On the road…again!
Afghanistan to Zambia
Chronicles of a Footloose Forester
By Dick Pellek
The Footloose Forester is the last person you would want to teach physics. Most of what he read in physics textbooks or heard in lecture halls went uncomprehended, and his grades proved it. He might have understood the words being spoken but not at all what they meant or how to apply them. Yet, in daily life, we all have to deal with the realities of physics, even if we do not understand what is happening or why it is happening. Some purists in the world of science say that there are only two pure sciences—chemistry and physics. Mathematicians may object to being left out of the discussion about pure science but because they are usually so adept at applying their knowledge toward interpretations and applications of both physics and chemistry that the layman may have difficulty in correctly labeling them. Besides, many mathematicians righty identify themselves as both physicist and mathematician when they spend their professional careers applying the fundamentals in both fields. On the other hand, the field of chemistry is so broad that it is also easy to mistake a physical chemist from a chemical physicist, based on their subject matter.
This sorry little chronicle is the tentative product of another nightmare. My apologies for posting it while knowing that the internal editor did not pick up on the Greek symbols used as part of the formulae used.
In recent years the Footloose Forester has frequently tried to make peace about his misgivings by writing about academic weaknesses and sometimes discussing them openly, rather than to continue to hide his ignorance. In some ways maybe it is an attempt to find answers during waking hours when the years of disturbed sleep and nightmares only presented problems that he could never explain or solve in his sleep. So, although he is far from being competent in physics, he will now attempt to formulate an equation or two that he hopes will explain some of the things he experienced while working in the woods. Maybe the best way to start is to give an example of a common misunderstanding.
In Central America, campesinos with machetes often cut down sugar cane and trees with the same tool. Cutting an acre of sugar cane with a machete takes far, far less effort than cutting down an acre of trees. So, while people might assume that clearing an acre of anything has the common unit area of one acre as a mathematical identity, the area of land is totally irrelevant. What is relevant is the cross-sectional area of the stems, themselves. Ignoring for a moment the fact that the stems of sugar cane are soft compared to trees, the total cross-sectional area of the stems is key in assessing the amount of sweat required to clear an acre. In mathematical terms: ∑,where is the average diameter of a sugar cane stem of 2cm, would yield 62,800cm2 of cross-sectional area.
∑A= (∕2)2 • ∏ thus, ∑A = (2/2)2 • 3.14 • 20,000
∑A = 62,800cm2
The same acre containing only 200 hundred trees with an average diameter of 50cm would yield;
∑A = (∕2)2•∏ thus, ∑A = (50∕2)2 • 3.14 • 200
∑A = 392,500cm2
So, even if the stems of trees were as soft as the stems of sugar cane, the cross-sectional surface area of 200 trees would require more than six times as much work to cut, than to cut 20,000 stems of sugar cane with an average stem diameter of 2cm. All other factors being equal, the 6.25 times greater surface area of the trees should give anyone pause before deciding how long the job of clearing an acre might take. In forestry circles, the cross-sectional area is known as Basal Area or BA. That leads this discussion into a general observation about physics.
The amount of time spent on a job, and the true cost of doing the job, should be based partly on the physical parameters that one faces. Seldom, however, is the approximate cost in terms of time and effort calculated correctly. Many, if not most bosses, think that their guesses are really what counts; and may take it as a sign of laziness if some underling suggests that it takes a lot longer than they think. Although the Footloose Forester never saw a physics formula or a mathematical equation to suggest what the expression of work might be, he suggests the following;
Work Required (W) = ∑BA2 • n where,
the individual Basal Area of each tree is more determinant of the effort required than the number of trees contained on a typical area of forest land. Dense stands, however, will contain more trees and thus the total number of trees (n) cannot be ignored.
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