How to Measure Angles Using a Theodolite - Part 2 Taking a measurement

How to Measure Angles Using a Theodolite

A theodolite is an instrument used commonly by builders and engineers to measure precise angles, which is necessary for large scale construction projects. A basic modern optical theodolite typically consists of a small telescope which is connected to two angle measuring mechanisms, one for measuring horizontal angles and one for measuring vertical angles. It sits atop a rotatable base with a leveling mechanism on a tripod. Once the theodolite is set up, the telescope is turned to spot the desired point and then the angle from the point that the theodolite is placed to the point spotted in its telescope can be read through the eyepiece of the scope.

Taking a measurement

Step 1

Unlock the upper horizontal clamp, and rotate the theodolite until the arrow in the rough sights is lined up with the point you wish to measure, then lock the clamp. Use the upper horizontal adjuster (not the clamp) to align the object between the two vertical lights in the sight.

Step 2

Look through the small eyepiece, and using the fine adjustment knob to get a precise horizontal line up with your object. The degrees from your reference are measured on the horizontal degree scale, the minutes and seconds on the fine adjustment scale (ex. 30 degrees 10'30").

Step 3

Unlock the vertical clamp and look through the sight while moving the theodolite up and down to find the precise spot vertically on your object that you'd like to measure. Lock the clamp and use the fine vertical adjustment knob to get a precise fix on the point you've chosen. Then look through the small eyepiece and read off the degrees, minutes and seconds from the vertical scale and the fine adjustment scale as you did for the horizontal scale. If your object is up high you'll need to do a rough horizontal adjustment first, then do the vertical measurement, then readjust for the final horizontal measurement. These two coordinates give the exact angle between your reference and your point of interest, but you can also measure the angle between two points by comparing their two measurements, or by setting the first point as the reference.

Map Projections

Even though they are easy to fold up and carry around,
neither greatly distorted maps nor disassembled globe
gores have much practical use. For this reason,
cartographers have developed a number of map projections,
or methods for translating a sphere into a flat surface. No
projection is perfect - they all stretch, tear or compress the
features of the Earth to some degree. However, different
projections distort different qualities of the map. "All maps
have some degree of inaccuracy," Turner explains. "We're
taking a round Earth and projecting it onto a two-
dimensional surface -- onto a piece of paper or a computer
screen -- so there's going to be some distortion."
Fortunately, the variety of available projections makes it
possible for a cartographer to choose one that preserves
the accuracy of certain features while distorting less
important ones.
Creating a map projection is often a highly mathematical
process in which a computer uses algorithms to translate
points on a sphere to points on a plane. But you can think
of it as copying the features of a globe onto a curved
shape that you can cut open and lay flat -- a cylinder or a
cone. These shapes are tangent to, or touching, the Earth
at one point or along one line, or they are secant to the
Earth, cutting through it along one or more lines. You can
also project portions of the Earth directly onto a tangent or
secant plane.

Projections tend to be the most accurate along the point or
line at which they touch the planet. Each shape can touch
or cut through the Earth at any point and from any angle,
dramatically changing the area that is most accurate and
the shape of the finished map.
A planar projection
IMAGE COURTESY NATIONAL ATLAS
Some projections also use tears, or interruptions, to
minimize specific distortions. Unlike with a globe's gores,
these interruptions are strategically placed to group related
parts of the map together. For example, a Goode
homolosine projection uses four distinct interruptions that
cut through the oceans but leave major land masses
untouched.
A Goode projection of the Earth
IMAGE USED UNDER THE GNU FREE DOCUMENTATION
LICENSE
Different projections have different strengths and
weaknesses. In general, each projection can preserve
some, but not all, of the original qualities of the map,
including:
Area: Maps that show land masses or bodies
of water with the correct area relative to one
another are equal-area maps. Preserving the
correct area can significantly distort the shapes
of the land masses, especially for views of the
entire world.
Shapes: In the pseudoconical Robinson
projection, the continents are shaped correctly
and appear to be the correct size -- they look
"right." However, distances and directions are
incorrect on a Robinson projection. It's a good
tool for studying what the world looks like but
not for navigating or measuring distances.
Distances: Maps that maintain correct
distances between specific points or along
specific lines are equidistant maps.
Directions: Many navigational maps have
straight rhumb lines, or lines that intersect all of
the parallels or meridians from the same angle.
This means that, at any point on the map,
compass bearings are correct.
You can learn more about the specific map projections and
their strengths and weaknesses from NASA , the National
Atlas of the United States and the U.S. Geological Survey .
Choosing the right projection is just one part of creating a
successful map. Another is finding the right data. We'll
look at where map information comes from in the next
section.