# Volume Calculation

Assisi supports a a large number of ways to calculate volume. This study is a discussion of what the options are and how volume is calculated. First an overview...

The volume in trees has historically been calculated using volume tables, volume equations or using tree taper. Assisi mostly uses the terms Volume Tables and Volume Equations to mean whole tree volume rather than the volume of logs. Assisi uses the term Log Segmenting to mean using taper models to calculate diameters at any point along the tree and therefore the volume of individual logs. The volume of logs is of course calculated using an equation, but for organizational purposes, Assisi groups volume calculate into these three types.

### Volume Tables

Volume Tables are tables of tree volume by species, DBH, height and often form class. The values were derived from field studies and were put into this form for convenience before computers were available. The volume in Volume Tables can be board or cubic, merchantable or total. The tables imply certain merch standards such as stump height, trim, merch diameters and a unit of volume. Sometimes there are multiple tables available covering a variety of merch options. Height can be expressed as feet or meters or expressed as the number of fixed length logs up to the merch diameter.

Volume Tables are whole tree volumes meaning a single number is looked up that is the estimated volume from stump to merch or total height top. To get the volumes of individual logs, a Volume Distribution table can be used. Volume Distributions give the percent of tree volume present in each individual fixed length log. Volume Distributions also imply certain merchantability standards such as log length and trim.

### Volume Equations

Volume equations also give the volume of whole trees, but require calculating an equation. Volume equations were initially made to estimate the volumes found in volume tables and so carry with them to same merch specifications as volume tables. Later equations began to add terms for the merch specifications themselves such as scaling diameter. Volume distributions can be used with volume equations as they can with volume tables.

### Log Segmenting

The Log Segmenting method of volume calculation uses equations for the volume of individual logs themselves. Log segmenting requires the length and diameters of each log be known. Therefore, taper equations are frequently used when volume is being calculated using log segmenting.

Log segmenting allows more merchandising flexibility because stump, trim and even the lengths of logs can be anything desired. The equations used to calculate the volume of individual logs, called log rules, do assume a certain within log taper however. Board volume log rules also assume a certain saw kerf and saw patterns.

When using the Log Segmenting method of volume calculation, there are many ways to specify the length of logs. Log lengths can be a fixed length. They can be variable lengths using market grades as a guide or they can be called in the field directly. Field measured allows calling out cull sections and assigning assumed grades as well.

### Taper Equations

Taper equations are methods to calculate diameters at points along a main tree stem. Taper differs by species, region, age site and other factors so there are many different kinds of taper equations. Each equation requires a set of measurements such as DBH, total height, merch height, form point height, etc. These must be known before taper equations can be used to calculate diameters.

### Example Log Segmenting

The process of log segmenting is often described as "walking" up a tree from stump to tip stopping at certain points to delineate individual logs. The diameters of the logs are calculated using the tree's taper function.

For example, say we have a 24" 150' Douglas fir tree. At stump we calculate a diameter and start "walking" up the tree. We stop at the top of the first log which may have been called in the field or has been set to a fixed length of 16'. Once there, we calculate the top diameter and use a log volume equation such as Scribner, international quarter inch or Smalian to calculate the volume of the first log. We then skip a small section called log trim and calculate the diameter of the what will be the bottom of the second log. Again we continue until the top of the second log is reached and calculate volume in the same way. This process continues until we reach a stopping point that is usually the height to a certain minimal diameter called the merch diameter. There are a lot of settings that can fine tune this process but this is the general idea.

### Field Called Segments

Estimating log lengths of a tree opens the door to many other options such as calling cull segments and grading in the field. One useful approach is to call not log lengths but section lengths. Sections are lengths that within which logs will be made. This is similar in concept to sawlog sections and pole or top log sections. The advantage to this approach is a single grade can be used within a section that will translate into grades for the logs made within the section.

For example, a quality of "sawlog" or "foreign" can designate a bottom portion of a tree to be made into sawlog quality logs. There could be a cull section next and then the top section could default to "pole" or "domestic" type logs. The length of the logs themselves can be either fixed length or optimized to grade specifications for the given section quality.