Based on the data collected, trees that began growth in the year of 1967 had longer branches than the other trees (on average), but the branch angles were equivalent to the other trees. Otherwise, this information shows that the tree age does not affect the results of this experiment, as it is not a limiting factor to the morphology in this case. This is because once angles are determined at the branching point of a tree, a ratio keeps the growth consistent in terms of tree height and branch length. Therefore, the branch angle, which was the main focus, was not affected by the age and growth of a tree. Angles are kept constant to maintain photosynthetic efficiency.

Overall, the statistical analysis, using these various different tests, has proven that a tree is controlling its branch angles through genetic or other mechanisms, therefore the branch angles measured were not due to random chance.The results of this experiment show the branch angles measured in Picea glauca coniferous trees are necessary for optimal light collection. The first hypothesis was that branches of the south side of a coniferous spruce tree should be, due to selection pressures, of an optimal apical form for collecting light energy for photosynthesis. This hypothesis is relevant, and has been proved correct, as many of the angles are at or near 90°. That is, all angles are relatively perpendicular to the sun. A statistical analysis has been completed on the data, and results have indicated that there is no significant difference between the angles near the tops and bottoms of a coniferous tree. However, the minor difference may be important to consider, as upper branches are exposed to the sunlight more, with less shade from nearby branches. Therefore, when considering possible arrangements for a photovoltaic panel system, higher branches should have an angle range from 90° to 100°, while lower branches should have a range of 80° to 90°. This allows for good exposure no matter what angle the sun strikes at.

These angles are a part of morphological phenotypes that have been genetically passed down from previous generations. This has been concluded because of the similarities between all of the different trees, indicating that the gibberelllin and auxin hormones are previously determined genetically before branching occurs in a tree. Coordination and response to these specific hormones are a result of natural selection processes. However, since there is a slight difference in the range of angles, it can also be concluded that the environmental conditions a tree is in can affect the morphology. The change is very minute, but does help in determining a precise angle for the highest level of photosynthetic efficiency. As well, the coarseness of a branch does not affect the angles, as proven by the data collected, since all data was similar. Photosynthate collection in specific branches does not affect the general response to hormones that has been genetically predetermined. Therefore, even though coarser branches improve photosynthetic efficiency of a tree, it will have no relevance to designing the solar tree system, as it is the placement of the panels on the branches that will be important.

Other conclusions that can be made regarding this portion of the project include the tree height to average branch length ratio. Based on data gathered from twenty different trees, a tree’s height divided by the average branch length ratio should equal approximately 0.426118209. The reason it does not equal precisely 0.426118209 all of the time is because of various environmental factors that may affect the growth of a tree slightly, such as snow cover, fertile soil, etc. Even so, this is crucial to know when constructing a model for solar energy collection because the tree height will ultimately determine the lengths of the branches. This also proves that growth of a tree and its branches do not affect the branch angle, which is the key to obtaining solar energy. These branches will hold the panels out to absorb energy. Even though some branches split out in Y’s and cross over each other, that is not necessary for the collector, as those morphological phenotypes are specific to that tree, and not in general. As well, the distance from the main structure that panels are placed at will be based on the mean bare branch length that was measured from several older trees that had shed their core useless needles. This average is 30.6 inches.

After studying the mathematics of these trees, a mathematical formula can be generated from the data collected to calculate a Picea glauca tree’s height.

(Average Branch Length in Inches) x 0.426118209 =
(Approximate Tree Height in Feet)

Now that the basic concept of branch angles and tree growth has been scientifically tested and found to be reasonable, a model of the proposed photovoltaic solar energy collecting system will be constructed based on the determined results of the data collection. The Picea glauca species of conifer tree is definitely a species that has the ideal mathematics for optimal solar energy collection.

This project is the intellectual property of Eden Full. Use of this information for one's own purposes is not permitted.