree-care.info 
[mailto:uktc-request@xxxxxx.tree-care.info] On Behalf Of David Evans
Sent: 01 March 2021 16:45
To: UK Tree Care
Subject: t/R 0.3 = 30 or 70% Hollowing

It's neither.

 

I recently shared this post on social media and thought it might be of 
interest to some of you.  The size of the files for the 'Why t/R Ratios 
Aren't Very Helpful' pdf and Paul Muir's Cross Sectional Area v Section 
Modulus graph are too large to share on the UKTC.

 

...

Recently, I caught a podcast where a tree was declared 'safe' if it's less 
than 30% hollow. I think they meant 70% hollow. Either way, this isn't right 
for several reasons.

I've posted about this before, but as long as this kind of mistake is being 
broadcast I think it's worth repeating so the message gradually gets home. 

 

The heart of the confusion is the t/R = 0.3 fallacy. t/R = 0.3 is when a 
residual wall thickness (t) is 30% of the stem radius (R). It's often cited 
as a failure threshold. It's not. The 'Why t/R Ratios Aren't Helpful' pdf 
explains why in detail and can be downloaded from VALID's website here.

 

https://valid.tiny.us/v65mz84a

In short, one reason is because of a geometric property called section 
modulus. Wind load and material properties remaining equal,  if you double 
the diameter you increase the load bearing capacity of a tree by 8 times.

To add to the confusion, t/R 0.3 is often referred to as 70% hollow. In fact, 
a 0.3 t/R ratio is only 50% hollow.  70% is the radius, which is one 
dimension. t/R 0.3 is the area, which is two dimensions.

 

This graph from Paul Muir shows the relationship of central hollowing on:

 

A = Cross Sectional Area

Z = Section Modulus

 

t/R = 0.3

A = 49% loss of cross sectional area

Z = 24% reduction in load bearing capacity

 

To make matters worse. A tree with a t/R ratio of 0.3 can have a very high 
likelihood of failure, or it can have a very low likelihood of failure.

 

If all that wasn't enough, it's seldom that where decay is of concern we're 
dealing with a cross sectional area of a tree that's a circle.

 

Cheers

 

Acer Ventura




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The UK Tree Care mailing list
To unsubscribe send mailto:uktc-unsubscribe@xxxxxx.tree-care.info

The UKTC forum is supported by Bosky Trees arboricultural consultancy and
Stockholm Tree Pits
https://www.stockholmtreepits.co.uk