Hi,
This gets a little more complicated because the sun drops in elevation before and after noon -- so using the noon sun elevation of 26.5 degrees on shortest day of the year at 40 lat will result in shading the 2nd row before and after noon.
The spacing equation out of "solar Energy Handbook", Kreider is:
D = sin (SunElev + ColTilt)*(Lc)/sin(SunElev)
Where:
D is distance between the front edge of the first row of collectors and the front edge of the next row.
ColTilt is the collector tilt angle from horizontal (18 deg in your case)
SunElev is the elevation angle of the when it is the lowest you want to design for (see below)
Lc is the length of your collector -- I'll assume 96 inches -- you can redo the calc if its more or less.
To figure out the sun elevation, get a SunChart free here:
http://solardat.uoregon.edu/cgi-bin/SunChart.cgi
for your location. This is a great thing to have on hand -- it gives you the solar bearing and elevation for every minute of the year.
To calc the minimum SunElev I'll assume you want the collector to work without shading form 9am to 3pm on Dec 21 (shortest day of year and lowest sun). For 40 deg lat, the sunchart gives a SunElev of just under 15 degs at 3pm on Dec 21.
The solar elevation at noon on Dec 21 at 40 lat is 26.5 degs, so the sun drops from 26.5 elev at noon to 15 degs at 3pm and 9am.
So, D is then:
D = sin(15 deg +18 deg )(96 inches)/sin(15 deg) = 200 inches
Remember this measured from where the front edge of the first row of collectors hits the roof to where the front edge of where the 2nd row of collectors hits the roof.
This scales directly with the lenght of your collector, so if your collector is really 48 inches long, D would be (48/96)(200) = 100 inches.
If this seems like too much spacing, you could just shorten the spacing up a bit and tolerate some shading on the 2nd and 3rd rows.
For example, if you were willing to tolerate some shading in mid winter -- say from about Nov 1 to the end of Feb, the 200 inches goes down to 155 inches.
This may not be a big sacrifice, as the 18 deg tilt is not very optimal for winter anyway.
Hope that makes sense?
Gary