View or download WWIICache.frink in plain text format
// Solution for the "WWII" geocache (GCYANP)
// "WAYPOINT #1
// There is a 14k+ mountain peak in CO that is named the same as the
// battleship where the Japanese signed their WWII surrender to the US."
// "If you stood on the summit of this mountain at 7pm UT on the day of the
// Japanese surrender signing, you would observe the Sun at an altitude of
// ____ degrees and at an azimuth (E of N) of ______ degrees."
// The ship will be trivial to anyone who has seen the fabulous Steven Seagal
// epic "Under Siege".
// Location of the summit of the mountain
// Grab in my sun/moon prediction library
surrenderDate = #September 2, 1945 7:00 PM UT#
println["Local time is " + (surrenderDate -> Mountain)]
// Calculate refracted, parallax-corrected apparent position of sun.
[azimuth, altitude] = refractedSunAzimuthAltitude[surrenderDate, summitLat, summitLong]
// Convert Meeus' odd coordinate system to normal coordinates
azimuth = (azimuth + 180 degrees) mod circle
println["Altitude is: " + format[altitude, "degrees", 5]]
println["Azimuth is: " + format[azimuth, "degrees", 5]]
// It's hard to guess what temperature and atmospheric pressure they assumed
// for the day, so use my defaults. The calculations show that the sun
// would be at an altitude of about 59 degrees (with refraction) so refraction
// error should hopefully be sort of low. Let's calculate it here.
println["\nMeta-Calculation of possible refraction discrepancy:"]
[airlessAz, airlessAlt] = airlessSunAzimuthAltitude[surrenderDate, summitLat, summitLong]
// Convert from Meeus odd coordinate system
airlessAz = (airlessAz + 180 degrees) mod circle
println["Airless Altitude is: " + format[airlessAlt, "degrees", 5]]
println["Airless Azimuth is: " + format[airlessAz, "degrees", 5]]
// Calculate refraction angle using my defaults.
refractionAngle = refractionAngle[airlessAlt]
println["Refraction angle is: " + format[refractionAngle, "degrees", 5]]
println["If they didn't correct for refraction, error is " + format[refractionAngle earthradius, "feet", 1] + "."]
// Running this shows that the refraction angle is small (about 0.01 degrees)
// so it shouldn't be a problem if we round to the nearest degree, but it is
// possibly a problem if we round to the nearest 0.1 degree, and certainly
// if we round to the nearest 0.01 degree.
// The problem solution doesn't state if/how they rounded the value. This is
// potentially a show-stopper.
// After more research, the USNO page seems to show one decimal place
// after the decimal point for altitude and azimuth. Can we assume that's
// what they were using? It's too big of an assumption to make carelessly;
// .1 degree on the earth's surface is (in Frink notation:)
// .1 degree earthradius -> miles
// that's still almost 7 miles! Far too large an area for me to hike.
// In addition, it's hard to know if they really corrected for the parallax
// of the summit, as opposed to just using the reference geoid. The problem
// statement says "from the summit," so let's assume so. Unfortunately,
// my parallax model only currently calculates from the reference geoid,
// so let's see how bad that might throw us off.
// Based on the link they gave to the USNO, http://aa.usno.navy.mil/ ,
// which doesn't have inputs for altitude, I might guess that they didn't
// correct parallax for the actual altitude of the summit, but rather just
// used the reference geoid or even something simpler. The USNO's notes
// don't say anything about parallax or refraction, but my previous encounters
// with USNO predictions show that they do have some refraction model close
// to my defaults (but theirs do a crazy step-function to zero as soon as the
// centerline of the sun or moon crosses the horizon.) Hmmm... let's
// calculate the magnitude of possible error due to parallax.
println["\nMeta-Calculation of possible parallax discrepancy:"]
// The maximum magnitude of the parallax error would occur if the sun were
// at the horizon, but since it's high, parallax is reduced.
parallax = parallaxAngleAlt[sundist, airlessAlt]
println["Total parallax angle is: " + format[parallax, "degrees", 5]]
// Running this, the nominal parallax angle is about 0.00126 degrees, which
// is small (but nonzero). The error due to not adjusting for geodetic
// elevation would be:
parallaxErrorFactor = summitHeight / earthradius
println["Parallax error factor is: " + format[parallaxErrorFactor, 1, 5]]
println["If they didn't correct for parallax at all, error is " + format[parallax earthradius, "feet", 1] + "."]
println["If they corrected for parallax for the geoid, but not for the mountain summit, error is " + format[parallax earthradius parallaxErrorFactor, "feet", 1] + "."]
// So again, multiplying this is small, at least for the sun. (It would be
// significant for the moon, which is 389 times closer!)
// We're still stuck by not knowing how much they rounded the alt/azimuth
// figures. Without knowing this, we might be off by as much as a degree
// (about 70 miles) in lat or long!
// Clarification has been requested. We'll see what they say.
roundAlt = round[altitude, 0.1 degrees]
roundAz = round[azimuth, 0.1 degrees]
println["Rounded altitude is: " + format[roundAlt, "degrees", 5]]
println["Rounded azimuth is : " + format[roundAz, "degrees", 5]]
// "Actual latitude (N) of Waypoint #1 is the Sun's altitude
// minus 19.23007 degrees."
W1lat = roundAlt - 19.23007 degrees
// "Actual longitude (W) of Waypoint #1 is the Sun's azimuth
// minus 72.63358 degrees."
W1long = roundAz - 72.63358 degrees
println["Waypoint 1 latitude is: " + format[W1lat, "degrees", 5]]
println["Waypoint 1 longitude is: " + format[W1long, "degrees", 5]]
// "WAYPOINT #2
// "At Waypoint #1 you will find a Rx pill bottle containing "adjusted" UTM
// coordinates for WP #2 and a specific factor ________________used in
// calculating the coordinates of Waypoint 2._______________ N and
// _____________________ E"
// Hmmm... by "unadjusted" do they mean what that usually means for UTM
// coordinates, that the easting is shifted by 500000 meters and is relative
// to the bounding meridians and not to the central meridian? Or do they
// mean that they're "normal" UTM coordinates and the "unadjusted" means that
// they just haven't added the numbers below? Must ask.
// "WP 1 is
// located in a small park named after a location where terrible events took
// place during WWII. These events were memorialized by a poem set to music. A
// number in the music title is used in calculating WP2 coordinates.
// The UTM values found at WP1 must be adjusted as follows to obtain the
// actual WP2 coordinates:
println["a. The mountain peak elevation, in feet, " + (summitHeight->feet) + ", multiplied by 0.97588."]
a2 = (summitHeight/feet) * 0.97588
println["result is $a2"]
// Do they round the Julian day? To the nearest day, or do they use
// all the digits? Are they including the 7 PM UT in the JD calculation?
// I guess it doesn't matter too much, because these are offsets to UTM
// coordinates and thus just have units of meters.
b2 = JD[surrenderDate] / days
println["\nAdd the UT Julian date of the Japanese surrender signing: "]
println[format[b2, 1, 5] + ", to result A."]
b3 = a2 + b2
println["b. result is " + format[b3, 1, 5]]
View or download WWIICache.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink Documentation or see More Sample Frink Programs.
Alan Eliasen was born 18205 days, 18 hours, 22 minutes ago.