Tilt Angles for high and low latitudes previous page: comparing tilts

This page is part of a series on tilt angles. An intro is at tilt angle. The other pages are:
load tilts,
optimal tilt,
tilt deviation, and comparing tilts.

Important! This page is a continuation of comparing tilts and all the tilt angle formulas on these two pages as well as the method for evaluating these formulas are explained on optimal tilt.

This page only covers cities in the Northern Hemisphere that are below 25 North and above 50 North. These latitudes are outside of the Macslab tilt formula's range (see optimal tilt). All solar panels are pointed due South (see comparing tilts).

Comparing Formulas - Latitudes outside of 25 - 50

In general, the Macslab tilt tended to be quite a bit too steep in the latitudes above its range of comfort (above 50 North) and too shallow in the latitudes below its range (below 25 North).

City (lat) ML Tilt MT kWh/ m2/ day Cen. PVW Tilt PWT kWh/ m2/ day %MT/ PWT Lat. Tilt kWh/ m2/ day %LT/ PWT elev. (met,ft)
London (51.2N) 42 3.15 34.5 3.17 122% 3.07 148% 62m, 203ft
Berlin (52.5N) 39.9 3.06 33.5 3.07 119% 2.96 157% 49m, 161ft
Dublin (53.4N) 43.7 2.90 34 2.93 129% 2.81 157% 85m, 279ft
Annette (55.1) 45 3.18 39 3.19 115% 3.10 141% 34m, 112ft
Helsinki (60.3N) 48.9 3.08 39.5 3.11 124% 2.97 153% 56m, 184ft
Fairbanks (64.8N) 52.3 3.43 51 3.43 103% 3.36 127% 138m, 453ft
The cities countries are named and the table abbreviations are explained here: 2.

Shallower Tilts up North

On optimal tilt we explained why higher latitude, cloudier places tend to need shallower tilts than you might expect. This trend was demonstrated on the first page on comparing tilts) and it also held true for all the high latitude places we investigated except Fairbanks, Alaska.

Fairbanks (Alaska, USA) seems to have sunnier springs and falls than European cities at similar latitudes and I think this might have something to do with the discrepancy. In particular, I wonder if - for the part of the year outside of winter at least - it is less cloudy than Northern Europe is. More in this footnote (1).

Steeper Tilts Closer to Equator

The cities that I investigated between say 15 North and 25 North seemed to do best with an at-latitude-tilt.

The cities around 10 North and below did best with a tilt steeper than at-latitude (most of these lower latitude cities didn't make it onto the table).

The Macslab annual optimal tilt is always lower than the at-latitude tilt and so it appears that once you leave the Macslab comfort range, the closer you get to the equator, the more "too shallow" a tilt found with the Macslab formula will be.

City (lat) ML Tilt MT kWh/ m2/ day Cen. PVW Tilt PWT kWh/ m2/ day %MT/ PWT Lat. Tilt kWh/ m2/ day %LT/ PWT elev. (met,ft)
Trivandrum (8.5N) 9.6 5.72 11 5.72 87% 5.11 77%
Rivas (11.4N) 11.8 5.11 14 5.11 84% 5.11 81% 53m, 174ft
Catacamas (14.9N) 14.4 5.11 15 5.11 96% 5.11 99%
Mumbai (19.1N) 17.6 5.30 21.5 5.31 82% 5.30 89% 14m, 46ft
Honolu (21.2N) 19.2 5.72 20.5 5.72 94% 5.72 103% 5m, 16ft
Aswan (24N) 21.3 6.81 24.5 6.82 87% 6.82 98% 194m, 636ft
The cities countries are named and the table abbreviations are explained here: 2.

I've wondered about this relative (ie: in comparison to Macslab's tilts) "steepening" of the tilts as the cities got closer to the equator. Could it be related to rainy seasons? Rivas's rainy season seems to be from May to October.

I used PV Watts (see optimal tilt) to see about how much solar radiation fell on Rivas throughout the year (using the "two-axis tracking" setting so that the solar panels constantly follow the sun) and found that sure enough, the most sun comes from December through May, peaking January through April.

At Rivas's latitude (11.45 North), at solar noon the sun is about 55 above the horizon on December 21 (winter solstice), 59 on January 21, 68 on Feb. 21, 79 on March 21 (spring equinox), 90 (overhead) on April 20 and 99 (aka: 81 above the horizon but in the Northern part of the sky).

The appropriate solar noon optimal tilt angles would then be (for Dec. 21 through May 21): 35, 31, 22, 11, 0 and -9 (aka: 9 but facing towards the North). Taking the average of these values, I get 15. The average of the very sunniest months (from Jan through April) would be 16. The PV Watts optimal annual tilt was 14.

So, my hypothesis for why places like Rivas did best with tilts steeper than you might expect is that the rainy season and the position of the sun in the sky (highest in spring/fall, equally low in winter and summer but in the summer pointing in the "wrong" direction for a South-facing tilt) conspire to favor winter tilts more than they are favored at higher latitudes. But, its just a theory.

If this page has been a help to you
please recommend it with Google+ below:

 

 

Footnotes

1. I used the PV Watts calculator (see optimal tilt) to see about how much solar energy falls on solar panels with "two-axis tracking" in Helsinki (60.3N) and Fairbanks (64.8N).

The impression I got was that Fairbanks is actually pretty sunny (at least 6 kWh/m2/day and much more in several months) from March through August and still sort of sunny (about 4.5 kWh/m2/day) in September but very unsunny (less than 2 Wh/m2/day and some months much less) the rest of the year. Helsinki's sun, however, seemed to be more evenly distributed over the year (over 7 kWh/m2/day from May through July, over 5 but less than 6 kWh/m2/day in August and April, less than 4 kWh/m2/day in March and September...). Although from November through January, Helsinki also got very little (less than 1 kWh/m2/day) solar radiation.

This made me guess that Helsinki spread its cloudiness out more over the spring and fall than Fairbanks did and that Fairbanks was not as overcast as Northern Europe (except maybe in winter when cities above 60N latitude hardly get any sun anyway because the days are so short).

If this is true, then it would make sense that Fairbanks would have a tilt that compromises primarily between the direct radiation falling in the spring/fall and the direct radiation falling in the summer and disregarding diffuse radiation but that Helsinki's tilt would compromise between both types of radiation falling in the spring/fall and the summer.

In both of these places, the appropriate tilt for solar noon on a sunny day (mostly direct radiation) would be about 40 at the summer solstice solar noon, 60 at the equinoxes and over 80 at the winter solstice. The PV Watts optimal annual tilt for Helsinki was 39.5. It was 51 for Fairbanks.

The Helsinki tilt was in keeping with the other Northern European tilts, suggesting it took diffuse radiation into account (see optimal tilt). The Fairbanks tilt was much steeper and was right in the middle between the best tilt to get direct radiation at solar noon in the spring/fall and the best tilt to get direct radiation at solar noon in the summer.

I was not able to find any data that showed how much diffuse versus how much direct radiation cities received each month and so I am not at all sure my hypothesis is correct.

2. In this footnote, first the country's that contain each city in the two tables are named and second, the abbreviations in the tables are explained. The solar radiation data was found using the PV Watts calculator (see optimal tilt for an intro; the PV Watts calculator is linked to in footnote #1 on that page; also in that footnote, is a description of how I used PV Watts to come up with an optimal annual tilt angle (Cen. PVW Tilt).
The cities' locations are as follows:
Rivas, Department of Rivas, Nicaragua
Mumbai (Bombay), Maharashtra, India
Honolulu, Hawaii, USA
Aswan, Aswan Governorate
London, England, Great Britain
Berlin, Berlin (its its own state), Germany
Dublin, Leinster, Ireland
Annette, Alaska, USA
Helsinki, Uusimaa, Finland
Fairbanks, Alaska, USA

The abbreviations are explained as follows:
City (lat) = City (latitude in degrees)
MT kWh/m2/day = how much solar radiation in kilowatt-hours was gathered per square meter per day (in an average year) with the tilt angle chosen using the Macslab annual optimal tilt formula. [(.76 * latitude) + 3.1 (see optimal tilt)]
Cen. PVW Tilt = the "center PV Watts tilt" - it is the optimal annual tilt angle I found using the PV Watts calculator (my method is explained in the second part of footnote #1 of optimal tilt).
PWT kWh/m2/day = how much solar radiation in kilowatt-hours was gathered per square meter per day (in an average year) with the PV Watts optimal annual tilt (the Cen. PVW Tilt).
%MT/PWT compares the Macslab optimal annual tilt with the PV Watts optimal annual tilt (the Cen. PVW Tilt). It was found this way: %MT/PWT = [((Macslab Tilt Angle)/(PV Watts Tilt Angle)) * 100%]. For example, for Cairo, the Macslab Tilt Angle was 26 and the PV Watts Tilt was 24.5, so %MT/PWT = [(26/24.5) * 100%] = 106%, meaning the Macslab tilt was a little steeper than the PV Watts tilt.
Lat. Tilt kWh/m2/day = how much solar radiation in kilowatt-hours was gathered per square meter per day (in an average year) by tilting "at-latitude" (tilting, for example, at 30.1 in Cairo because Cairo's latitude is 30.1 North).
%LT/PWT compares the "at-latitude" tilt with the PV Watts Tilt. It was found this way: %LT/PWT = [(("At-Latitude" Tilt Angle)/(PV Watts Tilt Angle)) * 100%]. For example, for Cairo (30.1 North), the "at-latitude" tilt is 30.1 and the PV Watts tilt is 24.5, so %LT/PWT = [(30.1/24.5) * 100%] = 123%, meaning the "at-latitude" tilt is considerably steeper than the PV Watts tilt.
elev. (met,ft) = "elevation (meters, feet)" - the elevation (aka: "altitude") above sea level is given, first in meters and then in feet.

 

If this page has been helpful
please recommend it with Google+ below:


Share |