## Wndsn Distance Meter

A tool for makeshift navigation and rangefinding, the Wndsn Distance Meter^{[1]} enables you to do more than merely guessing distances. Find an object of known size at the distance you need to measure and let the baked-in trigonometry do the rest for you; save for a single calculation.

### How to set it up

To install, knot the string to the card through the provided hole. Measure a length of 57.3 cm (22.44 inches) from eye to card. You can make a knot at the end or a loop; for measuring distances, hold onto the string with your teeth.

### How to use it

- Keep string taut, next to your eye
- Align baseline to object of known height
- Read factor at upper bound of object
- Multiply with known height for distance

### Accuracy

Accuracy is determined by two elements, provided that the string length is respected:

- The reading of the scale and approximation of the corresponding mark
- The estimation of the height of the measured object

For training and reference purposes, you may want to create a table of the exact height of common objects.

Note that you can measure in any unit (cm, in, ft) or system (metric, imperial, custom), the factors are always the same and return your distance in the same unit you used to approximate the object measured.

### FAQ

**Q: Why is the string length so important, and what's special about the 57.3?**

It says "baked-in trigonometry"; also, on the tool itself, there is a hint: `For d = 57.3 cm, arctan(s/d) in deg = s => 1° = 1 cm`

The explanation is the definition of radian^{[2]}, or rad: The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3° (when the arc length is equal to the radius). The circumference subtends an angle of 2π radians.

Now, at a radius (hence the string length) of 57.3 cm, 1 cm in measured size subtends exactly 1° and makes for elegant calculations; for example α becomes equal to s (in cm), so `D = S * d / s`

is equal to `D = S * d / α`

where:

- D = distance from eye to observed object of known size
- S = known size of the object observed
- d = distance from tool to observer's eye
- α = the angular size of the object observed at the distance d
- s = apparent size of the object observed

**Q: How do I use the degree scale on the right-hand side of the instrument?**

Where the left hand side gives multiplication factors, the right hand side gives the angular size^{[3]} of the object observed, in other words the measured height in degrees, (easily converted to multiplication factors at the distance of 57.3 cm) which can be used when the actual height of the object is unknown.

Example: the full moon viewed from Earth has a diameter of about 0.5° (30 arc minutes) which, knowing *neither* distance *nor* actual diameter, doesn't tell us anything about its *actual* size compared to other objects such as the sun, which, at a much bigger diameter and distance, has about the same angular size when observed from Earth. Now, knowing *either* distance *or* actual diameter, the angular size can easily converted to the respective other, absolute value.

Also note that: `α = (S * 57.3) / D`

Relationships between angular size and multipliers (valid for d = 57.3 cm):

10 mil = x100 1° = x 57 2° = x57/2 = x 28.5 50 mil = x 20 3° = x57/3 = x 19 4° = x57/4 = x 14.25 5° = x57/5 = x 11.4 100 mil = x 10 6° = x57/6 = x 9.5

**Q: How are the scales on the left and on the right side used together?**

On this instrument, the scales on the left and on the right are alternative and not used in conjunction. If for example your object is 3°, you obtain 19 (57 / 3) as a multiplication value in case you have a known height, width, etc. You would then proceed to multiply that value with the, (for example) height of the object in the unit you are working with; so at 4 m, your object would be 76 m away (4 * 19). If you have a measurement in feet and your object is 12 ft, your result would be 228 ft (12 * 19) (same unit you input), and hence again 76 m.

**Q: Can I measure the width instead of the height of an object?**

You can measure any dimension; width, height, etc., as long as it's on a plane that is perpendicular to you, the trigonometry doesn't care where in space the triangle is located.

**See also:**

**References:**