Wndsn Quadrant Telemeter: The Quadrant Side

The Quadrant side hosts an angular quadrant, an inclinometer, a shadow square, and trigonometric arcs.


Feature Overview

Quadrant side overview.

Quadrant side overview.

There are several parts on our quadrant

  • Vertex with slot for the string; all quadrant operations start here.
  • Plumb line; index and measuring string of the front side nomograph with an added weight.
  • Degree scale; difference in degrees from horizontal.
  • Percent scale; difference in percent grade from horizontal (rise/run).
  • Inclinometer scale; difference in degrees from vertical.
  • 10-division shadow square.
  • 12-division shadow square.
  • Sine, cosine arcs and 60-division scale; converting angles.
  • Obliquity arc; determining the sun's declination.

The angle scale

Along the curved side is a scale marked off in 90 degrees, grouped into ten and five degree sections. Used with the sights and a weighted string, the user can sight on a target and determine the angle of elevation by seeing where the weighted string lies on the angle scale.

The slope scale

Additional scale alongside the angle scale, expressing the percentage of slope, as in: 100 × rise / run.

The horizontal and vertical scales

Along each straight edge of the sine quadrant is a scale, traditionally divided into 60 units and subdivided into 12 five-unit sections. This base-60 (or sexagesimal) numbering is a hold-over from the ancient Babylonian number system that still survives in our divisions of time and angles. The horizontal scale is used for computing the sine of an angle, the vertical scale is used to compute the cosine of an angle.

The shadow square

The shadow square is used for surveying tasks such as finding heights, depths, and distances as well as for determining the tangent of a given angle.

The sine and cosine arcs

Two half-circle arcs, one centered on the sine scale, one centered on the cosine scale. These can be used in conjuction with the sine and cosine scales as an alternative method of converting angles.

The inclinometer scale

A 0.5° scale at the bottom of the instrument, going from 0° to 30°, used by (usually physically) aligning the left side of the instrument with the object to be measured, returning the difference to vertical, in degrees.

The obliquity arc

Another line of the sine quadrant is a circular arc centered on the origin point at the quadrant's right angle. With a radius of approximately 24 units, this arc is a projection of the earth's orbital obliquity (tilt). The purpose of this marking is to determine the sun's declination (angle above or below the equator) for any given day, allowing the user to then determine the sun's altitude at noon for that day.

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