Formula to compensate TPZ

[Glennak]

Sorry having trouble loading formula maybe I will try attaching a word doc. Hope that worked.
Hope this is usefull to someone even better if someone can give a more accurate formula. Builders seem to want to give trees the absolute minium area to grow in.

 

[pdqdl]

Quite frankly, the text with the document does not clearly explain what you are trying to measure. We can guess from the drawings, but you really need to explain it like it was a word problem in high school.

Formulas are nice, but they do not tell you what the problem is. Spell it out for us, please.

 

[Glennak]

Well the new Australian Standard says that the Tree Protection Zone is calculated by multipying the DBH by 12 the same as many USA ones that say 1' radius for every 1" in DBH. Less than Coder who says in a round about way DBH x 15.
The Aus Standard says that if this TPZ is cut into by a trench or what ever it is not allowed to take out more than 10% of the TPZ ( Thus the formula to calculate the area taken out by a straight line.) this area removed must be compensated for by adding to the TPZ in other directions. The second formula is to calculate a new TPZ radius for the remaining semicircle. My formula is slightly incorrect that's why I was asking for a better one but it is well within the accuracy of measuring DBH.
Basically the concept is simple but the maths isn't.

 

[treeseer]

Thanks for clarifying what is clearly an extremely restrictive standard. We allow much more rootzone lost, without losing trees.

Attached is one graphic we use.

 

[Boa07]

Thanks for clarifying what is clearly an extremely restrictive standard

Guy, the standard is anything but restrictive IMO, what it is trying to achieve is to ensure that a qualified Arborist is the person determining the degree of the impact on the tree/s in question.

I don't disagree with the implications of the US BMP but the same elements are included within our National Standard.

Our standard AS4970 The protection of trees on development sites, is very closely related to the British Standard.

In terms of the TPZ our standard states:

Cl 3.3.2 Minor Encroachment:
If the proposed encroachment is less than 10% of the area of the TPZ (radius calculated as 12 times the DBH) and is outside of the Structural Root Zone (SRZ) then additional detailed root investigations should not be required. The area lost to this encroachment should be compensated for elsewhere and contiguous with the TPZ. Variations must be made by the project Arborist considering relevant factors listed in Clause 3.3.4

3.3.3 Major Encroachment:
If the proposed encroachment is greater than 10% of the area of the TPZ or inside the SRZ the project Arborist must demonstrate that the tree/s would remain viable. The area lost ot this encroachment should be compensated for elsewhere and contiguous with the TPZ. This may require root investigation by non-detructive methods and consideration of relevant factor listed in clause 3.3.4.

3.3.4 TPZ Encroachment Considerations:
When determining the potential impacts of encroachment into the TPZ, the project Arborist should consider the following;
a) Location and distribution of the roots to be determined through non-destructive investigation methods. Phoitographs should betaken and a root zone map prepared.
b) The potential loss of root mass resulting from the encroachment: number abd size of roots.
c) Tree species and tolerance to root disturbance.
d) Age and vigour of the tree.
e) Lean and stability of the tree.
f) Soil characteristics and volume topography and drainage.
g) The presence of existing of past structures or obstacles affecting root growth.
h) Design factors.

There is a lot more but honestly it is probably enough to show that the standard is really just trying to codify what I beleive your BMP is directing.

A lot more than 10% can be permitted provided there is evidence to support the sustainable nature of that loss of root mass and future potential growing space.

In terms of the original question... the maths formula yes it is a little complicated I have a less than perfect excel formula that allows me to input approach distances and provides the % of TPZ area lost (not quite the sequence you are wanting...and not the sequence I was originally trying to produce but it works for me)

A very decent rule of thumb is to say one third of the TPZ radius equates to a 10% loss in area....in other words...
For a 9m TPZ you can encroach on one side by 3m (reducing the distance to the tree centre on that one side to 6m) and be within the 10% specification.

 

[treeseer]

Thanks much, Sean. I hadn't read the ISA BMP since the review drafts, and now find youre AS has some fine guidance that should be worked into ours 3 years from now at revision time.

 

[Glennak]

Boa07 I just calculated your 1/3 radius it is not that accurate actually removes 10.96% almost a 10% error. You would be better off measuring the angle and using the formula I gave in the word doc. I have this in a spread sheet along with the other formula to work out how much larger the radius has to be. Feel free to copy them it saves a lot of effort.

I also use a formula to calculate Mattheck's CRZ it is large and complex but it follows the graph perfectly. Much better than the very inaccurate one in the Aus standard but theirs is correct twice. If you want to try it put this in a spread sheet.
=0.055670882088896+0.010193823895656*A2-0.000015792217071675*A2^2+0.000000013725628719343*A2^3-0.0000000000058289033463574*A2^4+9.5123023115925E-016*A2^5
With the A2 being the diameter above the root base in mm.
I just love measuring the diameters putting them in a spread sheet and you have all the figures you need to write reports with minimal effort. But now I may have to use
Dsrz=(D x 50)^0.42 x 0.64 as rough as it is seeing it is an Australian Standard.

 

[Boa07]

Glennak, I was obviously not clear enough I don't use the 1/3rd roughie just meant it is useful to give some idea of when you are needing to be more precise.

You certainly like playing with the formula which is nice.

No-one is required to be more precise than the actual formula in the standard for SRZ, but I am sure you are right that there might be inaccuracies within that....always remember you have to have the Basal diameter measured to calculate SRZ.

I don't personally think anyone is ever going to pick up any Arb for not calculated the little triangles that are lost using the general grometry calcs for segment areas btw.

 

[Glennak]

Yes the 1/3 radius would be good to get a rough idea of the 10% limit, I will remember that one.
Here is part of my submission to the draft Australian Standard.
DR AS 4970
3.2.2.3.4
I assume your formula SRZ = (D * 50) ^.42* .64
Is an attempted to follow Mattheck’s data, the following formula fits Mattheck’s data far better than can be read from his graph at such a small scale.
F(x)=0.055670882088896+0.010193823895656*X-0.000015792217071675*X^2+1.3725628719343E-08*X^3-5.8289033463574E-12*X^4+9.5123023115925E-16*X^5
It is very long but this is what I use to calculate CRZ in my reports, I calculated it with Math Mechanixs that is also where the graph is from.
I’m sorry I converted your formula to mm because it was much easier to convert than mine.
As you can see your graph, in red, is not very good at less than 200mm right at 300mm and again at 1m (beyond this Mattheck has little data) but close enough except for less than .2m. You say for trees with diameters less than .15m SRZ = 1.5m. Now in Mattheck’s graph trees with diameters of .2m have CRZ of 1.5m. So maybe the standard should read “for trees with diameters less than .2m SRZ = 1.5m.” This would take the worst of your graph out as well. Another point is trees with diameters of 100mm (.1m) are not going to fall over if you dug 1m all the way around ( Mattheck’s data shows this as well) so why say they need 1.5m?
Perhaps you could use my formula to get very good data and use other software to get a simpler formula then if the lower end was more accurate you could say trees less than .1m in diameter have a SRZ of 1m and use the graph or new formula from there. Or you could use mine if you like.

I assume this .15m or less gives1.5m SRZ was added so there would not be a step in the graph and to reduce the lower end inaccuracies. As you said earlier you can justify smaller areas so this lower end inaccuracy should not be a major problem. Also small trees can just be replaced or moved.
As you may have guessed I have a science background but have worked with trees for 35 years.

 

[Glennak]

my graph didn't upload I'll try again.

 

[Ekka]

But now I may have to use
Dsrz=(D x 50)^0.42 x 0.64 as rough as it is seeing it is an Australian Standard.

Be careful, the red part should read Rsrz (radius) not diameter.

 

[Ekka]

Error in SRZ graph or formula or my calculator

DR AS 4970
3.2.2.3.4
I assume your formula SRZ = (D * 50) ^.42* .64

Interesting. There's a serious error in the Standard perhaps.

Here's the graph, I made lines so you can get the answer easier.

Now if you look at the graph with a 1.4m stem dia the answer is around 4.5m

But you get your calculator out and it's 3.81m

So I try another number, 0.8m stem dia and the graph reckons around 3.6m but get your calculator out and I get 3.01m

Anyone else want to check this, means the graph is way out in that Standard and extremely misleading or I cant use a calculator.

 

[Glennak]

Wow Ekka you're right they have stuffed up big time.
If you look at the graphs I put up one is my formula that foliows Matthecks graph perfectly and their formula but it looks like their graph is even worse. Will have a play tomorrow have to get some sleep been climbing all day and I'm not used to it and getting old.
Just looked their formula is much better than their graph. I think I will right to them again.

 

[sgreanbeans]

being the brother of one of the Midwest's largest custom home builder/ developer, I can say this with a fact. Builders don't care! Including my brother. I try and give him advice, all he wants to know is, how much, how long and when can ya start. The only thing that matters to these guys when it comes to the trees " I don't care if its gonna die in the next couple years, It wont be my problem then, I want it to stay, It looks better with that 100' Oak RIGHT NEXT TO my $750,000 Condo, leave it alone" They don't care if half the roots were ripped out with a excavator! GET ER DONE. " Were do I want the cement clean out, hmmmmmm, how about right next to that big ol tree over there, that way its out of the way, maybe that could be the base off a paver patio under that tree, yep lets do it, raise that curb appeal, lets excavate about 2 feet of the topsoil away from that tree so the patio has a good firm clay base"
Trying to educate these guys is like convincing a bear to go on a diet during the salmon run! TPZ is bad word to the landscapers as well, retaining walls and patios, run into root while digging? get the sawzaw!
I know this was kinda off to the side, just reading the comments about builders, just thought I would throw my 2 cents, hope it didn't hit anybody!

 

[Boa07]

I think perhaps it is true that the graph should have had a notation indicating that it was itself merely indicative of the curve produced by the calculation.

Glennak I have been giving your maths problem some thought, and can really do no better than the equation you provided on your word doc.

I would however point out to anyone using AS4970 that given the reality of root architecture in the ground....please pay attention to ensuring that the area (and therefore volume) being protected is reflective of the actual growing environment surrounding the specific tree, and the discernible pattern of root growth....I would not include the area under the main road 2m off the stem of the tree (unless you can justify the claim that it represents a viable root growing environment!) when calculating TPZ areas....existing constraints are to be identified and accounted for.

Very very few trees I have ever assessed come anywhere near the idealised model represented by perfect circles on a plan.

The standard provides a very simple formula for planners and designers to follow (if they can) to avoid signficant impacts on trees being retained, it is not (IMO) intended to be a short cut for Arborists to avoid carrying out detailed assessments of trees that are proposed for retention in close proximity to developments/buildings.

I know some of us had been incorporating the British standard for a few years before the draft was even a twinkle in the SA committee's eye, but for those who had been applying other methods actually applying AS4970 might be somewhat daunting and confusing.

 

[Glennak]

Thanks Boa07, when I was making my formula I did a rough scetch to see what I was doing and my outside circle was twice the size of the inner circle so the extra triangles were much larger than in realality. With 10% or less they are insignificant

 

[Ekka]

Just received confirmation form Standards Australia, ammendment due out soon.

Dear Eric

Many thanks for your email and the concern you have raised.

This has already been brought to our attention and we are in the process
of issuing a correction amendment.


Kind Regards

 

[Corymbia]

Where does the formula come from

I realise that it is from the AS4970 but where did they get it from? Where is the published papers ... perhaps that will explain the error in the graph

 

[Ekka]

It's in the standard

 

[Glennak]

I realise that it is from the AS4970 but where did they get it from? Where is the published papers ... perhaps that will explain the error in the graph

I can't understand what you are asking. Their formula is (I think) a poor attempt to follow Matthecks graph on wind thrown trees. Their graph is probably just an error while printing. If you read the previous posts it should be a bit clearer. I tried to use a formula like the one they used but I got similar misfits so I used a program to get an exact formula seeing I put it in a spreadsheet it doesn't matter how large and complicated it is.