Wndsn Range Calculator
High-precision range calculator. Companion to Wndsn Telemeters: Low tech, high utility graphical distance & altitude computers from the Wndsn applied science lab.
By way of using a Wndsn Quadrant or Telemeter measuring degrees or a hairline graticule measuring mil or moa or any other instrument or technique that returns the angular size of a known object, we can determine the distance to that object.
The angular relationship between height and distance.
Input
Results
- Size of the object observed:
s = 4.5 - Angular size:
α = 2 degreesor34.91 MIL(MRAD) or35.56 MIL(NATO-MIL) or120 MOA - Distance multiplier
1/tan(2°):d = s · 28.64 - Approximate distance:
d = 128.86
The display precision set is .2. To change that, edit the variable &digits=x in the URL where 0 <= x <= 9.
Explanation
[Load sample values (JSON) (XML) (CSV).]
Compare MIL vs. MRAD vs. NATO-MIL.
d = s · 1/tan(α)d = 4.5 · 1/tan(2°)- (We have one angle (2°) and the Opposite side (4.5), and want to determine the Adjacent side. According to SOHCAHTOA, we need to use Tangent.)
tan(2°) = opposite/adjacent- Thus:
4.5/d = tan(2°) - Switching sides:
d/4.5 = 1/tan(2°) - Multiplying both sides by 4.5:
d = 128.86 - (The small angle approximation for skinny triangles shows that the angle in radians approximates to the sine of the angle (for small angles, the hypotenuse is about equal to the adjacent); hence, the larger the angle, the bigger the difference between 1/sin(α) and 1/tan(α).)
Reference
1 rad = 57.3 deg
6.2832 rad = 360 deg = 6283.2 mil = 21,600 minutes (moa)
0.017453 rad = 1 deg = 17.453 mil = 60 minutes (moa)
0.0573 deg = 1 mil = 3.438 minutes (moa)
0.05625 deg = 1 natomil
Radian, degrees, mrad, NATO-MIL, and MOA.