208 FORM CLASSES AND FORM FACTORS 



172. Resistance to Wind Pressure as the Determining Factor of 

 Tree Form. The theory explaining the form of the boles of trees, 

 which is now generally accepted, was first advanced by Prof. C. 

 Metzger, a German. This was, that the stem or bole is constructed 

 as a girder to withstand the pressure of wind. Based on this theory, 

 A. G. Hoejer, a civil engineer of Stockholm, devised the general formula 

 for tree form discussed in § 173. Prof. Tor Jonson applied this 

 formula first to spruce and then to Scotch pine, and demonstrated its 

 correctness; as a consequence, developing the basis for tables of abso- 

 lute form and volume for trees, and a new method of estimating 

 timber (§ 203). 



Jonson's conclusions, based on these investigations, are that tree 

 form depends entirely on the mechanical stresses to which the tree is 

 exposed, and is therefore independent of diameter, and height, and also 

 of species, age, site or any other factor, except as these factors in- 

 fluence the form of the crown. The force of the wind operates on 

 the crown of the tree and is focused or centered on a point representing 

 the geometric center of the crown. The pressure of the wind on the 

 tree crown constitutes a force which compels the tree to construct its 

 stem in such a manner that the same relative resistance to strain is 

 found at all points, the smallest possible amount of material being 

 used. As the concentrated force of the wind strikes a point situated 

 lower or higher on the tree, dependent on the crown area presented, 

 we get larger or smaller taper respectively, which means bad or 

 good form class. As the location of the point of attack of the bend- 

 ing force is determinative of form, this point is called the form point, 

 and can be expressed as a per cent of total height. 



Here is a natural law, to which growth of trees, as mechanical struc- 

 tures designed to stand up against wind, corresponds. The full bole 

 of the forest-grown tree in a crowded stand, coinciding with a small 

 crown and high form point, meant that this location of the strain 

 required nearly equal strength along the total length of bole, which 

 could be attained by rapid growth of the upper bole. If the tree 

 were open-grown with a consequent long crown and a low form point, 

 this would permit of smaller upper diameters and require greater 

 strength lower down on the bole. 



Since the form of the crown, especially its length, with relation 

 to the length of bole, determines this form point, this relation of crown 

 to bole, expressed by form point serves as an index to classify trees as 

 to their relative form classes or form quotients. 



Any variation in average form, such as the admitted fact that the 

 average form quotient increases with age, is explained by a coincident 

 change in this crown and form point relationship. Open-grown trees 



