[{"data":1,"prerenderedAt":86},["ShallowReactive",2],{"example-row-spacing-en":3,"faq-row-spacing-en":54,"sources-row-spacing-en":85},{"input":4,"output":11},{"latitudeDeg":5,"moduleLengthM":6,"tiltDeg":7,"designCase":8,"rowAzimuthDeg":9,"criterionChosenByUser":10},48.8,1.13,30,"winter-9to15",180,false,{"solarAltitudeDeg":12,"solarAzimuthDeg":13,"azimuthDeltaDeg":14,"heightM":15,"shadowLengthM":16,"pitchM":17,"gcr":18,"pitchWithoutAzimuthCorrectionM":19,"azimuthCorrectionSavingPercent":20,"pitchAtNoonM":21,"latitudeDeg":5,"tiltDeg":7,"moduleLengthM":6,"rowAzimuthDeg":9,"steps":22,"warnings":41},7.355515369300822,220.8542673821513,40.854267382151306,0.5649999999999998,3.3105529953239192,4.289161701600335,0.26345474445003647,5.3554711775441755,19.910656608795552,2.742607789711073,[23,28,31,35,38],{"label":24,"expression":25,"value":12,"unit":26,"provenance":27},"solarAltitude","asin(sin phi * sin delta + cos phi * cos delta * cos omega)","deg","exact",{"label":29,"expression":30,"value":14,"unit":26,"provenance":27},"azimuthDelta","|A_sun - A_row|",{"label":32,"expression":33,"value":15,"unit":34,"provenance":27},"moduleEdgeHeight","L_module * sin beta","m",{"label":36,"expression":37,"value":16,"unit":34,"provenance":27},"shadowLength","h * cos(deltaA) \u002F tan alpha",{"label":39,"expression":40,"value":17,"unit":34,"provenance":27},"rowPitch","d_shadow + L_module * cos beta",[42,48],{"level":43,"code":44,"params":45,"anchors":46},"warning","SHADING_CRITERION_ASSUMED",{},[47],"designCase",{"level":49,"code":50,"params":51,"anchors":52},"info","HORIZON_NOT_CONSIDERED",{},[53],"latitudeDeg",[55,58,61,64,67,70,73,76,79,82],{"q":56,"a":57},"How far apart do solar panel rows need to be to avoid self-shading?","The shadow length is d = h · cos(ΔA) \u002F tan α, with module edge height h = L · sin β and the sun's altitude α on the design day — the winter solstice. The row pitch is d plus the projected module length L · cos β, and the ground coverage ratio follows as GCR = L \u002F pitch. The calculator applies to parallel rows of equal height on a level surface.",{"q":59,"a":60},"Which design time should I pick — shade-free at noon only, or from 9 to 15?","That is the question almost no free calculator asks: at 48.8° north the two cases differ by 56 % in land area. Silently computing only the noon case yields an array that is partially shaded three to four hours a day from November to February. The azimuth correction cos(ΔA) matters too: without it the afternoon shadow comes out 32 % too long in the reference case, because the sun strikes at an angle and the shadow runs obliquely between the rows.",{"q":62,"a":63},"Does this work on sloped ground or with trees nearby?","No — sloped mounting surfaces, north-south oriented rows, individual obstacles and the horizon are not covered; a tree or ridge to the south changes everything. The electrical effects of partial shading are strongly non-linear and are not modelled here either. If the sun is below the horizon at the chosen design time, the calculator refuses the computation rather than returning an infinite pitch.",{"q":65,"a":66},"How big is the difference between the design cases, concretely?","Huge. In the reference case (48.8° north, module edge 1.13 m, 30° tilt), “shade-free at noon only” needs 2.74 m of row pitch (GCR 0.41), while “shade-free 9–15 h” needs 4.29 m (GCR 0.26) — 56% more land for the same modules. On a flat roof this single assumption decides whether 40 or 26 modules fit. That is why the design case is a visible required choice here, not a silent default.",{"q":68,"a":69},"What does the azimuth correction do that other calculators skip?","In the morning and evening the sun stands sideways to the row — the shadow falls diagonally between the rows instead of straight onto the next one. The factor cos ΔA captures that. Without it, the 3 p.m. case at the reference site would give 4.38 m of shadow instead of 3.31 m — 32% too much shadow and thus about 20% too much row pitch, i.e. wasted land. The calculator shows both values so the difference can be checked.",{"q":71,"a":72},"Why does the calculator use December 21 of all days?","At winter solstice the noon sun is at its lowest (declination −23.44°) — shadows are longest on that day. If the layout is shade-free on December 21, it is shade-free all year. Any other reference date would mean: on the darkest days, when yield is lowest anyway, the array additionally loses to inter-row shading — and partial shading hurts disproportionately in electrical terms.",{"q":74,"a":75},"Is the rule of thumb “row spacing = 3 × collector height” correct?","Only for one very specific case. Behind every factor hides a shading limit angle — the sun altitude below which shading is accepted. Factor 3 corresponds to 18.4°, almost exactly the noon sun on December 21 at 48° north (17.8° → factor 3.1). So the rule of thumb is not a safety margin; it is the silent “shade-free at noon only” assumption for central Europe. At 53.5° north even the noon case already needs factor 4.3, and shade-free from 9 to 15 at 48.8° north lands at factor 5.9 — nearly double the rule of thumb. Even smaller factors in circulation (down to 1.5×) are more optimistic still.",{"q":77,"a":78},"What row spacing is typical on a flat roof with 10–15° tilt?","A worked example for 51° north, landscape-mounted module with a 1.13 m edge, 12° tilt: shade-free at noon only 1.95 m pitch (GCR 0.58), shade-free 9–15 h 2.89 m (GCR 0.39). The shallow tilt on flat roofs is no accident — it lowers the module edge height and with it row spacing, ballast and wind load all at once. Setbacks to the parapet and roof edge are a separate topic (wind edge zones), not part of this calculation.",{"q":80,"a":81},"What is a good ground coverage ratio (GCR)?","GCR = module edge divided by pitch — the share of ground area covered by modules. In the reference case (48.8° north, 30° tilt) it is 0.41 (noon only) or 0.26 (9–15 h); below 0.25 the calculator warns because the layout becomes very land-hungry. The strongest lever is tilt: at 48.8° north with the 9–15 design, 15° instead of 30° lifts the GCR from 0.26 to 0.40 — each module yields slightly less, but far more modules fit on a limited area, which in total often means more energy.",{"q":83,"a":84},"Does the calculator need weather data for my location?","No. Row spacing follows from pure solar geometry — latitude is all it takes, no irradiance dataset required. Rome (41.9° north): 2.21 m at noon, 2.88 m for 9–15 h. Stockholm (59.3° north): 5.41 m at noon — and the 9–15 case simply does not exist there, because above roughly 58.5° north the sun sets before 15:00 true solar time on December 21. The calculator says so openly instead of returning a fantasy value.",[],1786101732496]