Optimal 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

People with solar energy on the mind will often wonder, "What tilt will give me the most solar energy in winter? In summer? Spring and Fall?"

Or, "What one fixed permanent tilt will give me the most solar energy all year round? ... and why didn't I start to think about this before I started carrying this heavy solar panel around?"

On this page we look at a few methods for choosing an optimal tilt angle.

Two of them are what I call "latitude-based formulas", meaning that you plug your latitude into an equation and out on the other end of the algebra comes a suggestion about how to best tilt your solar panels or solar hot water collectors. The other method is a little more involved.

All of the methods assume you can point your solar panels due South in the Northern Hemisphere and due North in the Southern Hemisphere (a refresher for why this is a good idea is at the bottom of this page.

A cartoon man parades around with a circular solar panel around his neck.
"Why worry about optimal tilt angle when
you can just wear solar panels around
your neck and walk around facing the
sun all day long?"
.

Tilt Angle Formulas versus PV Watts

Since latitude-based formulas are just based on your latitude, they cannot account for all of the factors that influence insolation like your altitude above sea level or your local cloud-coverage patterns.

Fortunately, there is a free online tool called the "PV Watts calculator" (1) that uses site-specific weather-data to figure out how much solar energy you can expect to receive with a given tilt angle in a given place.

Since the data it uses is site-specific, it can account for things like altitude above sea level, cloudiness-trends and even trends in things like the extra reflected radiation that is in the sky when there is snow on the ground.

I used the PV Watts calculator to assess the two latitude-based formulas I introduce on this page and put the data on comparing tilts. My method for finding a "true optimal tilt" with PV Watts is in this footnote (1).

I found that the best latitude-based tilt formula did quite well as long as came quite close to the idealized situation it was calculated for. However, this idealized situation is quite far from the reality of many real-world situations. For example, for reasons we will explain in a moment, even the best latitude-based formula was quite a bit off in very overcast climates.

Shallow Tilts for Europe!

Latitude-based formulas can really let you down if you live in a cloudy place.

Recently some researchers in Ireland published a paper proposing a new method for finding optimal tilt angles in high-latitude, very cloudy places like Northern Europe. Unlike most tilt angle formulas which focus solely on direct radiation (see tilt angle), their method takes diffuse radiation into account. (2).

As explained on types of radiation, when the sky is completely overcast, all of the solar radiation is diffuse radiation and is best gathered by laying your solar panels out flat. It isn't surprising, then, that the optimal tilt angles in cloudy old Northern Europe are shallower than the ones found by typical tilt angle formulas (for much of Northern Europe, about half of the annual solar radiation is diffuse radiation (3)).

The researchers found that the optimal annual tilt for Galway, Ireland (53.3°N) was 33°. The classic "tilt-at-latitude for best year round performance advice" (discussed soon) would of course have recommended a tilt of 53.3 degrees for Galway. PV Watts did much better. Although they didn't have data for Galway, the PV Watts tilt for Dublin, Ireland (53.4°N and on the opposite side of the island from Galway) was 34°.

"Tilt-at-latitude" and the "Macslab tilt"

The old fashioned "tilt-at-latitude for best year round performance" advice is pretty common in internet-land. It is of course part of a larger bit of advice: "tilt at your latitude plus 15 degrees for best winter performance, your latitude minus 15 degrees for best summer performance and right at your latitude to optimize spring, fall and year-round performance."

A van Gogh painting of the sun high over the olive grove.
The sun is highest in the sky
(necessitating the lowest tilt angle)
at solar noon.
.

I assume these formulas are mostly focused on getting the sunlight in the middle part of the day to hit your solar panels directly. In the spring and fall, tilting at latitude maximizes the amount of solar noon sunlight that hits your solar panels directly. Also, the sun's spring and fall solar noon solar elevation angle is midway between its winter and summer solstice solar noon angles.

This "tilt-at-latitude" advice does a pretty good job of maximizing the solar energy you can get with a fixed tilt, but Charles Landau of Macslab decided to improve upon it by using a computer to figure out where in the sky the sun is all throughout the day all throughout the year.

He also factored in air mass (air mass is directly related to the angle of the sun above the horizon - see sun angle data) and figured out when to optimally adjust your tilt angle each season (the Macslab formula and a link is in this footnote: 4).

Comparing the formulas

The Macslab tilt suggestions are quite a bit shallower in the summer than the "tilt-at-latitude minus 15 degrees for summer" advice but the Macslab winter tilt suggestions are quite a bit steeper than "tilt-at-latitude plus 15 degrees for winter" advice.

The Macslab spring/fall tilt is just a tiny bit shallower than the "tilt-at-latitude for spring and fall" advice but the Macslab optimal annual tilt angle is quite a bit shallower than the "tilt-at-latitude for year round" advice.

Charles Landau discusses the reasons for the winter and summer differences on his website (5). The gist of his explanations (as I understand it) has to do with the fact that the sun is quite high in the sky for a large portion of the sky in the summer but the vast majority of its strength in the winter is centered around the middle of the day.

If you face your solar panels so that they are directly facing the sun at solar noon (this is a best-case scenario and so the Macslab formulas assume it), a shallower tilt does a better job of catching the sunlight that comes before and after midday - particularly in summer (for a discussion of why this is, see 5).

At the time of this writing (5/20/2011), the Macslab page doesn't discuss why its optimal annual tilt is so much shallower than other less rigorously derived formulas like "tilt-at-latitude." My guess is that it is because there is more sunlight available in the summer (when a shallower tilt is preferable) than winter (when a steeper tilt is preferable) and so it makes sense that a tilt that favors summer over winter (and to a lesser degree spring/fall), will capture more sunlight over the whole year.

The Macslab formulas come with many stipulations - for example, you have to be at sea level and between latitudes 25° to 50° (North or South). This suggests that the "one size fits all" notion of less rigorously derived latitude-based formulas is mistaken.

Comparing Formulas with PV Watts

I have a couple of pages of tables I made with PV Watts that compare how much solar radiation falls on solar panels with tilt recommendations made by these two formulas and PV Watts. To construct the tables, I looked at cities from 11° North to 64° North but focused mostly on cities that were within the Macslab latitude-range.

I found that - all other things being equal - very cloudy cities did tend to have shallower tilts than even the Macslab formula suggested. I also came away with the impression that perhaps - all other things being equal - solar panels in cities far above sea level seemed to do better with slightly steeper tilts (than would be appropriate for a city closer to sea level at the same latitude). The details are on comparing tilts.

Imperfect Tilts

I also made tables investigating how much solar energy you lose with an tilt less optimal than the optimal annual tilt and how much you gain with tilts that are more optimal than the optimal annual tilt angle.

Generally, tilting a little higher or lower than optimal is not a huge deal, nor is pointing your solar panels a little to the East or West of true South (or true North in the Southern Hemisphere). However, you don't want to get too carried away - especially in the East/West aspect. Also, two-axis tracking greatly increases the amount of solar energy your solar panels collect, but adjusting seasonally has a much less dramatic effect. For more details, see tilt deviation.

Point Due South in Northern Hemisphere

At latitudes farther to the North of the equator than the Tropic of Cancer (currently about 23.5° North), the sun stays in the Southern part of the sky year-round. So, in the Northern Hemisphere, all other things being equal (ie: shade from trees, clouds, etc don't interfere), you gather the most sun if your tilted solar panels are pointed due South (as in "true South", not "magnetic South".

The opposite situation is found in the Southern Hemisphere and so solar energy systems South of the Tropic of Capricorn (about 23.5° South) tilt due North when thats possible.

Footnotes

1. There are two versions of the PV Watts Calculator. A portal to both of them is currently here: About PV Watts. The NREL of the US government is responsible for the calculator. In making the tables and finding optimal tilt angles, I used the first version of the calculator.
To find the optimal tilt angle using PV Watts, I used trial and error to find all the tilt angles that provided the most annual solar radiation and then took the midpoint of those values as the "optimal tilt angle." As an example, in Tuscon, Arizona, no permanently fixed tilt gathered more than 5.68 kWh/m2 in a given year and the tilt angles that gathered this much solar energy ranged from 22° through 27° and so the "optimal annual tilt angle" was taken to be [22° + ((27° - 22°)/2)] = 24.5°.

2. This article is entitled "A new methodology to optimise solar energy extraction under cloudy conditions" and is authored by S. Armstrong and W.G. Hurle. The article was available online in Renewable Energy 35 (2010) 780–78 as of November 2009. At the time of publication, the researchers were affiliated with the Power Electronics Research Centre, Electrical and Electronic Engineering, National University of Ireland, Galway, Ireland.
The article can be found here here: A new methodology....

3. On page 781 of the article cited and linked to in footnote #2, it is stated that, in European countries above 45° North, about half of the annual solar radiation is diffuse radiation ("due to frequent heavy cloud cover").

4. The Macslab Formula is available online at optsolar
The Macslab tilt angle recommendations are as follows:
Winter: (.89 * latitude°) + 24°
Summer: (.92 * latitude°) - 24.3°
Spring/Fall: (.98 * latitude°) - 2.3°
Annual: (.76 * latitude°) + 3.1°
The Macslab solar seasons are:
Winter: October 7 to March 5
Spring: March 5 to April 18
Summer: April 18 to August 24
Fall: August 24 to October 7

5. Charles Landau discusses his tilt angle formulas on the webpage cited, linked-to and quoted in footnote #4.
About his winter tilt recommendation, Landau says,These angles are about 5° steeper than what has been commonly recommended. The reason is that in the winter, most of the solar energy comes at midday, so the panel should be pointed almost directly at the sun at noon. The angle is fine-tuned to gather the most total energy throughout the day. At the end of the page, he discusses a question I had - why is his summer tilt angle lower than the the tilt angle needed to gather the most sun when the sun is highest in the sky?
[for example, at 40° North, the height of the solar noon summer solstice sun (this is the highest the sun is throughout the whole year) is approximately (90 - (40° - 23.5°)) = 73.5° above the horizon. But the appropriate solar panel postion for that moment would then be (90° - 73.5°) = 16.5°; yet the Macslab summer tilt is shallower than that: ((40° * .92) - 24.3°) = 12.5°
Landau says, The answer is that we are considering the whole day, not just noon. In the morning and evening, the sun moves lower in the sky and also further north (if you are in the northern hemisphere). It is necessary to tilt less to the south (or more to the north) to collect that sunlight. To me, this was kind of confusing. I've been thinking of it like this: the steeper you tilt towards where the sun is at the middle of the day, the more you are tilting away from where the sun is the rest of the day. So, the more time the sun spends high in the sky away from its solar noon position, the closer to horizontal your solar panels should be.
I'm not sure if our two different ways of looking at the question are conceptually different or not.

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