First). Attention, Navigators, this is your Captain speaking,
It’s time to do so
First). Attention, Navigators, this is your Captain speaking,
It’s time to do something with your sextants. We are calling the inclinometer a sextant, now. The building of the sextant was worth ten points. Using it to measure the changing elevation of the Sun will also be worth ten points. The elevation of the Sun is the angle between the horizon and the Sun.
You will make observations of the Sun over a period of four hours, between 10 a.m and 2 pm. The Sun will reach its peak high in the sky at around (but not exactly) 12 pm. That time we call Local Noon. The objective of this project is to determine what time local noon occurs where you live.
Roughly point the ruler or straight edge at the Sun, just as you would aim the barrel of a gun. Do not stare at the Sun; use the Sun’s shadow. Orient the ruler or stick so that the size of its shadow is minimized, that is, made as small as it can be. If the ruler is parallel to the ground (not pointing at the Sun), the shadow will be big. The closer the ruler is to pointing at the Sun, the smaller the ruler’s shadow will be. When it is pointed exactly at the Sun, the ruler’s shadow will appear as a very short line. The weighted string will hang against one of the degree markings on the protractor. Press the string against the protractor as soon as you have minimized the ruler’s shadow. If you do not hold the string in place after you have minimized the shadow, the string will move, and you will wind up reading the wrong number. There are several photos in the module, showing the slowly shrinking ruler shadow as the ruler is pointing closer and closer to the Sun. Sorry about the crappy focus in some of the pix.
Record the degree number under the string. If the degree number is less than 90, subtract the degree number from 90. For example, if you recorded 70, 90 – 70 equals 20 degrees. Record the 20 degrees. That angle is the elevation angle of the Sun. If the degree number under the string is greater than 90, subtract 90 from the degree number. For example, if you recorded 120, 120 – 90 equals 30. Record the 30 degrees. That angle is the elevation of the Sun. If you are simply writing down numbers that you see under the string and nothing more, YOU ARE DOING IT WRONG. Those numbers are not the Sun’s elevation. You must find the difference between the number under the string and 90, as explained above. THAT is the Sun’s elevation. So, take an elevation measurement at about 10 a.m., then every half hour after that for four hours. Eight elevations. You should see the elevation numbers rising, reaching a max, then decreasing again. The numbers won’t change much between 11:30 a.m. and 1:30 pm. The time of that max is the time of local noon.
There is a video in this module that discusses how to aim and read the protractor, but ignore the part about aiming it by looking at the Sun. I do not want you to look at the Sun. Use the shadow method. The video does discuss how to read the protractor, so you might want to watch the video for that part. A new video is in the works but will not be ready this semester.
Submit a table of Time, Degrees, and Elevation.
You must have credit for your inclinometer/sextant (Project 1) to be eligible for points on this project.
Second assignment In this assignment you will use your inclinometer to find the height of a building, a tree, and a telephone pole. Something similar can be done to find diameters of planets. You don’t have the equipment necessary to actually find the diameters of planets, but you can learn about the technique by determining heights of everyday objects on Earth.
You are going to find the angle between the horizon and the top of the building. You will do it the same way you found the elevation of the Sun, but you will not be using the ruler’s shadow. Point the stick or ruler as if it were the barrel of a gun. Aim the ruler or stick at the top of the building and read off the number of degrees between the string and the 90-degree mark on the protractor. For example, if the string hangs over the 55-degree mark, the angle between the horizon and the top of the building would be 90 – 55 = 35 degrees.
Let’s say the angle is 35 degrees. The height of the building equals the tangent of 35, times the distance to the building, thus: height = tangent (35) x distance.
The tangent is an example of a trig function. Those of you who have taken algebra II are acquainted with trig functions (for better or worse). You don’t need to know what they are in order to do this project.
I will calculate the tangents of a range of angles for you:
tangent 10 = 0.176
tangent 15 = 0.268
tangent 20 = 0.364
tangent 25 = 0.466
tangent 30 = 0.577
tangent 35 = 0.700
tangent 40 = 0.839
tangent 45 = 1.0
45 degrees is the largest angle I want you to use. If your angle is bigger than 45, back up. Adjust your distance from the building until the angle from the horizon to the top of the building is one of the angles in the list. 25 or 30, for example, rather than 28. If you know how to get tangents from a calculator, you do not need to use the above list.
To calculate the height of the building, you also need the distance to the building, as mentioned above. The most accurate method to get the distance is to use a tape measure. If not that, you could measure the length of your shoe (your shoe size is NOT the length of your shoe) and walk heel to toe from your angle-measuring position to the building, counting the little baby steps. Multiply the length of your shoe by the number of baby steps, to get the distance to the building.
Example:
The measured angle between the horizon and the top of the building is 35 degrees. The length of my shoe is 11 inches. After measuring the angle, I walked 90 baby steps to the building. 90 x 11 inches = 990 inches. 990 inches / 12 inches per foot = 82.5 feet. h = tangent (35) x d
h = 0.700 x 82.5 feet
h = 57.8 feet
57.8 feet is actually how high the top of the building is above your eyeballs. How high is the top of the building above the ground? You figure it out. You just need to apply a simple, small correction to the measured height above eyeballs.
Do these two more times, for a tree, and for a telephone pole. For each calculation you must identify the object concerned, e.g., building, pole or tree.
Show all arithmetic operations, or NO CREDIT. Plus, I can’t give you feedback if I can’t see what you did.
You are not eligible for credit on this project until I am satisfied with your submission for project 2: “Using Your Sextant.” If you cannot point correctly in project 2, then you are wasting my time and yours trying to do this project.