StanFoster
Active Member
- Joined
- Nov 16, 2003
- Messages
- 17,139
- Location
- Paxton, Il
- Aircraft
- Helicycle N360SF
- Total Flight Time
- 1250
Vance just posted his amazing trip to 12,500 feet msl. His first picture which I posted here had me wondering how far the horizon was as it was so clear and you could see the curve of the earth, assuming it wasnt in his lenses.
Anyway I worked the problem out and posted it in the two drawings. By the way...the drawings angle is exaggerated for clarity. I was waiting on glue to dry, but this only took a few minutes.
First known is the radius of the earth...rounded off here to 4000 miles.
2nd known is Vances height above the earth...12500 feet..or 2.367 miles.
From this one can compute the angle from Vances eye perpendicular to the center of the earth and a line tangent to the earth...which will be the horizon.
The 2nd drawing shows this tangent line makes a right angle with the radius line of the earth.
We know that that line at the horizon to the center of the earth is 4000 miles...and the other side of this right triangle reaching Vance from the center of the earth is 4002.367 miles.
If everyone remembers the sine/cosine/tangent rule.....
Old Hags -------- Opposite/Hypotenuse = Sin
Always Have -------- Adjacent/hypotenuse = Cosine
Old Asses ------- Opposite/adjacent = Tangent
then this triangle can be computed quickly.
4000/4002.367 = Sin of the angle
.9994086 = sin
The angle Vance has to look down from perpendicular to the earths center is 88.02922 degrees.
Now the first drawing breaks down with another right triangle whose base one side points from the center of the earth to Vance....a line perpendicular to this that intersects the horizon visible by Vance.
This time we take the tangent of the angle opposite 88.02922799 degrees and this comes out to and this is 1.97077 degrees.
Tangent of 1.97077 degrees equals 0.034410031
Multiply this by 4000 and 137.64 miles is the answer.
I did this in haste, oriiginally posted an error by takng the tangent of the wrong angle in haste. I edited out the one drawing.
Stan getting back to gluing...
Anyway I worked the problem out and posted it in the two drawings. By the way...the drawings angle is exaggerated for clarity. I was waiting on glue to dry, but this only took a few minutes.
First known is the radius of the earth...rounded off here to 4000 miles.
2nd known is Vances height above the earth...12500 feet..or 2.367 miles.
From this one can compute the angle from Vances eye perpendicular to the center of the earth and a line tangent to the earth...which will be the horizon.
The 2nd drawing shows this tangent line makes a right angle with the radius line of the earth.
We know that that line at the horizon to the center of the earth is 4000 miles...and the other side of this right triangle reaching Vance from the center of the earth is 4002.367 miles.
If everyone remembers the sine/cosine/tangent rule.....
Old Hags -------- Opposite/Hypotenuse = Sin
Always Have -------- Adjacent/hypotenuse = Cosine
Old Asses ------- Opposite/adjacent = Tangent
then this triangle can be computed quickly.
4000/4002.367 = Sin of the angle
.9994086 = sin
The angle Vance has to look down from perpendicular to the earths center is 88.02922 degrees.
Now the first drawing breaks down with another right triangle whose base one side points from the center of the earth to Vance....a line perpendicular to this that intersects the horizon visible by Vance.
This time we take the tangent of the angle opposite 88.02922799 degrees and this comes out to and this is 1.97077 degrees.
Tangent of 1.97077 degrees equals 0.034410031
Multiply this by 4000 and 137.64 miles is the answer.
I did this in haste, oriiginally posted an error by takng the tangent of the wrong angle in haste. I edited out the one drawing.
Stan getting back to gluing...
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