**Why bonsai and trees loose taper over time**

It is one of those questions everybody has had when starting with bonsai. Why is the taper so extreme in bonsai? Trees in Nature do not have that taper. And.. Why is my tree losing taper during development? In other words: *Why do I have to start with extreme taper when building bonsai.*

**As a tree grows it gets a thicker trunk**

This is obvious, right? If a tree is alive, it stores energy from sunlight into sugars. And with these sugars cells are built. In order to move sap and nutrients around in the plant, the Xylem add a growth layer to the wood of the trunk each year (growth rings), while the phloem adds to the bark each year (see why trunks grow thick). The more photosynthesis a plant has, the faster the growth.

**How can we define bonsai trunk thickening?**

One can look at trunk thickening in 2 ways. One way is to look at the increase of the diameter of the trunk. This is the easiest to measure, and the way most people look at thickening. This is after all what you SEE when looking at your tree. Normally, in all speech this is the measure people use when looking at trunk size.

**Not diameter but area**

I would however like to look at trunk size from the perspective of ‘surface area’ of the trunk. In other words: If I were to cut the tree at a specific point, and would measure the area of the cut. How much surface area do you have. This can be calculated without cutting the tree. So don’t worry. I am not going to ask you to trunk chop your bonsai tree!

In order to calculate the area, I am going to approximate the shape of a trunk as a perfectly round column tapering from bottom to top. I know trees do not grow like this, but it makes it easier to follow. For any circle the area of the surface can easily be calculated. (Π is the number 3.1415…):

Area = Π * 1/2 * Diameter^{2}

**How is trunk thickening distributed in my bonsai?**

The mass added to the trunk at a specific point is directly related to the amount of foliage above the position in the trunk; After all, that section has to move the same amount of nutrients and water around. In fact, although for young/small trees, there is a near-linear relation to the length of the branch + the amount of sunlight it receives and the thickness of the trunk, this stops as the tree starts to grow side branches. As the tree matures and gets more side-branches, the effect of branch length disappears, and the total size of the canopy + the amount of sunlight determine the growth of the trunk. As such, one could say that growth of the trunk size *defined by surface area *between consecutive branches or below the lowest branch is the same all along that trunk section.

Now let’s look at the trunk taper. Say the trunk tapers from 10 cm diameter just above the roots to 5cm diameter just below the lowest branch. It I a good year, and the tree adds 5 cm of diameter to the trunk just below the first branch. What does this mean for the bottom part of the trunk? Will this add 5 cm too? No! At the bottom, the trunk will only add little over 3 cm.

I have added the numbers in the tables below (One in cm and one in inches, as I realize many of my visitors do not use the metric system). I will not bore you with the exact calculations. I basically inverted the formula above, to calculate diameter from surface area. Then I calculated the difference in area for 5 cm diameter (year 1) and 10cm diameter (year 2). This is 236 square centimetre. Add this to the surface area of the base in year one (315) and you get the surface area in year 2 (550). Using the earlier function you can now calculate the diameter at the base in year two, which is 13,2cm.

Important conclusion here is that although higher up the trunk the increment in diameter is 100%, this results in an increment of only 32% in diameter at the base. Over time you will therefor see see the taper disappear. This is not a problem for a well-developed bonsai. There branches are hardly left to grow, and therefore we see hardly any increment of diameter in established bonsai. However, in the early stages of growing out trees this poses a serious risk.

**Risk of losing taper in development**

As the top is left to grow to add girth to the trunk, and to create taper to branches by repeated grow-and-cut cycles, this reduces the taper. Once the base of the trunk is set, keep an eye at the branches that you let extend. Trim in time and do not let those branches get too thick. Also, when building a trunk, ensure you create extreme taper as this will even out over time while building the crown & main branches.

Area of a circle is pi times radius squared, not diameter.

Thank you. Typo adjusted!