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Floodlighting a 25 × 10 m monument wall

Short answer

8 fittings in 2 vertical tiers × 4 horizontal positions. Each lamp ~124 W → use 150 W. Total lumens required 115,200 lm. Beam spread 12.5° covers 6.57 m at 30 m. Arrange 4 ground positions 6.25 m apart, each with two projectors aimed at upper and lower halves.

A vertical red wall of size 25 m x 10 m (High) of the monument is to be illuminated by a floodlight from a distance of 30m by fittings planted in the ground. Find the number of fittings/lamps, their arrangement and wattage of lamps if the Average Illumination required is 120 lux, Beam Factor is 0.5, the Maintenance Factor is 0.625, the waste factor is 1.2, Lamp Efficiency is 116 lumen/Watt and Beam Spread (vertical) Angle is 12.5°.

Given: wall 25 m × 10 m, distance d = 30 m, E = 120 lux, beam factor (BF) = 0.5, maintenance factor (MF) = 0.625, waste light factor (WLF) = 1.2, lamp efficacy = 116 lm/W, vertical beam spread = 12.5°.

Step 1: Total lamp lumens required

Area A   = 25 × 10 = 250 m²
Total lm = E × A × WLF / (BF × MF)
         = 120 × 250 × 1.2 / (0.5 × 0.625)
         = 36 000 / 0.3125
         = 115 200 lm

Step 2: Coverage of one beam (decides arrangement)

At 30 m, a beam of total spread 12.5° covers a length of

D = 2 × d × tan(12.5°/2)
  = 2 × 30 × tan 6.25°
  = 6.57 m
  • Vertically: the wall is 10 m high; the wall subtends tan⁻¹(10/30) = 18.4° at ground-level fittings, which is more than 12.5°. One beam (6.57 m) cannot cover 10 m, so 2 tiers of aiming are needed (one row aimed at the lower half, one at the upper half).
  • Horizontally: 25 / 6.57 = 3.8 → 4 beams across the wall (assuming a symmetrical beam).

So number of fittings = 2 × 4 = 8.

Step 3: Lamp wattage

Lumens per lamp = 115 200 / 8 = 14 400 lm
Wattage         = 14 400 / 116 = 124.1 W

Choose the next standard size: 150 W lamps (e.g. 150 W metal-halide or LED floodlight). This gives a little extra margin (8 × 150 × 116 = 139 200 lm).

Arrangement

          25 m wall (10 m high)
 ┌──────┬──────┬──────┬──────┐
 │  U1  │  U2  │  U3  │  U4  │ upper aim
 ├──────┼──────┼──────┼──────┤
 │  L1  │  L2  │  L3  │  L4  │ lower aim
 └──────┴──────┴──────┴──────┘
   ↑ 4 ground positions, 6.25 m apart,
   30 m in front; 2 fittings per position

The fittings are placed at 4 points about 6.25 m apart, 30 m in front of the wall, with two fittings at each point – one aimed at the upper half and one at the lower half. Beams overlap slightly for uniformity.

Answer: 8 fittings (2 rows × 4), each about 124 W → use 150 W lamps; total lamp lumens required 115 200 lm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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