Angle estimation

The approximate determination of an angle - predominantly a horizontal angle - is referred to as an angle estimate . It is usually freiäugig and may be a more precise, often complex angle measurement replace if only accuracies in the range of degrees are required. With some experience, small angles (less than a few degrees) can even be estimated to a few tenths of a degree.

Estimating angles using the outstretched arm

Where angle estimates make sense

Instead of a measurement, estimates of angles are useful whenever they

should go fast, for example
out of a movement, or
no higher effort for a measuring instrument allowed,
and accuracies of about 0.5 to 3 ° are sufficient.

For example, two or more of these aspects apply

when hiking , mountaineering or sailing , if
- the own location on land or sea map is gepeilt (see also terrestrial navigation )
- the route with respect to a landmark (mountain, town) is to be determined
when adding local details to a building plan or point map
in topographic- cartographic sketches
in amateur astronomy for finding weak objects using a star map .

Historically, angle estimates were important in artillery , see angle group .

Methods of angle estimation

Angle less than 20 °

If no technical aids such as rulers, protractors , geometric triangles , right angles or stop angles are available, your own body can serve as a measuring device :

the hand span : with an outstretched arm 17 to 20 °, depending on body type
the fist : the finger bones mark about 3, 5 and 8 °
the thumb jump : depending on arm length and eye relief, mostly 5–6 °; is also well suited for estimating distances (object size times 10)
the finger width : about 1.5 °, thumb width 2 °; estimates of up to ¼ of a degree can easily be achieved.
smaller angles are obtained from estimated proportions of the finger width, e.g. B. measures a third finger width about 0.5 °

All estimates become more precise if you “calibrate” your own measurements. With the span, for example, by determining the number of hand spans over a full 360 ° rotation.

With celestial bodies:

In the starry sky , the Polweiser (α and β of the Big Dipper, 5½ degrees) or the stars of Kassiopeia (three stretches at 4½ °, one at 3½ °) are ideal. One of the two constellations is always high above the horizon.
Small angles can be found by comparing them with the apparent moon diameter (full moon width) . The full moon , like the sun disk , has a diameter of about ½ degrees (corresponds to the width of a finger).
With the “ eye tester ” in the Big Dipper (double star Mizar-Alkor) you can estimate 0.2 °.

In the case of elevation angles (tree, mountain, star, etc.), however, the angle value becomes larger because the extended hand comes closer to the eye. This can be easily checked with a 45 ° triangle or the Pole Star (height = geographical latitude ).

Angle from 20 to 60 °

Determined by stringing together the hand measurements.

For angles of 40 to 60 °, it is best to assume 45 °. You can easily set an angle of 45 °

by halving 90 ° (book, rectangular paper)
or by folding a square piece of paper diagonally (folding over the corner)

determine exactly. You aim over both edges of the paper (eye close to the corner point!), Estimate the remaining angle with the span of your hand or fist and add or subtract it.

Angles up to 180 °

For angles close to 90 °, it is best to start from a right angle (book, sheet of paper, etc.) and estimate the difference with the span of your hand or your fist. The same is done for angles close to 135 ° by folding the paper at an angle (to 45 °) so that 90 ° + 45 ° = 135 °.

At angles just under 180 °, aim along a straight edge in both directions and estimate the difference to 180 ° as above. The alignment method (extension of a straight line) can be used for higher accuracy . Angles over 180 ° are estimated in the other direction of rotation, so that they are less than 180 °.

literature

Wolfgang Schroeder: Practical astronomy for star lovers , with an appendix for building simple instruments. Kosmos-Verlag, Stuttgart 1960.
Carlheinz Gehlsen GmbH: Pocket book of navigation . Industrie-Verlag, Heidelberg 1967.
Wolfgang Regal: Jump of the thumb and Jacob's staff - measuring without a tape measure . Basic knowledge for outdoors, Volume 106, Conrad Stein Verlag 2001.
Detlev Block: Astronomy as a hobby - recognizing and naming constellations and planets , chapter Orientation on the celestial sphere . Bassermann-Verlag, Munich 2005.