Why isn't the sun's rate-of-change in elevation constant?

[irotas]

I have been experimenting with the 'solpos' library from NREL, which is a very nice library for computing solar position (and related) calculations given date/time and coordinates.

One thing that surprised me is that the sun's rate-of-change in elevation (angle from the horizon) is not constant throughout the day. In fact, the elevation changes about 7-8 times faster at sunrise/sunset than it does at solar noon.

Here's sample calculations for Toronto Canada for January 19, 2009:
07:52:00: azim=118.788 elev=0.109222
07:59:00: azim=120.007 elev=1.209
...
12:28:00: azim=179.905 elev=25.9437
13:18:00: azim=192.848 elev=24.9487

I'm sure there's some perfectly good trigonometric reason why this should be the case, but at the moment I haven't been able to come up with a good explanation.

Can anyone help unravel this mystery?

Thanks,
Adam

 

[mgb_phys]

You are measuring elevation from the horizon - you are not at the centre of the Earth.
Draw the picture - it will help ;-)

 

[russ_watters]

The sun moves across the sky at a constant rate, but in two dimensions, not just one.

 

[irotas]

Is there really a simple picture to clarify this observation? I've been scribbling diagrams all day and they all end up terribly complex and totally unenlightening. Any advice on how to draw this out?

 

[irotas]

The sun moves across the sky at a constant rate, but in two dimensions, not just one.

Yeah, I realized that a while ago, but I'd still like to be able to draw a simple picture to help illustrate the point. I might end up having to demonstrate this to higher-ups in my company so I want to make absolutely sure I've got a simple clear picture that they can intuitively understand.

I'll continue to work on this, but any guidance is certainly appreciated.

 

[russ_watters]

The diagram would be a sinusoidal arc, depicting the motion of the sun across the sky as viewed by a person standing on the earth, facing south. The sun travels along that arc at a constant rate and at any point in the arc, you can draw a triangle and do some trig to figure out how fast it is moving in the x and y directions.

 

[irotas]

Thanks for the help!

Here's the diagram I came up with (following Russ's suggestion):
http://public.irotas.fastmail.fm/Solar_elevation.png

Any comments/suggestions?

 

[russ_watters]

You got it!