GEO 309 Dr. Garver

 Study of the relationship between size and shape  First outlined by Otto Snell in 1892 and Julian Huxley in 1932  Practical applications; ◦ differential growth rates of the parts of a living organism ◦ Insects ◦ Children ◦ Plants Allometry

 Can we prove a relationship between tree height and trunk diameter?  Collect data using clinometers and meter tapes.  Start by standardizing our measurement techniques (First week of allometry exercise).

an optical device for measuring elevation angles above horizontal

◦ Week 1 of exercise – Print out a copy of clinometer_training.xls  Form small groups  Go to the 5 stations listed on worksheet, each group member will;  take a clinometer reading at each station.  calculate their height at eye level.  Each group member completes their own copy of clinometer_training.xls

Allometry exercise – Week 1 of exercise ◦ Each group will then create a new spreadsheet that combines the collected data and calculates the average heights for each of the 5 stations, and the average errors. ◦ When all groups are done we will then compare the results to the actual measured heights of the 5 stations. ◦ Each group needs to hand in their clinometer_groupweek1.xls with each member’s individual clinometer_training.xls sheet in order to get credit for today’s exercise.

= 575 m a = ? = 29°

 Based on the mathematics of right triangles.  Pace off a good distance from the object you want to measure.  Record that measurement ◦ This is the baseline of the right triangle  Second measurement is the angle between your line of sight and the ground (use a clinometer to make this measurement) ◦ Greek letter θ (pronounced thay'-ta).

 The tangent (tan) function.  For a given angle, the ratio of the length of those two sides is always the same.  a/b is equal to the tangent of the angle θ. In equation form, it looks like this: a/b = tan θ  Another way to write this same equation is: a = b * tan θ  So, the height we want to measure (a) is equal to the baseline of the right triangle (b) times the tangent of the sight angle (θ). 575 * tan(29) = 575 * = 319 m

= 575 m a = 319 m = 29° 575 * tan(29) = 575 * = 319 m

 Graph of tangent function from 0 to 89°  Values change slowly from 0° to 60° or 70°  Then values start to change more rapidly.  Want to make sure that you are far enough away from the object so that your sight angle is in the range where the tangent function is not changing rapidly.

 distance around a circle – circumference  The distance across a circle through the center - diameter.  Pi is the ratio of the circumference of a circle to the diameter.  divide the circumference by the diameter, you get a value close to Pi.

 Get in groups and standardize measurement techniques for improved data collection.  Next 2 weeks – we will collect and analyze campus tree data. Dr. G.. = 5.15 m Kyle

 5 locations outside – Bridge, Flagged railing, Balcony1, Balcony2, Balcony m Bridge Location Kyle clinometer reading = 18.5° Dr. G. clinometer reading = 20° Kyle eye hgt. = 1.73 m G. eye hgt. = 1.65 m

Location clinometer (deg) horizontal dist. (m)height (m) your eye hgt. (m) Final Object Hgt. (m) actual heghterror bridge - Garver bridge - Myrick

Full dataset n = 88 RSQR 25%50% Example of a Plot A

RSQ R 47% 69% Example of a Plot B