SYP shrinkage

[Jimbob]

If your were to flat saw a green Southern Yellow Pine log into say, boards that were exactly 2"x8", what would you expect them to shrink to after air drying to about 20% ?

Or, to put it another way, what size would you saw to get a rough lumber board that measured 1.5"x7.5" after air drying ?

Thanks,
Arky

[SwampDonkey]

In scientific notation....

→MC =  V_sh (FSP-MC)
  V_sh     FSP

→20 =  V_sh (FSP-20)
  V_sh    FSP

and

V_MC = V_g - →MC * V_g
                V_sh
                100

thus

V_MC = V_g*(1 - →MC)
                     V_sh
                     100

---------------------------------------------------------------------------------------
You say SYP, which species?

for loblolly pine G_g = 0.47, V_sh = 12.3% to oven dry condition

thus FSP = V_sh% = 12.3% = 26.17%  no shrinkage at this MC
                G_g       0.47

Thus,  V_sh% per each % MC loss is 12.3% 
                                                26.17% 

,which is G_g or what we call specific gravity in green condition and shows how it is derived.

The MC loss is 26.17 -20 in your request

So,

→20 = 12.3 * (26.17 -20) = 2.9%
  V_sh   26.17

And applying to your dimensions.... 2" x 8"

2" - (2" x 0.029) = 1.942 " (~1 and 60/64") thick

8" - (8" x 0.029) = 7.768" ( ~ 7 and 49/64") wide

so.........saw your boards

1.5" = X_th (1- 0.029)

X_th = 1.5"
       (1-0.029)

X_th = 1.5448 or ~ 1 and 9/16" thick

...................................

7.5" = X_w (1- 0.029)

X_w = 7.5"
       (1-0.029)
X_w = 7.724 or ~ 7 and 3/4" wide
---------------------------------------------------------
To calculate for others species

longleaf G_g = 0.54
shortleaf G_g = 0.47
slash G_g = 0.54


I don't have figures for pond and pitch pine

[zopi]

ScotDonkey...you are a dweeb.

Cut 'em about a sixteenth over..unless you want to be really precise that is...

[Lanier_Lurker]

 :D :D

A dweeb, indeed.  I have those tendencies myself - at times.  On other occasions I just use redneck engineering.

I rather enjoyed reading that.  Might be easier to work the calculations in metric and convert the results to English, tho.

[SwampDonkey]

You guys missed the answer  : It's not those 64th dimensions it's the 16th and 4th dimensions further down. I just answer the questions.  A 16th thicker and a quarter wider.

[SwampDonkey]

Ah, now I know why you guys got trigger happy. I was in edit mode doing some proofing and adding some real world numbers to the dimensions after you guys intercepted the initial post. You need to relax and not go off half cocked. 

Sorry I'm watching some Eastwood Westerns. :D :D

[beenthere]

SD
Then let us know when you are done with the "edit" mode.   8) 8) 8)

I'll save up and see if you have made all the edits.

[SwampDonkey]

I know beenthere.  :D  Sometimes when you type stuff and hit that dang post button it dawns on you that something needs fixing or adding or clarifying, stuff like fractions are all out of alignment, that kinda stuff.  Go ahead and have fun. ;)

[mechengineer13]

And using cold water as your lube makes the shrinkage worse.  ;D

I'm right with ya Swampdonkey, I followed your post completely and thought I was back in school.  Purely a sizing calculation first based on percent moisture content change/delta, and then solving for desired final dimensions.  Great algebra!

[zopi]

  Great algebra!

I gotta little chinese catfish keeps that stuff cleaned up.

[timberfaller390]

carp and pond suckers would help too. :D

[mechengineer13]

Must be some smart fish feeding on that.  Think how smart they'll get when they start feeding on third order differential equations.  :P

[Gary_C]

I did not take the time to follow your math, so just one two question(s).

Did you take into account the difference in shrink from radial to tangential?   ;D

Or did you use the volumetric numbers and assume the shrink is all the same (not)?

[SwampDonkey]

You are right Gary, one should use tangential shrinkage, in this case tangential shrinkage is 7.4 % for loblolly pine

We know FSP = 26.17% from previous calculation

So,

→20 = 7.4 *(26.17 - 20) = 1.74 %
T_sh    26.17

-------------------------------------------------------
Saw your boards

1.5" = Xth (1- 0.0174)

Xth = 1.5"
       (1-0.0174)

Xth = 1.526 or ~ 1 and 9/16" thick
........................................................

7.5" = Xw (1- 0.0174)

Xw = 7.5"
       (1-0.0174)
Xw =  7.633 ~ 7 and 11/16" wide

Not really a whole lot of difference though. I'd still saw it 7 and 3/4" wide. Your talking hairs. ;D


Quarter sawn, we would use radial shrinkage for change in width dimension, in this case 4.8 % for loblolly pine. And that would be utopian, assuming all the rings are vertical across the width. ;D

[SwampDonkey]

If I might add, I think I would saw according to tangential shrinkage so as not to saw yourself short.  But with such narrow dimensions your just trading hairs in this species example. ;D

[SwampDonkey]

Lets look as butternut just for fun.

Gg = 0.36 , V_sh = 10.6%, T_sh =6.4%

FSP = V_sh% = 10.6% = 29.4%
          G_g       0.36

So,

→20 = 6.4 *(29.4 - 20) = 2.04 %
T_sh    29.4

-------------------------------------------------------
Saw your boards

1.5" = X_th (1- 0.0204)

X_th = 1.5"
       (1-0.0204)

X_th = 1.531 or ~ 1 and 9/16" thick
........................................................

7.5" = X_w (1- 0.0204)

X_w = 7.5"
       (1-0.0204)
X_w =   7.656 or ~ 7 and 11/16" wide

Not very significantly different
+++++++++++++++++++++++++++++++++++
But, what about white oak

Gg = 0.59 , V_sh = 15.9%, T_sh =9.2%

FSP = V_sh% = 15.9% = 26.9%
          G_g       0.59

So,

→20 = 9.2 *(26.9 - 20) = 2.36 %
T_sh    26.9

-------------------------------------------------------
Saw your boards

1.5" = X_th (1- 0.0236)

X_th = 1.5"
       (1-0.0236)

X_th = 1.536 or ~ 1 and 9/16" thick
........................................................

7.5" = X_w (1- 0.0236)

X_w = 7.5"
       (1-0.0236)
X_w =   7.681 or ~ 7 and 11/16" wide


again, just hairs ;D

[SwampDonkey]

What about white oak quarter sawn so as the width is radial shrinkage?

R_sh =5.3%

FSP = 26.9 % in previous calculation

So,

→20 = 5.3 *(26.9 - 20) = 1.36 %
R_sh    26.9

-------------------------------------------------------
Saw your boards

7.5" = X_w (1- 0.0136)

X_w = 7.5"
       (1-0.0136)
X_w =   7.603 or ~ 7 and 5/8" wide

[beenthere]

I'm curious where you are getting the value FSP ?

[SwampDonkey]

FSP (fibre saturation point) is the point at which wood shrinks if the moisture content drops below this level, now a living tree can have way more than this. Wood does not have dimensional change above or equal to the fibre saturation point. When wood has more weight from water than from wood fibre the MC is considered greater than 100 %. So basically, if we want to find wood shrinkage we have to find the threshold of shrinkage, which is the FSP. This figure pertains to the moisture content bound by the cell wall and not cell lumens and is the maximum swollen volume of the cell wall.

FSP = Volumetric shrinkage from green to oven dry condition
          Specific Gravity in Green condition.

Those figures are in a table in the Wood Handbook as well as Textbook of Wood Technology.

Many folks make the assumption this is 30 % for simplicity, but when you have the data, might as well use it. :D

[SamB]

So would it be safe to come to the conclusion, a skinny 1/8"over on the thickness and a fat 1/8"over on the width? ???
PIE    R   ROUND?
COBLER  R  SQUIRE ?   :D

[zopi]

So would it be safe to come to the conclusion, a skinny 1/8"over on the thickness and a fat 1/8"over on the width? ???
PIE    R   ROUND?
COBLER  R  SQUIRE ?   :D

Depends on if yer buildin' a space shuttle or a barn...<G>

[SwampDonkey]

Keep in mind, that shrinkage is for 20 % moisture content. In my mind, maybe I'm out to lunch, but a more meaningful calculation would be for lumber at it's EMC (equilibrium moisture content) in the environment for which it will be used. If I recall the EMC for my area is around 12 %, in the Middle East it might be as low as 4%. Maybe in this gentleman's area it is 20 %, I don't know. It must have some meaning for him as he posed the question.

[SwampDonkey]

Let us look at what happens if we take the MC to 6 %.

Use tangential shrinkage of 7.4 % for loblolly pine as before.

We know FSP = 26.17% from previous calculation

So,

→6 = 7.4 *(26.17 - 6) = 5.7 %
T_sh    26.17

-------------------------------------------------------
Saw your boards

1.5" = Xth (1- 0.057)

Xth = 1.5"
       (1-0.057)

Xth = 1.59 or ~ 1 and 5/8" thick
........................................................

7.5" = Xw (1- 0.057)

Xw = 7.5"
       (1-0.057)
Xw =  7.95 ~ 8" wide

All of the sudden you decide to sit up and take notice when you have to leave an extra 1/2". ;D

[DouginUtah]

I just hope Jimbob, the OP, is aware that a standard 2x8 is 1 1/2" x 7 1/4" and not 7 1/2".

I hope I'm right about that--I hardly ever use 2x8s.  If he is matching to store-bought lumber he should measure one to be sure about what is actually is.

[beenthere]

Here is a good visual for figuring shrinkage (and note that FSP (fiber staturation point) for Loblolly pine is 21%).

http://timber.ce.wsu.edu/Supplements/Moisture/Default.html