GEO 309Dr. 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 * 0.5543 = 319 m

= 575 m

a = 319 m

= 29°

575 * tan(29) = 575 * 0.5543 = 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 mKyle

5 locations outside – Bridge, Flagged railing,

Balcony1, Balcony2, Balcony3

5.15 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

Locationclinometer

(deg)horizontal dist. (m) height (m)

your eye hgt. (m)

Final Object Hgt. (m)

actual heght error

bridge - Garver 20 10.00 3.64 1.65 5.29 5.15 -0.14

bridge - Myrick 18.5 10.00 3.35 1.73 5.08 5.15 0.07

Tree Diameter vs. Height

0

5

10

15

20

25

30

35

40

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Diamter (cm)

Hei

gh

t (m

)

Series1

Linear (Series1)

Full dataset n = 88 RSQ R

25% 50%

Example of a Plot A

Tree Diameter vs. Height

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

diameter (cm)

hei

gh

t (m

)

Series1

Linear (Series1)

RSQ R47% 69%

Example of a Plot B