On the horizon

It's been cold and clear recently, leading to great visibility.  A few days ago, Tim mentioned that he had seen the Farallon Islands from Meyers Grade Road (north of Jenner).  I haven't seen them from north of Point Reyes, so I decided that it would be a fun way to start the New Year.

This morning we drove up to Meyers Grade Road and looked south.  You might have to strain your eyes in this first picture, but there they were!  Point Reyes is to the left, and the Farallon Islands are on the far right.  (Click on the picture for a larger version.)

 

To make it easier, here's a highly-cropped and contrast-adjusted image: 

 

It was fun to see the Islands, but this started my mind wondering.  Why, exactly, can't I see them from Bodega Head?  Or can I?

On Meyers Grade Road, we were slightly farther west than Bodega Head, and we were at a higher elevation.

I'll address the "westerly" position, or the angle, first.  I had to figure out whether it was possible that the Farallon Islands would be hidden behind Point Reyes when viewed from Bodega Head.  To do this, I used Google Earth:

 

Although it was close, it appeared that the Islands could be viewed just past the tip of Point Reyes.

Then I had to consider elevation.  We estimated that we stopped at about 1,000 feet in elevation on Meyers Grade Road (much higher than Bodega Head).  Could that make enough of a difference?

This brought me to a tremendous lesson in geometry and physics, not all of which I can explain myself.  But the viewable distance to the horizon depends a great deal on your viewing height (hence the reason for tall lighthouse towers and crow's nests on ships).

To calculate whether you'll be able to see an object on the horizon, you need to know your viewing height, the distance to the object, and the height of the object.  Of course, there's a formula behind this that has to do with the curvature of the earth, but I also found a very handy calculator online.

For example, what's the highest point on Bodega Head?  How far away are the Farallon Islands?  What's the highest point on the Farallon Islands?

Ready for the answers?

Highest point on Bodega Head = 265 feet.

The Farallon Islands are ~42 miles from Bodega Head.

The highest point on the Farallon Islands is 338 feet.

When I plugged these numbers into the calculator, I was excited.  According to the numbers, if I was on Bodega Head's highest peak, then I should be able to see the Islands.

I had never seen the Farallon Islands from Bodega Head, and I had no idea if the numbers would be correct.  But off I went at sunset, up to the highest peak.  When I made it to the Overlook, I turned to the south, raised my binoculars, and saw this:

 

That's Point Reyes off to the left, and the Farallon Islands on the right!

I've been looking at Point Reyes from Bodega Head for years (ten to be exact), but usually from a lower elevation.  This is the first time I've realized that you could see the Farallon Islands from Bodega Head, so I wondered how sensitive the view was to a difference in elevation.

I walked down only about 25 feet or so, and this is how the view changed:

 

You can see that the Islands are just barely visible from Bodega Head.  You really need to be at the highest peak (the Overlook) to see them.  If you drop in elevation just a little bit, they start to disappear.  (And viewing conditions need to be good.)

I was glad to see the Islands from Bodega Head.  But a question remained.  What exactly was I seeing?  Here's a close-up of the view from Bodega Head:

 

So which part of the Islands is this?

To help with this puzzle, here's a better view of the Farallon Islands taken from just above Limantour Beach in November 2014: 

 

This is tricky, but my best guess right now is that the view from Bodega Head is the peak of Southeast Farallon Island.  My hypothesis is that although 265 feet is enough to see the peak, it's not high enough to see more of the Islands.  It begs the question, how much higher would we need to be to see more?  I'm not exactly sure, but it conjured up funny images in our heads — e.g., Eric suggested bringing a tall step ladder to the Overlook on Bodega Head to see if we could get high enough for a better view!  ;)

It's interesting that Bodega Head is just westerly enough, just close enough, and just high enough to provide a view of just the tip of the Farallon Islands.  Check it out sometime when the conditions are clear!

P.S.  If you have a different hypothesis for what portion of the Farallon Islands are visible from Bodega Head, please say so!