Solar Heat from a Winter's Sun

Radiant energy from sunlight striking the North East USA mainland during the month of December is minimal. To be objective about data collection I use this experimental, MTD sun shed, isolated from conventional sources of heat. The array of MTD collectors have a combined surface area of about 8 m2 for collecting heat and a 200 gallon drum storage system for storing the heat.

       Unfortunately the shed is surrounded by trees and oriented 20 degrees East of due South so that an optimum daily heat harvest is impossible. Fortunately there is no shading between the hours of 9AM and 11 AM so unhampered solar heat gain may be calibrated during these hours. Since the orientation and available sunlight to the shed is off an adjustment factor of 0.4 will be used to compare the solar gain of this shed with a comparable shed having an ideal orientation and full sun availability.


       According to the U.S. Solar Radiation Resource Maps the energy available to m2 on Long Island in December oriented south and tilted at latitude varies between 2 and 3 kW/day, but I soon discovered that this December 2008 supply of radiant energy was only about 1 KW/day. Fortunately there was enough sunlight available to prevent the 200 gallons of water from freezing.


       From the above graph observe the intense radiation available on December 22 and December 23. On these days the radiant energy peaked at 650 W/m2. On December 14, 15 and 18 scattered sunlight was available for brief intervals but a total of less than 6 hours of direct sunlight was available during this 9 day interval. Of course the amount of radiation will vary from year to year and from day to day, but it appears the average, usable, daily energy availability during the 2008 December on Long Island is about to 1KW/m2/day.  This is just a crude estimate based on the limited data.

       The December heat harvest from six MTD collectors will be examined later but first let’s take a peak at the power harvest from a .5m2 PV panel during this same 9 day interval. This PV power output may be calculated by observing the voltage across a 5 ohm load placed across the terminals of the PV panel. Notice the similarity between the flux intensity graph and the voltage output graph of the PV panel.



On December 23 we observe the peak voltage output from the PV panel is about 10 Volts. This translates to a power output of 20 watts. Since the sunlight intensity is only about half the full sunlight intensity we can estimate that the full intensity output from the .5m2 panel would be close to 40 Watts. This is about right since max PV output is rated at 50 Watts.


     The relationship between sunlight intensity, panel temperature and power output is difficult to observe. From the above graph I see no significant change in power output over this temperature range between 20 F and 80 F. Perhaps there are too many variables to make to make an accurate observation. As the season progresses and the panel temperature increases a discernible pattern of diminished power with increasing temperature may emerge.




Heat Gain from the MTD Shed


       We have just observed sunlight intensity and PV power output over a 9 day interval in December. Now we’ll compare the heat gain of the sunshed with the average daily radiant energy available in an ideal situation. We'll use 1kW/m2/day for a reference point and .4 as an adjustment factor to deal with the sunshed orientation and shadows. 1kW = 3000 BTUs.

       Since the sunshed glazing has a surface area of 8m2 we would expect the heat energy harvest over the month of December to be in the neighborhood of:

SOLAR ENERGY AVAILABLE = 8 x 3000 BTU x30 x.4    =     288,000 BTUs  

       The solar activity on and in the sunshed from December 1-23 appears confusing at first. This data has been collected at four minute intervals from four temperature probes attached to the: collector array, the last storage drum, the middle storage drum (average storage temp.) and the ambient temperature. As you can see the ambient temperature fluctuates from 12 F to 60 F. the collector temperature fluctuates from 12 F to 110 F and the average storage temperature fluctuates from 100 F to 50 F

       Relative heat gain at any moment may be estimated from the difference in temperature between the collector input temperature and the collector output temperature with a known flow rate. We’ll look at this later but first I’d like to calculate the overall heat gain for the month of December. For this estimate we’ll need to examine the heat loss from the storage tanks unaided by solar heat gain (in other words when the pump is off). We’ll also need an estimate of the gross heat loss from the 200 gallon storage system. The difference between them will be the solar heat gain of the 8 m2 MTD array. On average a drop of 40 F/ day is observed when the pump is off and gross average temperature drop of only 10 F/day. The solar heat gain may be estimated from these temperature differences.

temp drop without solar = 40/day
temp drop with solar      = 10/day

Q = solar heat gain for month of December 
(4-1) x 200 gal x 8 x30 day = 144,000 BTU

Efficiency of MTD array  144,000 BTU/288,000 BTU =50%  

This method of measuring collector efficiency is done by measuring temperature changes in the middle storage drum. This warm drum represents the average storage temperature of the 200 gallon system.

       144,000 BTU’s of heat may be insufficient to heat a house, but this method of collecting and storing heat demonstrates the potential to collect and trap the sun’s limited heat energy with a multi drum system in the month of December. If these heat storage drums were allowed to release their heat to a home or a DHW system a net heat gain would be observed even during this dark month.   The above graphs demonstrate the quantity and quality of radiant energy available for the entire month of December. A daily analysis may also be performed.  

Solar flux density peaked on Dec. 22 &23 between (9AM and noon to turn on the pump and harvest heat energy, but sunlight intensity on Dec, 20 &22 was too low for heat gain.



Storage temperature Dec. 20th = 620 F  
Storage temperature Dec. 22th = 540 F

That’s a 4 F drop per day. Notice the increase in ambient temperature Dec. 21 has no effect on storage temperature.  

HEAT GAIN TO 200 gal. STORAGE ( 9AM TO noon )  
Storage temperature Dec. 22th 9AM = 500 F  
Storage temperature Dec. 22th noon = 650 F
This is a gross storage temperature rise of 50 F/hr

SOLAR HEAT GAIN PER/hr HOUR    = 5 x 200 x 8 = 8,000 BTU  

SOLAR ENERGY AVAILABLE/hr        =  8 x 3,000 BTU x ( flux density factor .65) = 15,600 BTU

MTD COLLECTOR EFFICIENCY = 8,000/15,600 =  51%


INPUT/OUTPUT method of measuring collector efficiency

The pump turns on when collector temperature is 200 F above storage temp and shuts off when collector temp is within 20 F of storage temp. Without water flowing collector temp could reach 2000 F in mid winter with an ambient temperature of 200 F. In mid summer, when sunlight is most intense, MTD stagnation temperature climb higher. Richard Heiliger from Richmond Utah recorded a stagnation temperature of 265 F in July 2008 inside his MTD collectors, and his collectors are still alive and well. Of course when the pump is on and water is flowing through the TDM we would expect the collector temperature to drop within 20 F of the storage temperature as heat is transferred to storage containers. By knowing the flow rate of the pump and the difference in temperature between the water entering and leaving the collector and by knowing the sunlight intensity we may also estimate collector efficiency. 

From the solar flux graph above we know that that a peak sunlight intensity of 650 Wm2 was reached at 10 AM on December 22. Converting this into heat energy per square meter we get 3000 x .65 or about 2000 BTU/m2/hr available.

Input and Output temperature of MTD Collector  

Observe the collector input and output difference is 120 F at 10 AM when solar flux peaks. Since the flow rate of water through the array is 2 gal/min and since 2 gallons of water has a weight of 16 pounds we can estimate the heat gain/min.

Q/min. = 120 F x 16 lbs. = 192 BTU/min.  
Q/hr    = 192 x60 = 11,520 BTU/hr  

AVAILABLE ENERGY             = 2,000BTU/m2/hr x 8m2         = 16,000 BTU/hr 
COLLECTOR EFFICIENCY          = 11,520/16,000   = 72%



* 1. Input/Output heat gain method                72%
2. Daily heat gain method                              51%
2. Monthly heat gain method                          50%  

* The solar flux energy available estimate of 2,000 Watts/ m2 for this Input/Output estimate was made using a home made pyrometer calibrated from Richard's and Gary's pyranometer so this estimate may be off a little. There are many factors that go into calibrating collector efficiency such as flux intensity, temperature differential and flow rate but I believe all my estimates are within the ball park and the true MTD collector efficiency is somewhere between 50% and 70%. 

        The month of December may not be the best month for solar energy but it provides an interesting worst case challenge. Since both the MTD array and the PV panel are pitched at 45 degrees I’m confident the heat and power harvest from the experimental sunshed will improve as the season unfolds. I can only hope that home builders and home buyers will soon recognize the possibilities of energy efficiency and solar alternatives. Minimal back up power and heating systems are a reasonable precaution, but the sun will always be with us so let’s use all we can.  An ideal, energy efficient solar home requires thinking and planning. So let’s think before we plan and plan before we build. Retrofits are still possible if you have a roof oriented in the right direction. See what Richard did with his roof.