Number of Supplemental LED Lights Required: 22-Agric-A1 Applied Plant, Animal or Human Physiology, May 2015, Q6

Question 6: Number of Supplemental LED Lights Required (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Supplemental DLI required (from Question 5b)	7.4 mol·m⁻²·d⁻¹
Combined quantum output per Blue/Red LED light	0.51 µmol·m⁻²·s⁻¹

Find. The number of Blue/Red LED lights needed to supply the 7.4 mol·m⁻²·d⁻¹ supplemental DLI.

Approach. Convert the required supplemental DLI (a daily photon total) into the instantaneous combined PPFD needed over a full day, then divide by the output of one light to get the light count, rounding up since a fraction of a light cannot be installed.

Check: the question gives no photoperiod for the supplemental lighting itself, so the DLI-to-PPFD conversion below integrates over a full 24 h day (86,400 s), consistent with the "per day" (d⁻¹) units used throughout the question. In practice supplemental fixtures would run only during a chosen photoperiod at a correspondingly higher instantaneous output over fewer hours — the total daily photon delivery, and hence the light count derived here, is unchanged by that choice as long as the same total DLI is delivered.

Convert the supplemental DLI target to a combined PPFD. $$\text{PPFD}_{\text{required}} = \frac{\Delta\text{DLI} \times 10^{6}} {t_{\text{day}}} = \frac{7.4 \times 10^{6}}{86{,}400} = \boxed{85.65\ \mu\text{mol} \cdot\text{m}^{-2}\cdot\text{s}^{-1}}$$
Divide by the output of one LED light. $$n = \frac{\text{PPFD}_{\text{required}}}{\text{output per light}} = \frac{85.65}{0.51} = 167.9$$ Rounding up (a fractional light cannot be installed, and the count must at least meet the target): $$n = \boxed{168\ \text{Blue/Red LED lights}}$$

Quantity	Result
Required combined PPFD (supplemental)	85.65 µmol·m⁻²·s⁻¹
Number of Blue/Red LED lights (exact)	167.9
Number of Blue/Red LED lights (installed)	168

Concept & Theory

Topic: Sizing discrete supplemental-lighting fixtures to a continuous DLI target.

Key relations: $n_{\text{lights}} = \dfrac{\text{PPFD}_{\text{required}}} {\text{PPFD}_{\text{per fixture}}}$, with $\text{PPFD}_{\text{required}}$ obtained from the target DLI via $\text{PPFD} = \dfrac{\text{DLI}\times 10^{6}}{t}$.

Why this works: Because DLI is additive over time and space (photon counts simply sum), any combination of fixture count and run-time that delivers the same total daily photon count meets the same DLI target — the calculation only needs the target's total photon flux, not an assumed photoperiod, provided the same day-length basis is used consistently on both sides of the conversion.

Common pitfall: Truncating instead of rounding up the light count (167 lights under-delivers the target DLI) — a minimum requirement must be rounded up to the next whole fixture, not to the nearest one.

Source: Runkle, Daily Light Integral: A Useful Tool for Greenhouse Growers, Michigan State University Extension.

Question 6 of 6: Number of Supplemental LED Lights Required

Question 6: Number of Supplemental LED Lights Required (20 marks)