How much shade does that north-facing slope get?

Juli has a back yard area that slopes to the north that she has designated the "native plant zone". I'm in charge of that part. The native plant zone contains the garage (with deep shade around it due to close proximity of a retaining wall and the garage eaves), a partially paved alley, lots of weeds, and ivy from the neighbors. Juli gets the roses and grass in the main part of the yard that is visible from the house.

A tall, roofed, patio structure sits at the top of the native plant zone, completely eliminating any possibility of sun at this time of year. However, it looks like it does get summer sun, as shown in the Google maps satellite image below. (Most good satellite imagery will be around noonish so as to eliminate large shadows. Summer time is least likely to have clouds, so it's not surprising that the image appears to have been taken near noon in summer.) Her's is the house at the center of the image. The patio roof is the bright white horizontal band.  Above it is the garage and sloped hillside that is designated as the native plant zone.

When the angle of the sun in the sky equals the angle from the bottom of the slope to the top of the patio roof, then the sun will be shining at the bottom of the slope.  The time of year that this occurs might influence my plant choices, so let's be a little more rigorous about when we can expect sun to peak over the edge of the patio roof and down the hill. Since the hillside is almost entirely north facing, I don't have too many complications with this calculation - If the slope were NW to SE I might have to think more about morning sun versus afternoon sun. I'll just think about noon time sun and remember that the sun always has a southerly direction our latitude.

Measuring the slope of the hill
There's a couple iPhone apps to measure angles out in the field. I tried one called Sextant that doesn't really do the job very well for me. I should have known better when the blurb read "This shiny new gold sextant would make a pirate proud" I next downloaded a more sophisticated app called Clinometer by Peter Breitling which was free for a short time and immediately after my download popped up at $0.99. Finally, there's a visual clinometer called SlopeView by Sten Kaiser which seems a reasonable choice (also $0.99) which I may try if the previous two don't work out. I'll use one of them to take a field measurement of the angle from the bottom of the hill to the top of the patio.

Once I know the slope of the hill, the question then is at what time of year the sun will get to that angle in the sky.  Here's how I'll figure it out:

Maximum and minimum sun angle
I'll figure the relationship between time of year and angle of the sun using this method: I found the latitude of Juli's house using Google maps*. If the earth had no tilt, then the sun would shine directly down on the equator at 90 degrees and (90 - Juli's latitude) would be the angle of the sun to her house. But, there is a built in tilt of the earth is 23.5 degrees and we can take that into account as follows:

During winter solstice the northern hemisphere is tilted back at an angle from the sun so the sun shines at (90 - latitude - 23.5) degrees.

During summer solstice the northern hemisphere is tilted toward the sun so the sun shines at (90 - latitude + 23.5) degrees.

Interpolating linearly between solstices we get:

Date      Sun Angle
1/21/2010 40.99
2/21/2010 48.95
3/21/2010 56.14
4/21/2010 64.10
5/21/2010 71.80
6/21/2010 79.77 Summer solstice
7/21/2010 72.06
8/21/2010 64.10
9/21/2010 56.14
10/21/2010 48.43
11/21/2010 40.47
12/21/2010 32.77 Winter solstice

So, while I have yet to actually measure the angle of the hillside+patio roof, it is reasonable that it's entirely shaded now (when the sun is only at an angle of 40 degrees) since reasonable slopes probably don't exceed 45 to 50 degrees or so. However, in summer, it's a rare north-facing hillside that doesn't get at least a little sun when the sun has a steep sun angle like ~80 degrees. Up next to steep north-facing cliffs or edges of houses it will still be shaded at noon, but little else will be.

I guess this is all obvious stuff, since my major conclusion is that north facing slopes with reasonable angles of repose still get noontime summer sun.  Still, actually knowing a date when it will get sun can help guide plant selection. Of course, I'm ignoring the sun angle at times other than noon - the sun may rise north of east and set north of west in summer, thereby giving morning or evening light on north-facing slopes. However, we all know that morning or evening sun is less intense than noon sun.

Calculating hours of sunlight is a more difficult task. I found an iPhone app called DaylightCal that may suit my needs.  More later when I find out about that app.

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*It's buried in the Google Maps URL or link. So if I go to Google map San Pedro, CA and then look closely in the URL or at the embedable link, I'll see a bit of text that looks like ll=33.722696,-118.29117 buried mid way through the address. From that little bit of info I can glean that San Pedro, CA. is at 33.722696 degrees north latitude.