Impact of Tilt Angle intro page: tilt angle

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.

On optimal tilt we discuss several different methods for finding the optimal tilt angle. On this page we wonder how big a deal the optimal tilt angle really is.

I've made a couple of charts examining how much solar energy you lose if:
(1) you tilt higher or lower than the optimal tilt, or if
(2) you point your solar panels to the East or West of true South (or true North if you're in the Southern Hemisphere - although all the cities I investigated are in the Northern Hemisphere).

I also look at how much extra solar energy you gain with two-axis tracking or a seasonally adjusted tilt angle (this comparison is also discussed in the first section).

The cities investigated in the tables are all in the Northern Hemisphere and range from 11.4 North to 64.8 North. I used the PV Watts calculator to get the data for the tables (see optimal tilt).

General findings

After we discuss full tracking and seasonally adjusted tilts, the first part of this page shows that for latitudes from like 20 North through 50 North, a tilt equal to the tilt of most medium-pitched roofs often does as well or almost as well as an optimal annual tilt.

The second half of this page shows for latitudes from about 20 North through 50 North, pointing to the Southeast or Southwest of (aka: 45 away from due South)often loses you about 6 or 7% of your annual solar energy.

Pointing to the East or West (aka: 90 away from due South) at those latitudes will lose you so much solar energy that you are generally better off to have no tilt (and thus not be pointing in any direction) and just accept the approximately 10% loss in solar energy that usually comes with laying your solar panels out horizontally (no tilt) at those latitudes.

1. Full Tracking, Seasonally Adjusted Tilts & Optimal Annual Tilts

I didn't show the math in the table (below), but according to my analysis of the data, in most of the 11 cities I investigated, two-axis tracking (or "full-tracking" - when your solar panels constantly follow the sun, maximizing the solar radiation gathered) gathers about 20% more solar energy than an optimal annual tilt does. However, in Tuscon, Boulder and Fairbanks, the full tracking did closer to 30% better than the optimal annual tilt.

Solar tracking is generally not practical for most small phototovoltaic systems and so people usually just have to choose between a seasonally (or monthly) adjusted fixed tilt or a permanently fixed tilt.

City (lat) FT. kWh/ m2/d Opt. kWh/ m2/d (Tilt) Hor. kWh/ m2/d %Hor./ Opt. %Low/ Opt. %Med./ Opt. %Steep/ Opt.
Rivas (11.4N) 6.38 5.11 (14.0) 4.98 97.5% 100% 96.9% 88.6%
Miami (25.8N) 6.78 5.26 (24.5) 4.89 93.0% 98.9% 99.6% 95.2%
Cairo (30.1N) 7.15 5.68 (24.5) 5.26 92.6% 98.6% 99.6% 95.1%
Tuscon (32.1N) 9.21 6.59 (27.5) 5.78 87.7% 96.2% 100% 97.7%
Atlanta (33.6N) 6.76 5.19 (30) 4.66 89.8% 97.1% 100% 97.3%
Boulder (40N) 7.58 5.56 (38.0) 4.62 83.1% 93.2% 99.3% 99.5%
Madrid (40.5N) 6.41 5.08 (33.0) 4.43 87.2% 95.7% 100% 98.2%
Boston (42.2N) 6.01 4.63 (37.0) 3.92 84.7% 94.0% 99.4% 99.1%
Seattle (47.4N) 4.91 3.83 (34.0) 3.34 87.2% 95.6% 100% 98.7%
London (51.2N) 3.80 3.17 (34.5) 2.77 87.4% 95.6% 100% 98.7%
Fairbanks (64.8N) 4.76 3.43 (51.0) 2.56 74.6% 86.3% 95.6% 99.7%
The cities countries are named and the table abbreviations are explained here: 1.

For four cities (latitudes 30 through 42 North),

I compared a seasonally adjusted fixed tilt with an optimal annual tilt (the chart is at the bottom of this page). I found that in three cities the seasonally adjusted tilts gathered a little over 4% more solar energy per year than the optimal annual tilt, but in one city the seasonally adjusted tilts did about 8% better.

Optimal Annual tilt versus Roof

The chart at the left compares the average amount of solar energy gathered with two-axis tracking, an optimal annual tilt, no tilt (just laying your solar panels out flat) and a few common roof tilts.

[The cities countries are named and the table abbreviations are explained here: 1.]

The "no tilt" (Hor. for "horizontal" in the table) could also be representative of a solar panel on a flat roof. So, the table can give us a feel for how much solar energy we lose if we just mount our solar panels on four South-facing and typically-pitched roofs (from flat to steep) instead of giving them an optimal annual tilt (Opt.).

For the Low roof pitch, I used a tilt of 14 ("3 in 12" in roofer's lingo). My Medium roof pitch was 30.3 (7 in 12) and my Steep pitch roof was 45 (12 in 12).

As you might expect, solar panels on flat and low-pitched roofs did best in the more Southernly cities (where the optimal tilt angle is shallower anyway) and solar panels on steep-pitched roof did best in more Northernly cities (where the optimal tilt tends to be steeper).

Medium-pitched roof tilts did between 99 and 100% as well as an optimal annual tilt in every city except the most Southernly (Rivas - 11.4N) and the most Northernly (Fairbanks - 64.8N).

Excluding the "flat roof" (Hor.), the roof-tilts almost always did better than 95% as well as the optimal annual tilt. Exceptions were for low-pitched roofs in Boulder, Boston and espectially Fairbanks and high-pitched roofs in Rivas.

2. Pointing East or West of true South

So, if you have a pretty typically-pitched, South-facing roof, it might not be too terrible of an idea to just mount your solar panels or solar collectors on your roof (although, before you do anything so definite as mount solar panels, you should of course figure out how much solar energy you can expect to get at a given position and also make sure there are no shading issues by doing a solar site survey, etc.).

But what if your roof doesn't point due South (or due North if you are in the Southern Hemisphere - I've heard people live down there too...)? How much solar energy is lost with solar panels facing the Southeast or Southwest, or (God forbid) due East or West?

You'll recall (optimal tilt), that the sun is highest in the sky each day at solar noon and North of the Tropic of Cancer (about 23.5 North), the sun is always due South at solar noon (the sun is due North South of the Tropic of Capricorn - 23.5 South). So, optimal tilts generally point due South in the Northern Hemisphere (and due North in the Southern).

The table below investigates what happens if we point our solar panels somewhere other than due South. 45 Off represents pointing to the Southeast or the Southwest and 90 Off represents doing the unthinkable and pointing due East or West (see definitions). [There was always very little (if any) difference between being to the East or to the West of true South and so I averaged the values to save space.]

Shallower tilts better when you can't face the solar noon sun

It occurred to me that if you were not pointing due South, you would probably do better with a shallower tilt than the one that is optimal if you can point due South (a solar panel with a shallower tilt points less away from whatever direction it is not specifically pointing at and so if your solar panel is not pointing in the optimal direction...).

With this in mind, I decided to also examine what would happen if you tilted solar panels that were not pointing due South 25% or 50% lower than the optimal annual tilts for South-facing solar panels. As we will see, these shallower tilts improved things somewhat.

[I also looked at Southeast and Southwest tilts coupled with tilts steeper than the normal optimal annual tilt just to make sure that they did even worse than the normal optimal annual tilt. They did. To save space, I didn't include these steeper tilts in the table.]

City (lat) Opt. Tilt; kWh/ m2/ day Hor./ Opt. %45Off/ Opt. %90Off/ Opt. %25%L & 45Off/ Opt. %25%L & 90Off/ Opt. %50%L & 90Off/ Opt.
Rivas (11.4N) 14;5.11 97.5% 98.9% 96% 98.9% 96.9% 97.4%
Miami (25.8N) 24.5;5.26 93.0% 96.9% 89% 97.1% 90.1% 92.2%
Cairo (30.1N) 24.5;5.68 92.6% 96.4% 87.7% 96.7% 89.8% 91.5%
Tuscon (32.1N) 27.5;6.59 87.7% 95% 82% 95.1% 84.5% 86.4%
Atlanta (33.6N) 30;5.19 89.8% 95.4% 84% 95.8% 86.5% 88.3%
Boulder (40N) 38;5.56 83.1% 93.3% 76.5% 93.3% 79.2% 81.4%
Madrid (40.5N) 33;5.08 87.2% 94% 79.4% 94.4% 82.7% 85.2%
Boston (42.2N) 37;4.63 84.7% 93.4% 77.6% 93.5% 80.7% 82.7%
Seattle (47.4N) 34;3.83 87.2% 94.6% 80.5% 94.8% 83.4% 85.7%
London (51.2N) 34.5;3.17 87.4% 93.8% 79% 94.3% 82.3% 84.9%
Fairbanks (64.8N) 51;3.43 74.6% 91.5% 70.7% 91% 72.4% 73.5%
The cities countries are named and the table abbreviations are explained here: 2.
.

[The cities' countries are named and the table abbreviations are explained here: 2.]

From the table we can see that tilting to the East or West of true South caused more trouble at latitudes further removed from the equator.

Solar panels in Rivas (11.4N) only lost a little over 1% of their South-facing solar energy when they were facing to the Southeast or Southwest.

From there, things get worse as you go North and the optimal tilts get steeper.

By the time we've reached the cities between 40 North (Boulder) through 51 North (London), being 45 off results in a loss of around 6 or 7% of your optimal tilt solar energy.

And way up in Fairbanks (64.8N), these sort of shenanigans cost you almost 10%.

As the graphy shows, tilting 25% shallower than the normal optimal tilt generally improved the performance of the Southwest and Southeast facing solar panels by about half a percentage point.

However, with a 50% shallower tilt, the Southeast and Southwest facing solar panels did worse than with the normal tilt (to save space, I didn't inlcude this data in table).

Tilting due East or West is generally advised against, although as the case of Rivas shows, it isn't as big deal near the equator.

It seems worth noting that in every city I investigated (and this includes Rivas), you did better with no tilt than with the normal optimal annual tilt pointed due East or West. What's more, in every city, horizontal solar panels did better than a due East or West direction coupled with a tilt 50% shallower than the South-facing optimal tilt (recall that choosing a shallower tilt helps when you aren't facing the optimal direction).

This made me wonder if it was always the case that for solar panels facing due East or West, no tilt is better than any tilt. So, I spent some time looking at very low tilts.

Often, if you are facing due East or due West, you can't do better than horizontal with any tilt. However, sometimes it is possible to improve things very slightly with a tilt (Tuscon got 88% with a 5 tilt facing due East - that's .3% beter than just laying the solar panels out horizontally).

At any rate, if you have to face your solar panels due East or West, a horizontal tilt is about the best you can do and so, unless you are quite close to the equator, it seems that if you point due East or West, you can expect to lose about 10% of the solar energy you could've gotten with an optimal annual, South-facing tilt. Up in Fairbanks, you do much worse - losing about 25%!

Seasonally Adjusted versus Optimal Annual (the Table)

We close with the table discussed in the first section. It compares full tracking, seasonally adjusted tilts, optimal annual tilts and just laying the solar panels out flat (horizontal tilt).

City
(lat)
Full Track.; kWh/ m2/ day Seas. Tilt; kWh/ m2/ day %Seas. Tilt/ Full Track. Ann. Tilt; kWh/ m2/ day %Ann. Tilt/ Seas. Tilt Hor. Tilt; kWh/ m2/ day %Hor. Tilt/ Ann. Tilt %Hor. Tilt/ Seas. Tilt
Cairo (30.1N) 7.15 5.90 82.5% 5.68 96.3% 5.26 92.6% 89.2%
Atlanta (33.6N) 6.76 5.42 80.2% 5.19 95.8% 4.66 90.0% 86.0%
Madrid (40.5N) 6.41 5.52 86.1% 5.08 92.0% 4.43 87.2% 80.3%
Boston (42.2N) 6.01 4.83 80.4% 4.63 95.6% 3.92 84.7% 81.2%
The cities countries are named and the table abbreviations are explained here: 3.
.

For four cities in which the Macslab annual tilt angle formula was close to the PV Watts optimal tilt angle,
I decided to use the PV Watts calculator to check out the Macslab seasonal tilt recommendations (see optimal tilt for the background on PV Watts and the "Macslab" optimal tilt formulas).

[The cities countries are named and the table abbreviations are explained here: 3.]

As you can see, these cities ranged from 30.1 North to 42.1 North and adjusting seasonally usually resulted in about 4% more solar energy than just using a permanently fixed optimal annual tilt. The outlier was Madrid (40.5 North) where adjusting seasonally did about 8% better.

 

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Footnotes

1. In this footnote we first list the nations and states (or - for countries besides the US - whatever the equivalent to "states" is) that house each of the cities on the table. Then we explain the abbreviations. All of the solar radiation insolation data is from the PV Watts Calculator (Version 1) [see optimal tilt - particularly footnote #1].
The cities are:
Rivas, Department of Rivas, Nicaragua
Miami, Florida, USA
Cairo, Cairo Governorate, Egypt
Tuscon, Arizona, USA
Atlanta, Georgia, USA
Boulder, Colorado, USA
Madrid, Madrid, Spain
Boston, Massachussetts, USA
Seattle, Washington, USA
London, England, Great Britain
Fairbanks, Alaska, USA
The abbreviations in the table are explained as follows:
City (lat) = City (latitude in degrees)
FT. kWh/m2/d = how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with solar panels that have full-tracking (aka: "two-axis tracking" - the solar panels constantly follow the sun to maximize the amount of solar energy collected).
Opt. kWh/m2/d (Tilt) =
(1) The first part [Opt. kWh/m2/d] describes how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with solar panels that have been given the PV Watts optimal annual tilt (my method for finding the PV Watts annual tilt angle is covered in footnote #1 on optimal tilt).
(2) The second part [(Tilt)] is the PV Watts optimal annual tilt angle in degrees (my method for finding the PV Watts annual tilt angle is covered in footnote #1 on optimal tilt).
Hor. kWh/ m2/d = how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with horizontal solar panels (solar panels that are just layed out flat).
%Low/Opt. compares the amount of solar radiation gathered per square meter (in an average day) with a solar panel given a tilt equal to the pitch of a low pitch roof [14 ("3 in 12" in roofer's lingo)] with the amount of solar radiation gathered with the PV Watts optimal annual tilt angle (my method for finding the PV Watts annual tilt angle is covered in footnote #1 on optimal tilt).
It was found this way: %Low/Opt. = [((radiation gathered with low roof pitch tilt)/(radiation gathered with optimal annual tilt)) * 100%].
%Med./Opt. is similar to %Low/Opt. except the roof pitch is a medium pitch roof [30.3 ("7 in 12" in roofer's lingo)].
%Steep/Opt. is similar to %Low/Opt. except the roof pitch is a steep pitch roof [45 ("12 in 12" in roofer's lingo)].
2. The nations and states (or - for countries besides the US - whatever the equivalent to "states" is) that house each of the cities on the table are the listed in footnote #1. Here we explain abbreviations. All of the solar radiation insolation data is from the PV Watts Calculator (Version 1) [see optimal tilt - particularly footnote #1].
City (lat) = City (latitude in degrees)
Opt. kWh/m2/d describes how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with solar panels that have been given the PV Watts optimal annual tilt according to PV Watts (my method for finding the PV Watts annual tilt angle is covered in footnote #1 on optimal tilt).
Hor. kWh/ m2/d = how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with horizontal solar panels (solar panels that are just layed out flat).
%45Off/Opt. compares the amount of solar radiation gathered per square meter (on an average day) with a solar panel with the PV Watts optimal annual tilt but pointed 45 to the East or West of true South (to the Southeast or Southwest) to the amount of solar radiation gathered by a solar panel with the PV Watts optimal annual tilt and pointed true South (where it is supposed to be pointed). [my method for finding the PV Watts annual tilt angle is covered in footnote #1 on optimal tilt.]
It is found this way: [((radiation gathered with the PV Watts annual tilt angle pointed Southeast or Southwest (I took the average of the two direction))/(radiation gathered with optimal annual tilt)) * 100%].
90Off/Opt. is similar to %45Off/Opt. but the solar panels are pointed due East or due West.
25%L & 45Off/Opt. is similar to %45Off/Opt. but instead of being given the PV Watts annual tilt angle, the solar panels are given an angle 25% lower than the PV Watts annual tilt angle.
25%L & 90Off/Opt. and 50%L & 90Off/Opt. is similar to %45Off/Opt. but instead of being pointed to the Southeast or Southwest they are pointed to the East or West and the tilt angles are 25% and 50% lower than the PV Watts annual tilt angle.

3. In this footnote we first list the nations and states (or - for countries besides the US - whatever the equivalent to "states" is) that house each of the cities on the table. Then we explain the abbreviations. All of the solar radiation insolation data is from the PV Watts Calculator (Version 1) [see optimal tilt - particularly footnote #1].
The cities are:
Cairo, Cairo Governorate, Egypt
Atlanta, Georgia, USA
Madrid, Madrid, Spain
Boston, Massachussetts, USA
The abbreviations in the table are explained as follows:
City (lat) = City (latitude in degrees)
Full Track.; kWh/m2/day = how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with solar panels that have full-tracking (aka: "two-axis tracking" - the solar panels constantly follow the sun to maximize the amount of solar energy collected).
Seas. Tilt; kWh/m2/day = how much solar radiation in kilowatt-hours would be gathered per square meter per day (in an average year) with solar panels that are adjusted seasonally. The seasonal tilts and the starting and ending of the seasons are from Charles Landau of Macslab. The Macslab formula is introduced on optimal tilt. The tilts and season start/stop dates as well as a link to their source is in footnote #4 of the same page.
%Seas. Tilt/Full Track. compares the amount of solar radiation gathered per square meter (on an average day) with a solar panel with a seasonally adjusted tilt versus the amount gathered with full-tracking (aka: two-axis tracking. The seasonal tilt angles and start/stop of the solar seasons came from Macslab (Introduced on optimal tilt. The tilts and season start/stop dates as well as a link to their source is in footnote #4 of the same page.)
It is found this way: [((radiation gathered with the Seasonal tilt angles))/(radiation gathered with full-tracking)) * 100%].
Ann. Tilt; kWh/m2/day is similar to Full Track.; kWh/m2/day except instead of full tracking, the tilt is the PV Watts optimal annual tilt (my method for finding the PV Watts annual tilt angle is covered in footnote #1 of optimal tilt).
%Ann. Tilt/Seas. Tilt is similar to %Seas. Tilt/Full Track. except the two amounts of solar radiation compared are the amount gathered with a PV Watts optimal annual tilt (my method for finding the PV Watts annual tilt angle is covered in footnote #1 of optimal tilt) and the amount gathered with a seasonally adjusted tilt angle (the seasonal tilts are from Macslab. They are introduced on optimal tilt. The tilts and season start/stop dates as well as a link to their source is in footnote #4 of the same page).
Hor. Tilt; kWh/m2/day is similar to Full Track.; kWh/m2/day except instead of full tracking, the solar panels are just laid out horizontally (no tilt).
%Hor. Tilt/Ann. Tilt is similar to %Seas. Tilt/Full Track. except the two amounts of solar radiation compared are the amount gathered with horizontal solar panels (no tilt) and the PV Watts optimal annual tilt angle (my method for finding the PV Watts annual tilt angle is covered in footnote #1 of optimal tilt).
%Hor. Tilt/Seas. Tilt is similar to %Seas. Tilt/Full Track. except the two amounts of solar radiation compared are the amount gathered with horizontal solar panels (no tilt) and soloar panels with seasonally adjusted tilts (the seasonal tilts are from Macslab. They are introduced on optimal tilt. The tilts and season start/stop dates as well as a link to their source is in footnote #4 of the same page).


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