Bed-and-Breakfast Load Analysis on a Partly Shaded Roof
A four-bedroom bed-and-breakfast draws about 300 L of hot water per day at a 60 °C setpoint. Cold mains water falls to 8 °C in January and averages 15 °C over the year. The owner has a 200 L electric tank with a 3 kW element and a time-of-use meter that charges triple between 17:00 and 21:00. The proposed array location is an asphalt-shingle roof at 30° pitch, azimuth 25° east of true south, with about 12 m² of clear area. A Solar Pathfinder survey shows an open horizon except for a masonry chimney that shades the eastern third of that roof from 09:00 to 10:30 between November and February. The owner asks two things: can solar cover 'most' of the hot water, and can the existing tank stay?
1. Calculate the daily thermal load in kWh at the January mains temperature and at the annual average mains temperature, and state how long the existing element must run.
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Use Q = m × c × ΔT, with c = 4.186 kJ/(kg·K) and 1 kWh = 3,600 kJ.
- January: 300 kg × 4.186 × (60 − 8) K = 65,300 kJ → 18.1 kWh/day.
- Annual average: 300 kg × 4.186 × (60 − 15) K = 56,500 kJ → 15.7 kWh/day.
Element run time in January: 3 kW × 0.95 = 2.85 kW delivered, so 18.1 ÷ 2.85 ≈ 6.4 hours of element-on time per day. If most of that lands in the 17:00–21:00 peak window, the owner is paying triple rate for roughly 4 hours of it.
Two checks before quoting: first, add standing losses for an older 200 L tank (commonly 1–2 kWh/day), which pushes the budget to about 19–20 kWh. Second, confirm whether the 300 L is drawn at 60 °C or is end-use volume tempered to 45 °C at the tap. If it is end-use volume, the load at the tank is lower, because the draw is diluted with cold water. The calculation above is the conservative case and should be labeled as such.
2. Given the chimney shading, how should the array be laid out and sized, and what would you tell the owner about simply oversizing to compensate?
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The shaded window is in the morning, and the roof already faces 25° east of south, so the array's production is concentrated in exactly the hours the chimney blocks. The eastern third of the roof should not carry collectors. That leaves roughly 8 m².
Sizing rule of thumb for flat plate in a moderate climate is about 1 m² of net aperture per 50–60 L/day of load, so 300 L/day points to 5–6 m². Three collectors at about 2 m² each on the unshaded western portion is a better match than four collectors crammed into the shade. Verify with the sun-path chart that the December clearance really starts at 10:30 and not later; the Pathfinder reading should be checked at the collector's actual tilt plane, not at the horizontal.
Do not oversize to compensate for shade. A shaded collector still circulates cold fluid, loses heat at night and adds pump hours, so it can be a net energy loss. If the client needs earlier-morning output, the alternatives are a ground mount at the clear part of the lot or accepting a later production profile that matches the evening peak draw, which is actually valuable given the 17:00–21:00 tariff.
3. Should the 200 L tank stay? Support the recommendation with numbers.
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Rule of thumb is 50–75 L of storage per m² of collector, and roughness 1.5–2 times the daily draw when a high solar fraction is wanted. Against 300 L/day, a 200 L tank provides under 0.7 days of storage, so it will swing widely and the element will carry most evening loads.
A useful second number is usable hot water: 200 L at 60 °C tempered to 45 °C at the tap yields about 200 × (60 − 10) ÷ (45 − 10) ≈ 285 L. That is barely one day's draw with no solar input and no reserve for the four-hour peak window.
Recommendation: move to a 400–500 L tank with a load-side heat exchanger, good insulation, and a thermostatic mixing valve so the tank can be held at 60–65 °C (scald and legionella control) while delivering 45–50 °C at the tap. Pair it with a controller that lets the element act only after the solar day. If 400 L cannot fit, keep the 200 L but size the collector to about 3 m² and tell the client honestly that the solar fraction will fall to roughly 40–50 percent, not 'most.'