Technodiversity Glossary

System performance is the productivity of a working system in products per hour. In forest harvesting, normally the products are not indicated by the trees, but by the cubic meters (m³) that are harvested per hour.

The performance of a working system depends very much on the attributes of the working object. Besides the tree species, the dimension of the harvested trees has a high influence to the productivity. In scientific publications about working systems, performance is normally represented by a typical curve (green line):

•       It is low for smaller work objects (in our case: trees)

•       It increases with the work object size according to a non-linear degressive trend.

Some graphs also report time consumption in minutes per cubic meter (red curve). Again, we recognize a typical curve:

•       Time per cubic meter is higher for small trees compared with big ones

•       The trend is degressive.

This system behavior is known as the principle of tree volume. The time to process a given work object increases, but not as much as the volume of the object increases. The problem is that we know this overall trend, but we don’t have the exact parameters case-by-case. This makes prediction difficult and laborious.

In Technodiversity, we suggest a simple solution: Scientific experience has shown that the time consumption per tree depends on its volume according to a typical relationship:

•       The bigger the tree, the longer the time needed

•       The data cloud can be well represented by a linear regression

•       The regression line crosses the y-axis above the origin.

Of course, in scientific case studies different curve types will offer a better fit, but the linear function is fairly good, too, and gives us the chance to get an overall estimation of the performance. This general assumption makes it possible to forecast the system performance even with very few data points.

Provided that we can accept the linear approximation, we can describe the relationship between time per tree and tree size with the equation just below:

The time t_i is composed by two summands:

b₀ is the fixed time required for processing one single tree. It does not depend on the size of the tree. It is typically the time to walk to the tree, clean the area around it etc.

b₁ is the time required for processing a single tree. It depends on its size, so we say it is variable. b₁ indicates the time consumption at one tree that has exactly the volume of 1 cubic meter. Is the tree smaller, let’s say only 0.5 m³, than the product of b₁ times its volume v_i is also 0.5 compared with 1 m³.

Given this basic line, the time per m³ is

with

This curve t_i,m3 includes our two independent variables b₀ and b₁ with the consequence that it looks different for each working system.

Now, dividing 60 min/h by the time consumption t_i,m3 we get the performance in m³/h

with

and

It shows the typical degressively increasing curve of performance (green):

•       the bigger the average tree the higher the performance per hour

•       but the increment gets less and less.

•       Why do we need to complicate our lives by tracing the process all the way back to the time consumption per tree?

•       Because that way we get to the original source of time consumption.

•       We know that the relationship between time consumption per tree and tree size can be represented by a linear regression with two parameters b₀ and b₁. Those two parameters contain all the information that we need.

•       To find those parameters, very few time measurements are enough.

•       We can also modify the two parameters of the regression formula for rough forecast purposes:

•       When we see, that in our case the preparation time b₀ per tree is higher than normal (because of thornbushes, slippery ground etc.), we can “correct” this parameter with a best estimate.

•       When we know that our operator is quicker than an average operator, we may adapt the parameter b₁ to his performance level.

(See more at TDiv PR1-C03)

See system performance