I need some math help.

[Dave McClung]

I need some help with solving a very practical problem. I can visualize the geometery, but I have not figured out the math.

When I sit at our kitchen table, I am at 48 ft above sea level. When I look at 177 degrees I can see the outline of a mountain in the distance.

When I draw a line on a Topo Map at 177 degrees, I see "The Rockies" at 42.89 miles are 3,454 feet high.

Mt. St. Helens is at 75.26 miles and is 7,200 feet hight.

Which mountain am I seeing? I realize that I am seeing The Rockies in the foreground, but I think the outline is Mt. St. Helens.

[Barbara Moulton]

Ohhh...my head hurts.

I'll let smarter minds than mine figure this out. Math was always a poor subject for me.

[Jon Twitchell]

Dave,

I'm not clear on what you mean by 177 degrees. Is that 177 degrees above the horizon?

In any case, I did the elevation/distance trig for both mountains, and have attached the diagrams below. I used an online pythagorean theorem calculator, found here: http://www.1728.com/pythgorn.htm

Peace,

Jon

[Dave McClung]

Thanks, Jon. That is exactly what I needed. Your calculations confirm that I can see Mt. St. Helens eventhough The Rockies are between my home and Mt. St. Helens.

The calculations also show that on a very, very clear day I should be able to see the peak of Mt. Hood above Mt. St. Helens. Mt. Hood is directly behind Mt. St. Helens at 138 miles. It is almost 12,000 feet tall. It will require a day with very low humidity for me to be able to see that far, but now I know where to look.

My reference to 177 degrees was to degrees on a compass. 177 degrees is south southeast. (If a pilot were flying due north, he would refer to it as 5:30 o'clock low.)

[Jon Twitchell]

Ah...I see...I didn't think of the compass bearing...I was trying to make that fit into my triangle somewhere, and couldn't! :)

Grace and Peace,

Jon

[Jon Twitchell]

Of course, my calculations don't take into account the curvature of the earth, which would theoretically come into play at some point along the way. (I think it would be negligible at these sorts of distances, but I don't know for sure.)

(I did subtract out the 48 feet from each side of the equation...but I think that probably is pretty negligible!)

Peace,

Jon

[Pete Vecchi]

OK, guys, I am REALLY mathematically challenged, but I think that the curvature of the earth probably DOES come into play based on an experience of mine as a teenager.

I was visiting the warren Dunes in Michigan -- on the eastern shore of Lake Michigan. It was a very clear day, and all I saw when I looked out at the lake was water. However, when I climbed to the top of the tallest sand dune and looked across the lake, I could see the Sears Tower and a couple of other buildings across the lake in Chicago.

I don't know how far above or below sea level that area is right off hand, but I was always told that it was the curvature of the earth that made it impossible for me to see the buildings from the shore of the lake, but posible from the top of the dune because that gave me a better angle viewing over the curvature of the earth.

I may be WAY off base here because with this math stuff I am WAY out of my league. All I know about a hypotenuse is that it can be a dangerous animal.

[Jon Twitchell]

My only thought about the curvature of the earth here is that the mountains in question are quite tall...

perhaps I should fire off an email to my father the physics teacher.... :)

[Dave McClung]

You are right that the curvature of the earth would impact the calculations by a few feet, but it isn't a practical difference here.

Every since I moved to Gig Harbor I have wondered about the mountains I can see. Mt. Rainier is obvious, but the other mountains are not so obvious. Recently, I have been comparing the pictures I take from my home, the Google Earth map, the Topo Map and what I can find on the ground.

The attached photo shows the scene I have been studying this week. Mt. St. Helens is the one in the center. It has snow on the peak.

[David Ward]

Recalling a bit of trivia from my few months working in a highway survey party some 25 years ago, I was told that the curvature of the earth accounted for about 8 inches per mile. I never questioned that, nor have I even thought about it since then ... until now. It was just one of those numbers to remember, like the number of square feet in an acre (43,560) that might help you win in a game of Trivial Pursuit.

The mathematical calculations would not take into consideration any "mirage" effects caused by temperature differences in the atmosphere layers, but whose eyesight is that good anyway!

:fav03 Guess I need to pull out the geometry and trig books to see if the survey party chief was pulling my leg ....

[Joel Merrill]

Did you live there when Mt. St. Helens erupted? That would have been interesting to see.

Joel

[Dave McClung]

Thanks, David
I could never have guessed even a "ballpark" number, but I would have said that from my house to Mt. St. Helens would have made about 100 feet of difference. I was a little too high with my estimate.

I also thought about the "mirage effect" but humidity makes more of a difference than temperature. On a warm, moist day, I can't even see the mountains. One a cold, dry, crisp day, I can see them clearly.

Now that I have figured out exactly where to look, I think I will probably be able to see Mt. Hood sometime this winter. I have a good spotting scope.

[Dave McClung]

Did you live there when Mt. St. Helens erupted? That would have been interesting to see.

Joel

No. We were still in Texas when Mt. St. Helens erupted ("the big one").

[David Ward]

[QUOTE=Dave McClung
I also thought about the "mirage effect" but humidity makes more of a difference than temperature. On a warm, moist day, I can't even see the mountains. One a cold, dry, crisp day, I can see them clearly.
[/QUOTE]


What made me think of the "mirage effect" was a scientific explanation of a phenomenon in the northwestern NC mountains known as the Brown Mountain Lights. There's an overlook on the Blue Ridge Parkway where we used to go to look for them during the fall of the year. Another park ranger did a program on "the lights" when I worked there and she talked about the temperature differences in the layers of air that bent light emitted from distant cities back down toward earth. The cold, dry crisp nights in October and November produced the best chance for seeing them.

I'll admit to seeing them twice out of dozens of attempts, so I know they exist. I cannot explain them, and I remember getting chills :o that were not temperature related when I saw them.

I enjoy wintertime hiking because of the better visibility you mentioned. Now wintertime camping :fun01 is another issue . . . .