Calculations for common CEA elements

Environmental Control Calculations

Where:

• SVP = 0.6108 × exp[(17.27 × T) / (T + 237.3)]
• AVP = RH × SVP / 100
  T in °C, RH in % | VPD (kPa) quantifies the drying power of air. Ideal range for most crops: 0.8–1.2 kPa. |
  | Saturation Vapour Pressure (SVP) | SVP = 0.6108 × exp[(17.27 × T) / (T + 237.3)] | Required to calculate VPD. Expressed in kPa. |
  | Air Exchange Rate (ACH) | ACH = (Q × 3600) / V
  Where:
• Q = airflow rate (m³/s)
• V = room volume (m³) | Air changes per hour (ACH) to ensure proper ventilation, CO₂ distribution, and humidity control. |
  | Canopy Light Interception | % Interception = 100 × (1 - e^(-k × LAI))
  Where:
• k = extinction coefficient (typically ~0.5)
• LAI = leaf area index | Estimates how much light is absorbed by the plant canopy. |

Light and Photosynthesis Calculations

Where:

• PPFD in μmol/m²/s
• Photoperiod in hours | Indicates total light plants receive daily. Critical for determining growth potential. |
  | Lighting Energy Efficiency (PPE) | PPE = PPFD / PowerMeasured in μmol/J | Photosynthetic Photon Efficacy. Higher values indicate more efficient lighting. || Photosynthetic Rate Estimation | P = α × I / (1 + (I / Iₛ))
  Where:
• P = photosynthesis rate
• α = quantum yield
• I = light intensity
• Iₛ = light saturation point | Non-linear model; specific to species. Helps evaluate light-limited growth.

Photosynthetically Active Radiation (PAR)

Definition: The portion of the light spectrum usable by plants for photosynthesis (400–700 nm).

• Unit: µmol/m²/s (micromoles of photons per square metre per second)
• Measured using: Quantum sensor
• Note: Typically not calculated but measured; however, estimated from total luminous flux using spectral conversion factors for different light sources if sensor data is unavailable.

Photosynthetic Photon Flux (PPF)

Formula:

PPF=Total PAR output (µmol/s)Time (s)\text{PPF} = \frac{\text{Total PAR output (µmol/s)}}{\text{Time (s)}}PPF=Time (s)Total PAR output (µmol/s)​ 

• Definition: Total number of photons in the PAR range emitted per second by a light source.
• Unit: µmol/s
• Note: Often provided by lighting manufacturers.

Photosynthetic Photon Flux Density (PPFD)

Formula:

PPFD=PPFArea=µmol/sm²=µmol/m²/s\text{PPFD} = \frac{\text{PPF}}{\text{Area}} = \frac{\text{µmol/s}}{\text{m²}} = \text{µmol/m²/s}PPFD=AreaPPF​=m²µmol/s​=µmol/m²/s

• Definition: The number of PAR photons striking a given surface area per second.
• Used to: Evaluate light intensity reaching the plant canopy.

4. Daily Light Integral (DLI)

Formula:

DLI=(PPFD×Photoperiod (hours)×3600)÷1,000,000\text{DLI} = \left( \text{PPFD} \times \text{Photoperiod (hours)} \times 3600 \right) \div 1,000,000DLI=(PPFD×Photoperiod (hours)×3600)÷1,000,000 #

• Unit: mol/m²/day
• Definition: The total PAR light received by a square metre in one day.
• Use: Essential for crop planning; varies by species and growth stage.

Light Use Efficiency (LUE)

Formula:

LUE=Biomass Produced (g)Total Light Received (mol)\text{LUE} = \frac{\text{Biomass Produced (g)}}{\text{Total Light Received (mol)}}LUE=Total Light Received (mol)Biomass Produced (g)​ 

• Unit: g/mol
• Definition: Biomass production per unit of light energy; used to evaluate crop response efficiency.

Photosynthetic Photon Efficacy (PPE)

Formula:

PPE=PPF (µmol/s)Power Input (W)\text{PPE} = \frac{\text{PPF (µmol/s)}}{\text{Power Input (W)}}PPE=Power Input (W)PPF (µmol/s)​ 

• Unit: µmol/J
• Definition: Efficiency of a lighting fixture in converting electrical energy to photosynthetically useful photons.
• Benchmark: Higher PPE = better energy efficiency.

Lighting Power Density

Formula:

Lighting Power Density=Total Electrical Power (W)Growing Area (m²)\text{Lighting Power Density} = \frac{\text{Total Electrical Power (W)}}{\text{Growing Area (m²)}}Lighting Power Density=Growing Area (m²)Total Electrical Power (W)​ 

• Unit: W/m²
• Used to: Plan power infrastructure and thermal management.

Total Daily Energy Consumption

Formula:

Energy Consumption (kWh/day)=Lighting Power (W)×Photoperiod (h)1000\text{Energy Consumption (kWh/day)} = \frac{\text{Lighting Power (W)} \times \text{Photoperiod (h)}}{1000}Energy Consumption (kWh/day)=1000Lighting Power (W)×Photoperiod (h)​ 

• Used for: Operational cost and energy efficiency calculations.

Light Distribution Uniformity

Formula (Uniformity Ratio):

Uniformity=Minimum PPFDAverage PPFD\text{Uniformity} = \frac{\text{Minimum PPFD}}{\text{Average PPFD}}Uniformity=Average PPFDMinimum PPFD​ 

• Use: Ensures even light across crop canopy to avoid growth variability.
• Ideal Value: ≥ 0.7 for uniform commercial production.

Conversion from Lumens to PAR (approximate)

Formula (approximate, for white LEDs):

PPF (µmol/s)≈Lumens×Conversion Factor\text{PPF (µmol/s)} \approx \text{Lumens} \times \text{Conversion Factor}PPF (µmol/s)≈Lumens×Conversion Factor

• Conversion Factors: Vary by light source:
• Cool white LED: ~0.014–0.015 µmol/s/lumen
• HPS lamp: ~0.012 µmol/s/lumen

Note: This is a rough estimation. Spectral power distribution data should be used when possible for accuracy.

Optional Related Calculations

Light Saturation Point

Definition: The light intensity beyond which photosynthesis no longer increases.

• Measured experimentally; varies by species and crop stage.

Heat Load from Lighting

Formula:

Heat (W)=Total Power Input (W)×Percentage Converted to Heat\text{Heat (W)} = \text{Total Power Input (W)} \times \text{Percentage Converted to Heat}Heat (W)=Total Power Input (W)×Percentage Converted to Heat

• Typical conversion: ~70–90% of input power is lost as heat in older systems; LEDs ~50–60%.

Nutrient and Water Management

Energy and Climate Calculations

Growth and Production Metrics