How to make and use a simple theodolite
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You will require:
* Card
* String
* Something to make a small weight (like plastocine)
* A protractor / angle measurer
* A pen
* A small tube (like a drinking straw)
* Scissors
* Sellotape
* A ruler
* A calculator that can do "tan" (or a computer)
To make:
1) Cut the card into a sensible size (say 12" square)
2) Stick the string to the middle of the top edge of the card about halfway
along
3) Draw a straight line, perpendicular to the top edge of the card, starting
where the string is attached.
4) Attach the straw to the top edge of the card (might be an idea to cut it
to 2" long or so first)
5) Attach the weight to the end of the string
To use:
1) Measure the distance from the object to the point you will stand to
measure it. Picking a nice round number sometimes makes calculations
easier.
2) Hold the card up to your eye, so you are looking through the straw
3) Let the string hang down vertically
4) Make a mark on the card where the string is
5) Measure the hight off the ground from the top of the string (from your
eye-level is probably a good approximation)
6) Draw a pencil line from the top of the string to the point you marked on
the card.
7) Use the protractor to measure the angle between the vertical line you
drew to start with and the pencil line.
8) Plug the values into the formula below:
d = distance from you to the object
a = angle measured on the card
e = distance between ground and eyelevel
h = height of the object
h = tan(a) * d + e
Remember to use the same units throughout. If you measure one thing in feet,
measure everything else in feet.
How the formula was derived:
From simple trigonometry:
/| sin(i) = o/h
h/ |o cos(i) = a/h
/ | tan(i) = o/a
i----
a
The line on the card is perpendicular to the hypoenuse, so the angle between
the line you drew and this line (a above) is equal to i.
You want to know the value of o.
You know i and a (length of "ajacent").
tan(i) = o/a
=> tan(i)*a = o
You measured it from a few feet off the ground, so add this to your value to
get:
height of object (o) = tan(angle measured(i)) * distance from object(a) + height
off the ground