Efficiency Modifiers For Solar Water Collectors

SRCC conducts its performance testing of solar water heaters at nearly a perpendicular angle to obtain its data for the efficiency equation. Most of the sun's power does come during the peak of the day, and most traditional collectors (flat panel) lose efficiency when the sun is at an angle so most do not consider the potential gains from a sun on the horizon. However, when it comes to vacuum tube collectors, there is much more heat to be gained under these circumstances.

Since the SRCC equation is based on gross area and evacuated tube collectors have spaces between the tubes, the efficiency intercept will usually appear much lower than a flat panel collector, which has an absorber area that covers nearly the entire gross area of the collector. In the case of the 15 tube Duda Solar collector, the gross area is 2.342m². However, the absorber area (the surface area of the tubes) is only 1.219m². This means that the maximum efficiency that this tubular collector can obtain is 1.219m²/2.342m² = 52%? This is not true for efficiency equations based on gross area.

The Transverse Incident Angle Modifier

In general, the sun rises in the east and sets in the west. Only at roughly noon does the sun pass directly overhead and perpendicular to a collector as it translates across the sky. For a visual explanation, see the information about the azimuth angle here.

Because the solar vacuum tubes are round, the angle at which the sun beams into them does not effect efficiency, unlike with flat panel collectors. When it comes to expensive and inefficient PV cells, you'll see a lot of consideration put into using trackers to follow the sun. There is no need for a tracker for tubular collectors since the tubes themselves passively track the sun as it translates across the sky. In fact, when calculating efficiency based on gross area, they even gain in efficiency when the sun is on the horizon since the light which normally escapes between the tubes gets intercepted by the sides and back ends of the tubes, thus enlarging the absorber area of the collector.

SRCC also does testing for what it calls the incident angle modifier. This modifier should be multiplied to the calculated efficiency η in order to find the adjusted efficiency for that angle. For flat panel collectors, this factor will be less than 1 for any angle which is not 0° (perpendicular to the collectors). However, for tubular collectors, the modifier will often be greater than 1 when the angle is greater than 0°.

As shown in the table above, the collector efficiency actually increases as the sun angle increases from the sun's location being in the East or the West. The peak transverse efficiency comes at around 60°, and then it begins to decrease. The IAM should be approximately 0 when the angle is 90° since at this point, the sun is now parallel to the collector.

As an example on how to use this data, take the 42% efficiency intercept of the Duda Solar collector (assumes no ΔT), multiply it by 1.55, which is the IAM at 60°, and 65.1% is the efficiency found by gross area.

The Longitudinal Incident Angle Modifier

Not only does the sun rise in the east and set in the west, it also complicates things by changing in elevation throughout the day. When the sun is on the horizon, it is 0° in elevation . When the sun is directly above, it is 90° in elevation.

To further complicate things, the sun's elevation through the day also depends on the time of the year, due to the tilt of the earth. The maximum elevation for the day in the northern hemisphere is 90° - Latitude + Declination, where the declination varies throughout the year ±23.5° (the Earth's tilt). For a detailed explanation of how this works, see the this page about the Elevation Angle of the sun.

Where this comes into play with the solar water heaters is just like with the transverse angle modifier. There is also a modifier for the longitudinal angle. Flat panel collectors and vacuum tube collectors have similar longitudinal incident angle modifiers. When comparing the two types against each other, the longitudinal IAM can be assumed as 1 for easier comparison.

The longitudinal angle modifier for the Duda Solar 14mm Heat Pipe Solar Water Collector can be found in the table below.

As can be observed, the Longitudinal IAM does not change much with less than a 50° angle. After 50°, the efficiency rapidly degrades. For this reason, the solar collector should be oriented within this 50° threshold.

Tilt of the Solar Collector

The tilt of the solar collector depends on a few factors. One is factor is according to which hemisphere it is located in. For the northern hemisphere, the collector should be oriented towards the South, and in the southern hemisphere, it should be oriented towards the north. The time of year which the collector will most often be used also determines the most appropriate tilt.

During the equinox, the peak elevation angle of the sun is equivalent to the latitude where the collector is located. During the winter solstice, the sun's peak elevation is at the lowest (latitude minus 23.5°) and during the summer solstice the sun's peak elevation is at its highest (latitude plus 23.5°). For this reason, the collector should not be oriented more or less than these maximums and minimums.

It also needs to be considered that the angles mentioned above are the peaks of the sun's elevation. The sun is more often lower in the sky during the day than its peak elevation at noon, and so the collector should be oriented an extra 5° - 15° steeper towards the horizon if the goal is to achieve peak efficiency year-round. Generally speaking, if more summer efficiency is desired, the additional 5° degrees is best while if more winter efficiency is desired, the additional 15° is best.

While the sun's elevation angle changes a lot throughout the day and year, it must be reinforced that the array tilt relative to the sun is not as important as it may seem. Even with a 50° angle, the efficiency loss is only 10%. Choosing a simple 45° angle for a year round average will generally guarantee that the efficiency stays within that 10% loss range since the sun on the horizon (0° elevation) is 45° away and the sun directly above (90° elevation) is still only 45° away.