G-bob, the skywriter, had some treasure to hide away for safekeeping. His only reliable means of recording position was on his skywriting biplane. So on a dead calm, cloudless May 6th 2004 near solar noon, he enlisted the help of his pit crew, Paul and Erik, in a scheme to hide the loot and record the position.
G-bob rose into the sky and leveled off at exactly 1000 feet (elevation above ground). He started his smoke trail. He recorded the position of the start of the smoke trail as:
N44 49.752, W93 09.750
He proceeded in a straight line until shutting off the smoke at:
N44 47.229, W93 07.800
He looped around (remaining at 1000 ft elev) and started the next smoke trail at:
N44 47.229, W93 10.830
This time, he recorded the bearing as 32.257 degrees (clockwise from north) and he kept the smoke stream running for 4 miles.
At exactly 1:09:13 pm, local time, Paul and Erik, looking up, saw that G-bob had drawn an "X" in the sky. They noticed that the "X" was painted, in shadow, on the ground as well. So they hustled to the spot and hid the treasure where the "X" marked the spot.
Well, when they met up at the airport a bit later, G-bob was having trouble with the math to figure where the spot was, and Paul and Erik, had (surprise, surprise) totally forgotten the location as well.
Giveaway hint (still requires a little calculator work):
Look at this website:
http://www.wherearewe.co.nz/greatcircle.html
You'll need to move to and from deg min sec.xx format, but the tool in the website will calculate the intersection of the smoke "X" for you.
Where the shadow contacts the ground is based upon the angle of the sun at that time. It's trigonometry and the value is: (elevation divided by the tangent of the sun angle ). You'd need to figure out that shift north (in feet) and compute a waypoint projection at zero degrees to find the final coordinates. WHEW! - of course, any engineers out there are not allowed to use a web tool - excel should be enough.