The customer points at the tree and asks whether the panels will still work in winter. The honest answer is a picture of where the sun will be, and a sun path simulator draws it.
Part of the series Survey and design: getting the roof right before you quote.
The survey sees one hour of one day. The roof gets the rest of the year.
A surveyor stands in the garden at two on a Tuesday in May, looks at the tree, and writes "some shading, SW" on the sheet. The sun will rise somewhere different every morning, climb to a different height every noon and throw that shadow somewhere else every week, and nobody can go back and look. A sun path simulator puts the sun where it will be for any day and hour, casts the shadows from it onto a house, and works out what a clear sky would give the panels at that moment.
Three inputs place the sun: the date, the time and the place
The simulator uses the standard astronomical formulas, the ones in the SunCalc library. From latitude, longitude, the day of the year and the time it returns two angles: how high the sun is above the horizon, and its bearing on the compass. Sunrise, sunset and solar noon come from the same formulas. Latitude sets how high the sun can climb, the day sets where between its winter and summer limits it gets to, and the time sets where it is along the day's arc. Times are standard time for the longitude, which in a British winter is the wall clock.
Two arcs bound every day of the year
The sun-path diagram is the sky seen from above: the edge is the horizon, the centre is straight overhead, and the rings are 30 and 60 degrees up. Each day the sun draws one arc from east to west. On 21 June it rises in the north-east, climbs high and sets in the north-west. On 21 December it rises in the south-east, stays low and sets in the south-west. Anything that blocks the December arc blocks the sun at its worst. Anything that blocks the June arc blocks it all year.
Pitch and bearing decide how squarely the light lands
A panel makes the most power with the sun straight in front of it. For every moment the simulator works out the angle between the sun and the panel's face. The cosine of that angle is the share of the direct light that lands: sun square on, all of it, sun behind the panel, none. Bearing decides how much of each arc the panels see. South meets the noon sun square on all year, east sees the morning and turns its back on the afternoon. Pitch decides which season they favour. A steep roof faces the low winter sun and loses the high summer one, a shallow roof does the opposite.
The power is a clear-sky model, and the year is scaled to the sky we get
For every moment of the day the simulator takes the array's rated watts and applies four things in turn.
- The angle of incidence, above, to the direct light, which is 78 per cent of the clear-sky total.
- A diffuse share. The other 22 per cent is treated as light from the whole sky, scaled by how much sky the panel can see. A flat panel sees all of it, a panel at 35 degrees sees 91 per cent.
- An air-mass factor. Low sun passes through more atmosphere and arrives weaker.
- System losses. 15 per cent comes off for the inverter, the wiring and temperature.
The day's kWh is the area under that curve. A clear sky every day is not the British climate, so the year is 365 clear-sky days multiplied by a clearness factor for the climate band, 0.47 for Britain and Ireland.
Worked example: Manchester, 21 December
Set the place to Manchester and the day to 21 December, and leave the roof as the tool's defaults: twelve 440 W panels, 5.28 kWp, on a 35-degree pitch facing due south. These inputs are the example's own. The tool shows sunrise at 08:24, solar noon at 12:08 and sunset at 15:52. At noon the sun is 13 degrees up at a bearing of 178. Work the noon figure through by hand.
- Angle of incidence. A sun 13 degrees up against a panel pitched at 35 degrees, 2 degrees off square in bearing, gives a cosine of 0.74. The direct share is 0.78 times 0.74, which is 0.58.
- Diffuse. 0.22 times the 0.91 of the sky the panel sees is 0.20. Together, 0.78 of the array's rating before the atmosphere has its say.
- Air mass. At 13 degrees the light passes through 4.4 times as much air as from straight overhead. The correction is 0.60.
- The result. 5,280 W times 0.78 times 0.60 is about 2,480 W of DC. Take 15 per cent off and 2.1 kW reaches the meter, which is what the screen shows.
Drag the time back to 09:00. The sun is 3 degrees up in the south-east, the cosine has fallen to 0.47 and the light is passing through 18 times as much air, so the correction is 0.12. The array makes 0.31 kW, a seventh of the noon figure, and the clear-sky day comes to 9.6 kWh. Drag the day to 21 June: the noon sun is 60 degrees up, the array makes 4.7 kW and the day is 41.7 kWh. Then read the year. 365 clear-sky days add up to about 10,150 kWh, and multiplied by the 0.47 clearness the tool shows about 4,770 kWh, about 900 kWh per kWp.
What a shadow at nine on a December morning means
Leave the tree to the south-west switched on, keep 21 December, and drag through the afternoon. From about two its shadow stretches across the roof and the readout under the power figure counts the panels it covers. At three the sun is 4 degrees up and the array is making 0.58 kW under a clear sky. The panels the tree covers at that hour were making almost nothing anyway, and the same goes for a shadow at nine in the morning, when the array makes 0.31 kW. The atmosphere took the light before the tree got to it.
The shadows that matter are the ones across the December arc at midday, which block the sun for weeks either side of the shortest day, and the ones that persist into March and October, when a clear day gives this array around 30 kWh rather than 10. Drag the day to 21 March and watch the same tree. If its shadow has left the roof by nine, the tree is a winter nuisance. If it still crosses a row at eleven, that row is losing light in the months that carry the year. On a string inverter a shaded panel pulls its whole string down to its own level, so keep a row that catches the shadow on its own string or fit optimisers to the panels it touches. And when you show the customer, set 21 December at noon. That is the picture they asked for.
Installa puts the sun over the customer's own roof
- Stop working from a stand-in house. The designer builds the site from satellite imagery and a height model of the building, its neighbours and its trees, and finds the roof planes from Google's building data.
- Stop counting panels on a sketch. Panels are laid on the real roof planes, and each one is checked against the roof edges and the obstacles as you move it.
- Stop guessing where the sun will be. The sun is placed from the site's own latitude and longitude with the same formulas as the simulator, with sliders for the day and the time, so you can see where it sits against the roof for any hour of any day.
- Stop debating which plane to panel. A heat map shows a year of modelled sunlight on every surface, from Google's annual flux data.
- Stop typing the yield into the quote. The design's annual estimate follows the MCS method, with a shading factor taken from Google's measured sunlight for that roof where the data exists, and carries through to the proposal.
Sun from the astronomy, shadow from the model, yield from the sky you get. Try it on the sun path simulator, then see how the 3D designer in Installa does the same on a real roof.