You should probably know...
The cache is not at the above coordinates. It would be a
very good idea to work out the solution at home first!
How Your Tools Work
In real-life, a VOR (VHF Omnidirectional Radio) transmits a beam
of electromagnetic radiation in a single direction. This beam
is rotated as a rate of around 1800 RPM. Airplanes have
instruments that interpret this beam to determine a bearing TO or
FROM the station. By finding your bearing to/from two
different stations, you can quickly triangulate your position over
the ground. We'll simplify this for our purposes.
Let's say that these VORs transmit a distinct signal in all
directions at the same instant the rotating beam aligns to the
North (or 0/360 degrees). Your receiver takes this
transmitted signal and illuminates a small light at the same
instant. Then, every time the beam (radiating in one
direction only) points directly to your receiver, your receiver
then sounds a tone at that instant. It is important to know
that this beam takes exactly 10 seconds to sweep across all 360
degrees of the compass, and rotates in a clockwise direction.
For your convenience and accuracy, your receiver displays the
number of seconds that elapse between the distinct signal and the
passage of the beam.
Using the elapsed time between the distinct signal and the
passage of the beam, you can determine which bearing FROM the
station you are on. For instance, if the elapsed time is 0
seconds exactly, then you are on the 0/360 degree radial FROM the
station. This means if someone were to point to you while
standing at the station, they would also be pointing to 360 degrees
or North. Likewise, if the elapsed time is exactly 5 seconds,
you are on the 180 degree radial FROM the station. Exactly
2.5 seconds would mean you are on the 90 degree radial, and 7.5
seconds would mean you are on the 270 degree radial.
The Solution
You decide to triangulate your position using two radio
transmitters located near the Rocky Mountain Regional airport and
Denver International Airport to triangulate your position.
These navigational aids (NavAids) are called VHF Omnidirectional
Radios, or VORs. The cache is located within reach at the
intersection of two lines radiating from each of the two
VORs. Use the attached waypoints as references (which are the
real-life locations of these navaids) to triangulate your
position.
- The elapsed time while receiving the BJC VOR is 4.425
seconds.
- The elapsed time while receiving the DEN VOR is 5.712
seconds.
Given Information
- The Earth is flat.
- Use only True North, not magnetic North
- Electromagnetic Radiation travels at the speed of light,
meaning the time it takes for the radiated signal to reach you is
negligible.
- For the sake of triangulation, your aircraft is hovering in
place, as a helicopter.
- You can reach the final cache while your feet are firmly
planted on the ground.
- Your location is within 40 statute miles of both VORs.
- Because triangulation is difficult to pin point without some
serious math, the last digits of the final location are:
N DD MM.M56
W DDD MM.M55
Helpful Hints
Though it is not required, a Denver Terminal Area Chart and some
knowledge of how to use it could be quite useful (Online version of
this chart can be found at http://skyvector.com/ by selecting the
"Charts" button, then selecting the "TAC" button, and clicking on
the box around the Denver area). A map that is drawn to scale
with the two reference points (VORs) precisely marked will suffice
(Google Earth or MS MapPoint could be used).
If you're not afraid of a computer, you can try using the tools
at this site. However, I tested and could achieve an accuracy of
about 170 feet (close enough when you're flying, but could leave
some folks frustrated when looking for something this small), and
you will have to do some conversions: http://www.movable-type.co.uk/scripts/latlong.html.
You can check your answers for this puzzle on
GeoCheck.org:
Room enough for small trade items and travel bugs.
Congratulations to animjason and Sassydil for a neck & neck race
for the joint FTF!