Optimum Tilt of Solar Panels
To get the most from solar panels, you need to point them in the direction
that captures the most sun. But there are a number of variables in figuring out
the best direction. This page is designed to help you find the best placement
for your solar panels in your situation.
This advice applies to any type of panel that gets energy from the sun;
photovoltaic, solar hot water, etc. We assume that the panel is fixed, or has a
tilt that can be adjusted seasonally. (Panels that track the movement of the
sun throughout the day can receive 10% (in winter) to 40% (in summer) more
energy than fixed panels. This page doesn’t discuss tracking panels.)
Solar panels should always face true south if you are in the northern
hemisphere, or true north if you are in the southern hemisphere. True north is
not the same as magnetic north. If you are using a compass to orient your
panels, you need to correct for the difference, which varies from place to
place. Search the web for “magnetic declination” to find the correction for your
location.
The next question is, at what angle from horizontal should the panels be
tilted? Books and articles on solar energy often give the advice that the tilt
should be equal to your latitude, plus 15 degrees in winter, or minus 15
degrees in summer. It turns out that you can do better than this - about 4%
better.
Fixed or Adjustable?
www.latlong.net › Countries › Nigeria › Cities
Lagos,
Nigeria Lat Long Coordinates Info. The latitude of Lagos, Nigeria is
6.465422, and the longitude is 3.406448. Lagos, Nigeria is located at
Nigeria country in the Cities place category with the gps coordinates of
6° 27' 55.5192'' N and 3° 24' 23.2128'' E.
Latitude: 6.465422
UTM Northing: 714,671.72
Longitude: 3.406448
DMS Lat: 6° 27' 55.5192'' N
It is simplest to mount your solar panels at a fixed tilt and just leave
them there. But because the sun is higher in the summer and lower in the
winter, you can capture more energy during the whole year by adjusting the tilt
of the panels according to the season. The following table shows the effect of
adjusting the angle, using a system at 40° latitude as an example. (The
comparison would be a little different for different latitudes.) Each option is
compared with the energy received by the best possible tracker that always
keeps the panel pointed directly at the sun.
|
Fixed
|
Adj. 2 seasons
|
Adj. 4 seasons
|
2-axis tracker
|
% of optimum
|
71.1%
|
75.2%
|
75.7%
|
100%
|
In short, adjusting the tilt twice a year gives you a meaningful boost in
energy. Adjusting four times a year produces only a little more, but could be
important if you need to optimize production in spring and fall. You can jump
to the section on the best
fixed
tilt angle, or skip to the sections on
two-season or
four-season adjusting.
The graph below shows the effect of adjusting the tilt. The turquoise line
shows the amount of solar energy you would get each day if the panel is fixed
at the full year angle. The red line shows how much you would get by adjusting
the tilt four times a year as described below. For comparison, the green line
shows the energy you would get from two-axis tracking, which always points the
panel directly at the sun. (The violet line is the solar energy per day if the
panel is fixed at the winter angle, discussed below.) These figures are
calculated for 40° latitude.
If your solar panels will have a fixed tilt angle, and you want to get the
most energy over the whole year, then this section is for you. A fixed angle is
convenient, but note that there are some disadvantages. As mentioned above,
you’ll get less power than if you adjusted the angle. Also, if you live where
there is snow, adjusting the panels to a steeper angle in winter makes it more
likely that they will shed snow. A panel covered in snow produces little or no
power.
Use one of these formulas to find the best angle from the horizontal at
which the panel should be tilted:
- If your
latitude is below 25°, use the latitude times 0.87.
- If your
latitude is between 25° and 50°, use the latitude, times 0.76, plus 3.1
degrees.
- If your
latitude is above 50°, see Other
Situations below.
This table gives some examples for different latitudes. It also shows the
average insolation on the panel over the year (in kWh/m
2 per day),
and the energy received compared to the best possible tracker.
Latitude
|
Full year angle
|
Avg. insolation on
panel
|
% of optimum
|
0° (Quito)
|
0.0
|
6.5
|
72%
|
5° (Bogotรก)
|
4.4
|
6.5
|
72%
|
10° (Caracas)
|
8.7
|
6.5
|
72%
|
15° (Dakar)
|
13.1
|
6.4
|
72%
|
20° (Mรฉrida)
|
17.4
|
6.3
|
72%
|
25° (Key West, Taipei)
|
22.1
|
6.2
|
72%
|
30° (Houston, Cairo)
|
25.9
|
6.1
|
71%
|
35° (Albuquerque, Tokyo)
|
29.7
|
6.0
|
71%
|
40° (Denver, Madrid)
|
33.5
|
5.7
|
71%
|
45° (Minneapolis, Milano)
|
37.3
|
5.4
|
71%
|
50° (Winnipeg, Prague)
|
41.1
|
5.1
|
70%
|
If you are going to adjust the tilt of your solar panels twice a year, and
you want to get the most energy over the whole year, then this section is for
you.
The following table gives the best dates on which to adjust:
|
Northern hemisphere
|
Southern hemisphere
|
Adjust to summer
angle on
|
March 30
|
September 29
|
Adjust to winter
angle on
|
September 12
|
March 14
|
If your latitude is between 25° and 50°, then the best tilt angle for summer
is the latitude, times 0.93, minus 21 degrees. The best tilt angle for winter
is the latitude, times 0.875, plus 19.2 degrees. If your latitude is outside
this range, see
Other Situations
below. This table gives some examples:
Latitude
|
Summer angle
|
Winter angle
|
Avg. insolation on
panel
|
% of optimum
|
25°
|
2.3
|
41.1
|
6.6
|
76%
|
30°
|
6.9
|
45.5
|
6.4
|
76%
|
35°
|
11.6
|
49.8
|
6.2
|
76%
|
40°
|
16.2
|
54.2
|
6.0
|
75%
|
45°
|
20.9
|
58.6
|
5.7
|
75%
|
50°
|
25.5
|
63.0
|
5.3
|
74%
|
If you are going to adjust the tilt of your solar panels four times a year,
and you want to get the most energy over the whole year, then this section is
for you. This would be your situation if you are connected to the grid and can
use or sell all the power you produce.
The following table gives the best dates on which to adjust:
|
Northern hemisphere
|
Southern hemisphere
|
Adjust to summer
angle on
|
April 18
|
October 18
|
Adjust to autumn
angle on
|
August 24
|
February 23
|
Adjust to winter
angle on
|
October 7
|
April 8
|
Adjust to spring
angle on
|
March 5
|
September 4
|
If your latitude is between 25° and 50°, then the best tilt angles are:
- For
summer, take the latitude, multiply by 0.92, and subtract 24.3 degrees.
- For spring
and autumn, take the latitude, multiply by 0.98, and subtract 2.3 degrees.
- For
winter, take the latitude, multiply by 0.89, and add 24 degrees.
If your latitude is outside this range, see
Other Situations below.
If you want to adjust the tilt of your panels four times a year, you can use
these figures to keep capturing the most energy year-round. This table gives
some examples:
Latitude
|
Summer angle
|
Spring/autumn angle
|
Winter angle
|
25°
|
-1.3
|
22.2
|
46.3
|
30°
|
3.3
|
27.1
|
50.7
|
35°
|
7.9
|
32.0
|
55.2
|
40°
|
12.5
|
36.9
|
59.6
|
45°
|
17.1
|
41.8
|
64.1
|
50°
|
21.7
|
46.7
|
68.5
|
In winter, a panel fixed at the winter angle will be relatively efficient,
capturing 81 to 88 percent of the energy compared to optimum tracking. In the
spring, summer, and autumn, the efficiency is lower (74-75% in spring/autumn,
and 68-74% in summer), because in these seasons the sun travels a larger area
of the sky, and a fixed panel can’t capture as much of it. These are the
seasons in which tracking systems give the most benefit.
Note that the winter angle is 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.
The summer angles are about 12 degrees flatter than is usually recommended.
In fact, at 25° latitude in summer, the panel should actually be tilted
slightly away from the equator.
Tilt Fixed at Winter Angle
If your need for energy is highest in the winter, or the same throughout the
year, you may want to just leave the tilt at the winter setting. This could be
the case if, for instance, you are using passive solar to heat a greenhouse.
Although you could get more energy during other seasons by adjusting the tilt,
you will get enough energy without making any adjustment. The following tables
assume that the tilt is set at the winter optimum all year long. They show the
amount of insolation (in kWh/m
2) on the panel each day, averaged
over the season.
Latitude 30° Tilt
50.7°
|
Season
|
Insolation on panel
|
% of winter insolation
|
Winter
|
5.6
|
100%
|
Spring, Autumn
|
6.0
|
107%
|
Summer
|
5.1
|
91%
|
Latitude 40° Tilt
59.6°
|
Season
|
Insolation on panel
|
% of winter insolation
|
Winter
|
4.7
|
100%
|
Spring, Autumn
|
5.8
|
123%
|
Summer
|
5.1
|
109%
|
Latitude 50° Tilt
68.5°
|
Season
|
Insolation on panel
|
% of winter insolation
|
Winter
|
3.4
|
100%
|
Spring, Autumn
|
5.4
|
158%
|
Summer
|
5.1
|
150%
|
Confused about tilt angles?
A zero tilt angle means that the face of the panel is aimed
directly overhead. A positive tilt angle means that the panel faces more
towards the equator. In the northern hemisphere that would mean tilting so it
faces towards the South. Rarely, the tilt angle can be negative; this means the
panel faces away from the equator.
Time-of-Use Rates
In some grid-connected systems, energy is more valuable
during peak periods. To see the effect of this on panel orientation, look at my
time-of-use page.
Perhaps your panels are on a roof that is not oriented exactly to the south.
Or you are at a latitude outside the range for which these formulas work. These
situations are more complex than can be handled by a simple formula.
I can do calculations for your custom situation for a
consulting fee.
See
my rates.
Assumptions
These calculations are based on an idealized situation. They
assume that you have an unobstructed view of the sky, with no trees, hills,
clouds, dust, or haze ever blocking the sun.
You may need to make adjustments for your situation. For example, if you
have trees to the east but not the west, it may be better for you to aim your
solar panels slightly to the west. Or if you often have clouds in the afternoon
but not the morning, you might aim your panels slightly to the east.
The calculations also assume that you are near sea level. At very high
altitude, the optimum angle could be a little different.
If you are estimating energy output, remember that temperature affects the
efficiency of photovoltaic panels. They produce less power at higher
temperatures. Panels vary so you will need to contact your panel manufacturer
for their specifications.
Don’t obsess about the exact angles just because I’ve calculated them to the
tenth of a degree. A difference of a few degrees will make very little
difference in the energy you gather.
Why does this work?
The recommended angles can seem counterintuitive. For example, consider
summer at 40° latitude. At noon on the solstice, the sun is 40° - 23.5° which
is 16.5° from directly overhead. To capture the most sun at that time you would
tilt the panel 16.5° to point it directly at the sun. On other days of the
summer it is a bit lower in the sky, so you would want to tilt the panel a bit
more. Yet we say to tilt it only 12.5°. The sun is never that high. How can
that be right?
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.
How these numbers were calculated
For each configuration of latitude and season, over 12,000
data points were calculated for various times throughout the day and the year.
For each data point, the equations of celestial mechanics were used to
determine the height and azimuth of the sun. The intensity of the sun was
corrected to account for the increased absorption by the atmosphere when the
sun is lower in the sky, using the formula:
intensity in kw/m2 = 1.35 *
(1.00/1.35) sec(angle of sun from zenith)
This formula assumes that the earth is flat, so a factor was applied to
account for the curvature of the earth (and therefore the earth’s atmosphere).
These factors, and the angle of the sun with respect to the panel, then
determine the insolation on the panel. An iterative method then determined the
angles that give the maximum total insolation during each season. Given those
angles, the beginning and ending dates of the season were then adjusted to the
optimum, then the angles recalculated, until the process converged. After the
optimum dates and angles were calculated, it was determined that a linear
formula closely approximates the optimum. The formulas are only accurate within
the specified range.
Other published articles on tilt angles have used less accurate
calculations. For example, Richard Perez and Sam Coleman, in “PV Module
Angles”, Home Power n.34 p.14-16, 1993, recommend an angle that puts the panel
perpendicular to the sun’s rays at noon. That is indeed the best angle at noon
on that day, but it does not take into account the best angle for capturing
solar energy at other times of the day. That article also leaves it to the
reader to estimate the best angle over the period until the next time the tilt
is adjusted.
Percentages may not be exact due to rounding.
Links
You may find these links useful.
This site has good information for
the homeowner considering going to solar power.
The National Renewable Energy
Laboratory has copious data on solar energy available at different locations in
the United States, a performance calculator for PV systems, and more.
This site has sunrise, sunset, and
insolation data for worldwide locations.
This page was last updated on 11 November 2015.
Written by Charles R. Landau.
Copyright © 2001, 2002, 2008, 2010-2012, 2014-2015. All rights reserved.
Email me at
charlie@solarpaneltilt.com
Lagos,
Nigeria’s largest city, sprawls inland from the Gulf of Guinea across
Lagos Lagoon. Victoria Island, the financial center of the metropolis,
is known for its beach resorts, boutiques and nightlife. To the north,
Lagos Island is home to the National Museum Lagos, displaying cultural
artifacts and craftworks. Nearby is Freedom Park, once a colonial-era
prison and now a major venue for concerts and public events.
Weather: 79°F (26°C), Wind SW at 3 mph (5 km/h), 83% Humidity
Efficient Energy saving techniques to help reduce your carbon footprint
