Wndsn Calculators [Wndsn Expedition Team]

Wndsn Calculators

Companion tools to Wndsn Quadrant Telemeters: Low tech, high utility graphical distance & altitude computers from the Wndsn applied science lab.

To supplement our instruments, and to provide educational materials and diverse ways of accessing our devices and techniques, we are making available a number of calculators, to accompany our printed manuals, as exercise tools, to get a 'third opinion', and to demonstrate underlying principles.

Shadow calculator: Measure, visualize, and convert between angles, tangents, and their ratios with a shadow square.
Range calculator: Measure distance from angular size in degrees, mil, or moa, e.g. distance to object of known dimension(s), depth of a well, etc. Or measure height from a known distance, e.g. height of object, elevation of landmark, etc. Also convert MRAD ⇄ MIL ⇄ MOA.
Elevation calculator: Measure altitude difference relative to shared base, e.g. the distance to a lighthouse of known height, measured from a skyscraper of unknown height, or the altitude of a structure on a mountain, measured from a valley, or the distance and altitude of an airplane of known size.
Dipping distance calculator: Calculate the dipping distance at which a lighthouse or other object just becomes visible to an observer over the horizon.
Map scale calculator: Convert map scale to ground distance and vice versa.
Sun calculator: Measure local latitude and determine declination for a given date, to calculate a number of latitudinal, diurnal, and/or instantaneous solar values.
Moon Clock: Determine the phase and position of the Moon from its age or a date, with moonrise and moonset for your place, on the interactive Wndsn Moon Clock.
Star calculator: Determine culmination, azimuth, and hour angle based on a star's declination and altitude.
Sight reduction calculator: Reduce a sight to a line of position: the computed altitude Hc and true azimuth Zn of a body from its declination and hour angle at your latitude, and the intercept from an observed altitude, with a worked example.
Duv and CCT calculator: Calculate the correlated color temperature (CCT) and Duv of a light, its distance from the Planckian locus, from CIE 1931 x, y or CIE 1960 u, v. Move the point on the interactive chromaticity diagram and read the values as it moves.

Bookmarks and the API

The calculators are RESTful: every calculation lives in its address. The values you enter go into the link together with their units and the page's settings, so a bookmark or a shared link brings back the same result.

The same address also answers as an Application Programming Interface (API). Add format=json to it, or format=xml or format=csv, and the calculator returns its result as data instead of a page, for your own scripts and spreadsheets. This address, for example, asks the Range calculator for the distance to an object of 4.5 m seen at 2°:

https://tycho.wndsn.com/range/?size=4.5&alpha=2&angular_unit=deg&unit=m&calc=yes&digits=1&format=json

It answers with the values given, the values calculated, and the precision:

{"input":{"alpha":2,"angular_unit":"deg","size":4.5,"unit":"m"},
 "output":{"distance":128.9,"multiplier":28.6,"degrees":2,"mil":34.9,"natomil":35.6,"moa":120},
 "digits":1}

What you need to know:

Where to start. Each calculator lists its parameters under "URL and API parameters" in its Explanation. And the Results heading links the JSON, XML, and CSV answer for whatever is on screen, so the easiest way in is to calculate on the page and copy one of those links.
Calculate. An address needs calc=yes to calculate. Without it, the page shows, whatever the format.
The answer. JSON and XML share one structure. input holds what was given, under the parameter names and with its units, and output holds what was calculated. notes follows when there are any, and digits sits at the end. Numbers are numbers, and a value that does not exist is null in JSON and empty in XML and CSV.
CSV. One header line and one row, with the same columns for every query to a calculator, so the rows of many queries stack into one table. The input column names the values given, such as alpha+size.
Precision. digits sets the decimals of the results, from 0 to 9. Inputs come back as you gave them.
Errors. Invalid input answers with notes and digits and no result, so a script can read what went wrong ("The angular size must be a number.").
Calling it. No key or account is needed. But the answers may only be read by pages on tycho.wndsn.com, so a script on another website cannot fetch them in its visitor's browser. Call the API from a server or the command line instead.
One call per second. Please send no more than one call per second. An address that gives every value gives the same answer every time, so keep the answers you have rather than asking again.
Old links. Parameter names we have replaced still work, such as known_size for size, so your bookmarks keep working.

Tycho Brahe

A Danish astronomer, Tycho Brahe (1546 – 1601) was known for his comprehensive astronomical and planetary observations. Tycho's view of science was driven by his passion for accurate observations, and the quest for improved instruments of measurement drove his life's work. He was the last of the major naked-eye astronomers, working without telescopes for his observations.

Well known in his lifetime as an astronomer, astrologer and alchemist, he has been described as "the first competent mind in modern astronomy to feel ardently the passion for exact empirical facts." His observations were some five times more accurate than the best available observations at the time.

Yet in this my stars were not Mercury as morning star in the angle of the seventh house, in quartile with Mars, but they were Copernicus, they were Tycho Brahe, without whose books of observations everything which has now been brought by me into the brightest daylight would lie buried in darkness.
Johannes Kepler