tree arch

This topic submitted by andy, lori, scot, georgia ( at 5:52 pm on 10/18/00. Additions were last made on Wednesday, May 7, 2014. Section: Myers

Andy Culbertson
Lori Mikesell
Scot Teti
Georgia Wang


If sunlight does affect the branch structure of a Sugar Maple, then exterior tree branches would have an acute angle in relation to the ground, and interior tree branches would have an obtuse angle in comparison to the ground. The amount of sunlight each interior and exterior branch receives should be similar. Trees with acute angles would have shorter distances between the cross branches, and in turn have a higher weight stress and greater load support. Therefore, exterior trees would be more prone to damage due to their lack of support. Interior trees, because of their growth response to sunlight and overall structural development, can support more weight than that of the exterior trees.
We wanted to look at tree or leaf structure for our lab. Sugar Maple (Acer saccharum) is native to the United States and Canada, but most abundant in eastern Asia. The maple grows 75 to 100 feet tall and up 2 to 4 feet in diameter. In crowded woods it has a long, branchless trunk. In the open, it has a shorter trunk and large, rounded crown. The maple's hard wood is best used for furniture and cabinetwork. Sugar Maples perform best in pastures and fields, with clean air and undisturbed soil, where the roots and branches have room to spread out. Additionally, the maple is a favorite during the fall because of its brilliant leaf colors. After our class decided to focus on landscape ecology, we decided to conduct a more specific experiment on tree architecture. Through a significant amount of brainstorming, we narrowed our ideas down from studying leaf structure to branch structure. We wanted to know how light affects branch structure and their stability in Sugar Maples. We decided on these specific questions because they will best reveal the architectural aspect in trees.
As a group, we planned to accomplish and understand how branches might be effected by sunlight. We will compare the angles and distances between cross branches, stability, and the amount of sunlight received on the interior and exterior sections of the forest.
This research is relevant because our section is looking at landscape ecology. This is interesting to our particular group because we are all architecture majors and want to investigate its relevance within nature.

Relevance of Our research question:

Honda and Fisher (1978) state that right and left branch angles would vary. To receive the maximum amount of light the tree will have either a very dense leaf layer or a loose one among its branches. Because tree branches are three dimensional, it is difficult to analyze them and their orientation. The different types of symmetry of the two branches ìmaximizes,î leaf surface area for light. ìWhen two new branch units arise from the distal end of a previous unit, there is a regular asymmetry in the branch angle.î Therefore, the main point in the article is that trees have a particular branch structure that collects a maximum amount of light. Tree angles are positioned where they are receptive to maximum sunlight. When the sun is low in the sky, there is no direct sunlight into the interior of the forest. Areas of the tree that receive sunlight twice as much during the day are considered to have sunlight overlap. Also, the branches of the trees must be high enough to receive the light to compete with other trees. Therefore, all of these components of time, sunlight, and competition all affect how high the tree branches will grow. However, the article does not discuss the branchesí ability to withstand certain weight loads. Therefore, we know that branch structure is particularly positioned and symmetry does reflect the sunlightís influence on their growth. Our experiment will address this issue by testing the amount of sunlight received at random positions around the entire tree as well as the patch.
In an article by Schreiner ET al (1996), it explains how the structure of branches are very similar to the arterial system. Experimentors have looked at segment radial, branch lengths and how they relate to branch angles as well as segment diameters. The geometric model investigates how structure relates to functional abilities. This model also shows how branch structure helps with its ability to reach light in order to grow. The treeís branch structure is going to adapt depending on its location (environment) within the forest or outside of a forest. If the tree is in the interior, the branches will not be as spread out as they would be a field, but rather it would angle its branches upward to compete with the other trees in the area. This supports our hypothesis in the sense that branches of the same type of tree, but different locations in the forest will have different branch angles but achieve the same amount of light to ensure proper growth.
An article by Perttunen (1996) describes how a model LIGNUM describes the structure of trees three dimensionally and how growth relates to this aspect. The growth of a tree is due to photosynthesis and is based on the amount of light and water available to the tree. The segments are based on branch angles, which are grown to receive ample sunlight. The angles allow the leaves to reach the amount of sunlight needed to grow annually. Despite the fact this article is about leaves, it confirms the theory that branches have particular angles for optimal sunlight that is needed to aid photosynthesis in leaves.
The article by D.F. Robinson (1996) discusses the big picture of the study of tree architecture. Robinson discusses the different theories and models other scientists have created to describe tree architecture. He does mention Hondaís (1971) article, which focuses on regularities of length and angle in branching structures. It also mentions an article from Kuuluvainen (1992) that stated flat extended foliage is the best shape for acquiring light at high altitudes. Additionally, the article goes into detail about the Halle and Oldeman theory about tree architecture. The theory describes that trees are structurally classified by tree trunk and branch structure. This model illustrates that there are constraints on the size and shape of a tree depending on the tree and branch structure. The model also discusses the fact that a treeís ability to take up optimal space for reception of sunlight is predetermined by its genetics. The article highlights an aspect of the treeís branch structure that could provide a source of error. Robinson states that certain branches that do not bare other branches are short lived and have low functionality. Therefore, throughout the experiment students should avoid such branches because of their limited relationship to the reception of sunlight. Also, the article lists basic terms for branch and trunk structures of a tree. Despite the very broad approach to the article, it lays the foundation to then build upon studying tree architecture. This article highlights factors students should be aware of about branches. Additionally, the article points out that tree architecture is not purely random but a very systematic process that possesses the particular goal of survival.
An article by Garber (1987) suggests there are great differences between various kinds of maple trees. For example, the wood of the red and silver maple trees is weak therefore; the branches are prone to cracking under stress from high winds, heavy snow, and even ice loads. This article reaffirms the fact that Sugar Maples are most successful in open areas. Sugar Maples are very tolerant under stressful conditions (weather). Therefore, the data concerning stability should have low numbers in movement reflecting their ìtolerance of stressful conditions.î
Another article by McClure (2000) states that within four species of maples: sugar, beech, red, and yellow patterns exist in their canopies according to their height growth, and gap formation. This is necessary for the trees to obtain sunlight, and proper nourishment. Sugar Maples grow slower than the others do after gap formation, however, the Sugar Maple did grow at a more constant rate and reached the proper height for nourishment over a thirty-year period. Sugar Maples also have the oldest stems, and therefore, it can be hypothesized that Sugar Maplesí branches are sturdy and can withstand high stress. This relates to our load hypothesis in the sense that load is a factor in tree development, but we will take this a step further by observing the differences between stability of exterior and interior trees (and the relation to branch angles).
The article by Genard ET al discusses how three-dimensional models of trees simulate how photosynthesis is conducted in trees. Models were conducted on computers and interpreted. Light meters were used to collect the data and data was compared through the use of computer programs. Photosynthesis increased as the distance between leaves and the angles between the main stem increased. This relates to our hypothesis because it is an example of light meter use that shows how photosynthesis is conducted due to sunlight availability.
The article by Hilbert and Messier discusses models using artificial trees to study the effects of light, branch type, branch spacing, and transmission by a Sugar Maple. The experiment shows that light interception helps to define the significance of tree form from light interception, and its interaction within a specific environment. The results showed a significant difference in leaves found in the sun and the shade. This was in response to growth in high versus low light. Therefore branches were constructed differently in different light environments. This relates to our hypothesis in that one of their conclusions on light interception by branches was that they discovered lower branches in a tree have a larger angle to obtain light. Branches that receive more sunlight, have smaller angles.

Our research relates to how the position of tree branches and trees in general effect or contribute to the areaís landscape ecology. During this project, we will hopefully be able to make a broader base of human knowledge on how structural nature develops. We want to know how the branch structures are created in particular ways for survival. Similar to why and how buildings are designed architecturally ensuring that the trees and buildings that are created withstand abuse from weather. Both have aesthetically values as well as functional values to survive in an environment.

Materials and Methods:
We plan to locate and select a number of Sugar Maples from both the exterior and interior area of the forest. Specifically, our group will test two trees, one from the interior of a wooded area and the second from the exterior of a wooded area. We will collect data that includes stability, amount of sunlight absorbed, branch angles, and distances between cross branches. For each tree, we will place the light meter at the first branch closest to the ground on opposite sides to test how much light is available during a 24-hour period. The light meter data should be similar between the acute, exterior branch compared to the obtuse interior branch because the tree situates its branches to gain the maximum amount of sunlight to grow. To determine the different angles, we will use a protractor, record the data, and then compare the results. To determine the distance between cross branches, we will use a ruler (in inches) to measure the distance between each cross branch, and then compare the results. To determine the stability of the tree, we will record the number of inches the branch will move after the force is applied. We will take all the data and find the averages and statistics, and relate it to our hypothesis.
However, the class will be split into two groups that will be assigned two of our members. Group one will test stability by measuring the distance a branch moves before it breaks off the tree as well as distances between cross branches, and the branch angles of interior trees. Group two will collect the same data for the exterior trees. Each group will test 30 trees either in the interior or exterior of the forest giving them each 30 intervals of data. We decided for times sake we would have the students in class focus on these three variables. The students will combine their observations with the information provided from our model and data of the two trees we tested. Additionally, upon returning to class the students will quickly calculate their averages and compare their results with ours to get a final verdict about our hypothesis.
The experiment is statistically sound because we are using a large number of random samples, thus allowing for a proper average of statistics. Additionally, we are only looking at two specific trees to insure there is a random sample statistic. We will insure unbiased results by observing different patches and looking at interior and exterior Sugar Maple trees. We will record sunlight to be able to compare interior and exterior Sugar Maple trees.
To ensure that the data collected by the class can be trusted, we will explicitly state the procedures for collecting the data. When we type up our procedures, we will indicate the importance of consistency in the data collection and analysis through repeated bold directions.

Protractor- visual observation to determine the angles of the tree branches
Light meter- placement for 24 hours in a specific location to determine to the amount of sunlight available at that time
Ruler- visual observation to determine flexibility of a branch
The class will take our hypothesis and test its acceptability by collecting data using our same methods to conduct the experiment. The class will need to obtain the averages of the sunlight readings, and the angles and the distance of movement of the lowest branch of interior and exterior Sugar Maple trees. We will also be creating a model of our experiment to present to the class.
We will also provide a data sheet from our tests. The data will also be compared and analyzed by the class, such as means and the histogram of the data.
Our timeline will consist of 24 hours of data collecting.


Our primary results are available through our own groupís observation of the Sugar Maple structure as well as the classí observations. We already know that an exterior tree has flexible structure due to the effects of weather (sunlight and wind specifically). We also know that interior tree branches have obtuse angles to the ground in order to receive the proper nourishment. In addition, we know that exterior trees are more susceptible to damage caused by man and/or nature. Further results to be included in the final report
To analyze our results we will find the means of the angles from the exterior and interior branches, the amount of sunlight received in 24 hours, the distance between cross branches, and stability of the trees. We will compare all the means of our data collected from the Sugar Maples in the various patches, and then compare and contrast our results. As a result, we want the angles of the interior and exterior Sugar Maple trees to be similar in each patch. All other data should be significantly different if it is in a group of exterior and interior Sugar Maple trees within a patch.
Further Results to be included in final report.
Discussion and Conclusions:
Further results to be included in final report

Works Cited:

1. Honda, Hisao; Fisher, Jack B. Science. New Series 199(1978):888-890
2. Robinson, D. F. A Symbolic Framework for the Description of Tree Architecture Models; Botanical Journal of the Linnean Society, 121(1996):243-261
3. Terbough, John. Diversity and the Tropical Rain Forest. New York, Scientific American Library, 1992.
4. Structural Quantification and Bifurcation Symmetry in Arterial Tree Models Generated by Constrained Constructive Optimization; Department of Medical Computer Sciences. 1996(161-174)
5. Ledezma, G. A. Journal of Applied Physics. 82(1997):(89-100).
6. Thompson, Franklin J., The Urban Naturalist: Maple, 1988
7. McClure, Jan W., Forest Ecology and Management. 127(2000):181-189
8. Perttunen, J. Annals of Botany. LIGNUM: A Tree Model Based on Simple Structure Units. 1996(87-98).
9. Hilbert, D.W., Functional Ecology. 10(1996):773-783
10. Genard, M., Ecological Modeling. 128(2000):197-209
11. Internet: ìhttp://www.jstor.orgî

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