suppose solar panels at $2 per watt, the number of sun-hours per day in missouri Columbia is average of 4.73 so a 1Kw rated array gives you only 4.73 kWh per day vs 24 kW hours for biomass.

But then the biomass burner can work at night and over cloudy periods so if you wanted 24 kWh per day, solar panel systems are usually designed with enough battery to last you for a 3 day cloudy period so 72 kWh. Wikipedia says VRLA batteries are about $0.125 per Wh, so that is $ 9k capital cost, and they wear out at 8% or so each year[16], nickel iron might be about 4 times onger lasting though that's getting further into speculation.


So capital cost for solar system that gives average of 24 kWh per day not including inverter etc which is the same for biomass: $10,000 for collector plus $9,000 for batteries for $19,000
Running cost for a year: $720 for batteries, plus cleaning of collector and other tasks.

For biomass :

Capital cost:
battery capital costs: For biomass you need a much smaller battery, suppose it needs to store a half of a day's energy although that migh tbe excessive, 12 kWh, so $1500
Estimated engine costs: $3 per watt for engine, $3000 (that seems awfully high), $0.3 for burner, $300
Total: $4800


Ongoing costs: Battery replacement: $120

fuel costs:
$200 income for farmers per acre not clear if that is profit or total , remember from king corn documentary that an acre of corn was about $160 in actual costs (absent any subsidies) to grow so suppose $360 for an acres yield, [5][6][7]
crop yield can vary greatly but reference [17] says 7 tons or so from switch grass per acre, the valley project got 1.266 MWh per ton so for one year at 1 kW we need that's 6.9 tons or about $360. If it has to be pelletized though, on alibaba.com it looks like in quantities of 100 tons biomass pellets are about $100 per ton so $690.

From more basic calculations, the heat energy released bu combustion of 1 kg of biomass of the dryness we are talking about (11-13%) is about 17 Mj/kg [8] (4.72 kWh/kg) and so if it is converted at 28% that's 1.32 kWh per kg, so 11.582 tons of biomass for a year (31.7 kg per day) or $595 for plain biomass straight from field and $1158 for pelletized if purchased bulk thouugh eg alibaba.com, if purchased retail that's a lot though, on ebay $2651.82 up to some people retail are charging $400 per ton, so $5303.64 [10][11][12][13].

In the winter biomass combustion will displace a lot of fuel though that would have otherwise have been burned anyway so for periods when heating fuel would be needed subtract the amount of fuel that woudl have been needed for heating anyway or the amount needed to produce all electricity, whichever is less (except that you might have been using solar for heat instead... that would need to be factored in obviously, need to lookup the cost of flat plate collectors ) I think we might fairly suppose this is one quarter of the total biomass used, a 3 month heating period, though it of course could be higher depending on if the heat can be put to use, in a climate above say 40 degrees latitude.


Hot water heating for a typical american house I don't know, if it was 150 liters of hot water (50 liters each for 3 people) heated from 5 degrees to 45 degrees c ( a comfortable shower) that is 40degrees*150kg*4Kj/degree-kg=24000 Kj or 6.6 kWh, at 4.72 kWh per kg that's not going to dent the net biomass costs any really.


Link [16] indicates that as much as 6000 kWh (21.6 Gj) or 16 kWh per day of heat for hot water alone may be used by the average american household. Some of these sources are very poor quality. A more in depth analyis with decent quality sources should be done because all these errors really add up. That's a lot of water. Clearly heat exchangers like the powerpipe and water saving stuff will reduce that greatly so if we are to plan for the viability of a scheme like biomass cogen that needs to be factored in. Also clearly the low hanging fruit is efficiency but we need to move forwards on all fronts and people will hopefully catch up.

Link [16] also indicates that the total heating requirements average for the US are also about 6000kWh for heating. Obviously it's going to be far higher than that though in a colder area.


If natural gas was used to provide the heat at $4.23 per Gj that would be about if it is converted to 24 kWh at 28% efficiency that's 112.6 Gj needed $476, no wonder fossil fuels are favored - no ash no nothing! [8][9] If propane were used though that is about $1.2 per kg at 46 Mj per kg that's, $2447.

The total area required is obviously dependent on crop yield but about 0.4 acres to 7 acres, probably 1 acre is realistic.




Also the 24 kW that a solar panel system produces also offsets heating fuel costs, to be fair.

note [15] indicates that overall 22% might be more realistic if the engine is 28% efficient, though some sunpower engines are 36% efficient at tcold/thot ratio of 3 maybe these are hard to do or something. However this reduction in efficiency vs. the engien efficiency will apply to steam just as well.

Total ongoing costs: $715 for plain biomass. Could be reasonably expected to be $2771 if you had to buy biomass though. Plus cost of engine maintenance (next to none for stirling) and dealing with ash etc. (ash content can vary from 1% to more than 5% so this could be quite substantial if not used in farm context). If steam engine needs parts replaced twice a year could be substantial cost there, couple hundred bucks easily maybe more when you factor in labor time.

Conclusion: Biomass probably makes a ton of sense and can be cheaper both in capital and running costs if you can grow your own biomass and further investigation is needed to determine the value of being able to use the waste heat. Efficiency matters quite substantially though as the biomass is not free and only a fraction of the waste heat will likely be used. Improvements in efficiency on the demand side is also important.


To improve accuracy:

In favor of pure solar, no ash, no transport or fuel handling

Against solar mirror cleaning, potential breakage due to storms

in favor of biomass portable, lower installation costs, less susceptible to damage from storms (except reduced biomass yield), can use an alternator which might reduce cost of inverter a bit