## Importance of Thinning Timberland

#### with nerdy calculations to prove it...

#### Thinning timberland has many benefits such as improving stand health, lessening of catastrophic fires, making room for young trees to start & grow, and increasing the growth rate of mature trees.

#### The last benefit will be the focus of this page. *But before we begin, note that we are using assumptions that are not representative of all trees or stands. The calculations below are only for curiosity. *With that said, let's begin...

#### Here is a 20-in (approximate) diameter log.

#### Thinning occurred at approximately 70 years. The tree rings are noticeably thicker starting at 72 years, but it takes few years for the tree to 'realize' it has room to grow.

#### Before this time, the rings are tightly compressed. After 72 years, the tree rings are much more spaced out. The area increase is immediately evident at year 73.

#### But how much of a difference did it make? Let's quantify it.

#### The total radial distance is approximately 10-in over 100 yrs. During the first 70 years there is approximately 4.4-in of radial growth.

#### Using the area of a circle gives us the following:

#### Before Thinning

#### A = π r^{2}

#### A = π 4.4^{2} = 60.8 in^{2}

#### 60.8 in^{2} of growth occurred over 70 yrs

**After Thinning ***

#### A = π (R^{2} - r^{2})

#### A = π (10^{2} - 4.4^{2}) = 253 in^{2}

#### 253 in^{2} of growth occurred over the last 30 yrs

##### * The *after thinning* area formula is for the outside ring only.

#### It is obvious that thinning resulted in a significant amount of mass being added to the tree over a relatively short period of time.

#### But how would this compare for the same tree if no thinning occurred?

#### To determine the anticipated radial growth without thinning, we need to calculate the growth rate per year (before thinning) and then multiply by 30 years.

#### Here is the calculation: (4.4-in / 70 yrs x 30 yrs = 1.9-in)

#### Had thinning not occurred, the tree would have only added another ~1.9-in of anticipated radial growth.

#### Therefore, 4.4-in + 1.9-in = **6.3-in of radial growth without thinning**

#### We now can determine the area growth difference with & without thinning.

#### A = π (R^{2} - r^{2})

#### A = π (10^{2} - 6.3^{2}) = π (100) - π (39.7) = 314 - 125 = 189 in^{2} (1.31 ft^{2})

#### The 189 in^{2} area represents the additional growth from thinning. The anticipated area of the tree without thinning would have been 125 in^{2}.

#### 189/125 = 1.51

*Thinning resulted in 51% more mass vs. not thinning. *In addition, this is where the most valuable growth occurs also since larger diameter logs often sell for a premium.

#### Next we calculate the board feet (bf) equivalent for this additional volume.

#### We assume this increased area extends an average of 30-ft high, we get ~39 ft^{3}.

###### Note that calculating the added volume of a tree is essentially determining the circumferential volume of a hallow cone. This is a complex calculation and will not be derived for these calcs.

#### Converting 39 ft^{3} to bf gives us 472 additional bf for the tree.

#### Assuming there are 50 similar (large) trees per acre and 100 acres to be harvested, we get the following board feet.

#### 472 bf x 50 trees/acre x 100 acres = **2,360 mbf (additional)**

###### One could argue that without thinning you would still have the original trees, which would contribute to the volume. This is true, but overstock conditions result in stressed trees, which are prone to disease and possibly death. Plus ALL the trees would then be smaller diameter resulting in less height and lower payout vs. larger diameter trees.

### Takeaway

**Trees in overstock conditions grow significantly slower than trees with room to grow.****While most managed timberland trees don’t grow for 100 years, the picture makes a compelling case that growth rate significantly increases after thinning occurs.****Trees with room to grow are healthier since they have less competition for water and nutrients. Therefore they are less prone to disease and death.****Intermittent thinning can give owners some cash while setting up mature trees for significant growth over the next few decades.**