Abstract

This document defines the calculation methodology used by Growing Spaces to estimate heating load, cooling load, ventilation requirements, passive-system contribution, heat-pump capacity class, supplemental heat need, and order-of-magnitude annual electrical energy for 15 to 42 ft Growing Dome greenhouses across representative U.S. climate bands.

The methodology is published as a transparent technical reference. It is intended for Growing Spaces staff, HVAC partners, contractors, advanced customers, technical reviewers, and other readers who want to understand or reproduce the sizing logic behind the Growing Spaces Greenhouse Climate Calculator and Heating & Cooling Guide.

This document is the canonical technical reference for formulas, assumptions, climate classification rules, sizing tables, source notes, and stated limitations. Customer-facing pages, calculator outputs, and launch content may simplify this information, but should not redefine the underlying calculations.

1. Purpose and scope

This document is the technical methodology for sizing heating, cooling, and ventilation equipment in Growing Domes. It explains how dome geometry, climate inputs, passive systems, and physical operating targets translate into heating loads, cooling loads, airflow requirements, heat-pump capacity classes, and supplemental heat calculations.

It is not a product specification, final equipment selection, local-code determination, stamped engineering design, warranty, or guarantee of interior temperature, crop yield, utility cost, or equipment performance. Capacity tables in this document show calculated nominal capacity classes. Final package recommendations are made through the Growing Spaces Greenhouse Climate Calculator and project-specific review.

Use this document to:

• Verify that Growing Spaces sizing math is consistent with first-principles physics and standard greenhouse engineering practice.
• Reproduce sizing calculations for any standard dome size at a U.S. site.
• Adapt the methodology to non-standard configurations or site conditions.
• Compare passive and mechanical strategies for climate control.
• Trace calculator and selector outputs back to their technical assumptions.

All values are reference points. Local code, altitude, wind exposure, construction quality, equipment availability, and grower goals may justify different choices.

1.1 Model status

This methodology is a sizing and comparison model. It uses representative climate bands, simplified steady-state heat-transfer assumptions, calculated dome geometry, published or internal material assumptions, passive-system assumptions, and rounded equipment capacity classes. It is intended to support planning, calculator logic, staff review, and partner review.

Results should be interpreted as modeled reference values. Actual performance depends on site conditions, installation quality, wind, altitude, solar exposure, shade use, crop density, humidity, pond installation, owner operation, utility availability, controls, selected equipment, and maintenance.

1.2 Unified sizing method with case-stratified inputs

This methodology uses a single physics-based formula to size heating equipment across all customer cases:

Q_required = max(floor, UA × (T_target − T_design) − Q_pond_credit)

The four customer cases defined in §10.2 produce different equipment recommendations not by switching to a different formula, but by stratifying the inputs:

Cases 1-3 are sized for typical cold-weather operation with the customer accepting dome temperature drift below T_target during the cold-tail event. The customer's gardener tolerance is the explicit design assumption: equipment is not asked to hold T_target through the worst few hours per year. Cases 1-3 use January average low as the design temperature for this reason.

Case 4 represents the most conservative sizing, applied for customers committing to year-round productive operation with no temperature drift accepted. Case 4 layers two vectors of conservatism on top of the case 3 framework: the cold-tail design-temperature multiplier (0.15 × annual range below January average low) and the depleted-pond assumption (Q_pond_credit = 0, representing the design event of multi-day overcast cold conditions in which pond charge has been exhausted).

Both vectors apply to case 4 only. Cases 1-3 explicitly do not get the cold-tail multiplier on T_design, because compounding gardener-tolerance drift acceptance with cold-tail design conservatism would over-size equipment for those customers.

Equipment selection on top of Q_required (heat pump, supplemental, or both) is determined by a calculator-internal optimization that balances heat-pump capacity at site-specific design temperature, supplemental delivery limits (single-unit standalone capacity cannot exceed 10 kBtu·h⁻¹ in the configurations Growing Spaces sells), modulation behavior, and rough cost factors. The optimization is not exposed in detail because the underlying variables (utility rates, fuel availability, customer run-time preferences) vary too widely across customers to model precisely.

The Greenhouse Climate Calculator implements this framework. Strict mode in the calculator UI maps to case 4. Operating mode (3-season / 4-season cool / 4-season fruiting) and the strict-mode toggle together select the case.

2. Operating envelope

2.1 The 50 to 90 °F band for warm-season fruiting crops

The primary modeled design target for full warm-season production:

Maintain interior temperature within a 50 to 90 °F operating band under modeled conditions, with short excursions limited to about one hour at a time.

Below 50 °F, many warm-season crops experience chilling stress within hours. Above 90 °F, pollen viability and fruit set can decline measurably; sustained excursions can reduce production quality and yield. The one-hour tolerance window reflects a practical recovery interval for ventilation, pond mass, or active equipment. It is not a crop-performance guarantee.

2.2 Three operating modes

Operations may target one of three operating modes, each with a different winter indoor maintain temperature. The cooling-side maintain (90 °F max) is identical across all three.

The three modes generate three parallel heating-load tables in Section 4.6. The cooling-load methodology in Section 5 is unchanged across modes.

2.3 Indoor design temperatures used in load calculations

Most residential HVAC sizing assumes approximately 70 °F indoor for occupied buildings. That assumption is conservative for a greenhouse, which operates at the lower band edge of the §2.1 envelope during winter design events.

The case-stratified target temperatures (T_target) used in §9.4 step from 33 °F (3-season pond and structural protection) through 48 °F (productive year-round at the cold-tail design event with depleted pond). Each case's T_target reflects the binding lower bound the customer is willing to commit equipment to hold under that case's design assumptions. Cases 1-3 accept dome temperature drift below T_target during the cold-tail event; case 4 does not.

2.4 Control hierarchy and equipment cascade

The shell, the pond, the vents, the fans, and the shade cloth all carry part of the load. Heat-pump (HP) and supplemental heat sizing assume that.

Heating cascade:

1. Daytime solar gain through the cap, with vents closed and shade cloth retracted.
2. Pond thermal mass releasing heat absorbed during the day.
3. Heat-pump heating.
4. Supplemental heat (sized for coldest nights).

Cooling cascade:

1. 50 % aluminet shade cloth (deployed for cooling season).
2. Active mechanical ventilation while outdoor air is below indoor temperature.
3. Pond thermal mass absorbing daytime heat.
4. Direct evaporative cooling, where installed (dry climates only).
5. Heat-pump cooling for residual sensible and all latent load that the cascade above cannot handle.

The heat pump is never the first stage in either mode.

2.5 Observed dome performance and field-validation status

The methodology is informed by observed operation of installed Growing Domes and by support history across a range of climates, dome sizes, seasons, and operating practices. These observations are used as a qualitative sanity check on the sizing model.

Field experience indicates that a properly built dome with pond installed, vents closed, shade retracted, and limited air leakage can often operate roughly 20 to 30 °F warmer than ambient through passive mechanisms alone during favorable winter conditions. Those mechanisms include daytime solar gain, pond storage, reduced nighttime ventilation, and infiltration control.

Field experience also indicates that a properly built dome with shade deployed, vents and doors open, and fans running often operates close to ambient during warm weather, although performance varies materially with sun, wind, humidity, crop density, ventilation state, and owner operation.

These observations anchor the methodology but should not be read as guaranteed temperature differentials. Growing Spaces is developing a structured field-validation dataset to compare modeled results against instrumented dome performance by dome size, climate band, season, operating mode, pond state, shade state, and mechanical state. Until that dataset is published, field-performance statements should be treated as qualitative calibration context rather than statistical validation.

3. Climate zoning

3.1 Data inputs

Site classification uses long-term monthly normals from NASA POWER, accessed via the following pipeline:

1. ZIP → city, state, latitude, longitude via zippopotam.us.
2. Lat / lon → elevation via open-meteo.com.
3. Lat / lon → multi-year monthly climatology via NASA POWER monthly climatology API, pulling three normals:
   • T2M_MIN for January (mean January daily minimum temperature)
   • T2M_MAX for July (mean July daily maximum temperature)
   • RH2M for July (mean July relative humidity)
4. Three normals → climate band via the ruleset in 3.2.

Classification thresholds are applied to raw monthly normals, not to design-condition extremes. Raw normals are robust signals for site climate type. Design-condition extremes (ASHRAE 99 % heating, 1 % cooling) are used separately in the engineering load calculations (Sections 4.6, 5.5, and 9.6).

3.2 Six engineering bands

The band rules are applied with priority order in the classifier. CZ is checked first (any site with Jan T_min < 5 °F goes to CZ regardless of summer conditions). Hot bands are checked next based on July high. Mixed bands are then split by humidity. Marine mild catches the residual.

The CZ band covers a wide range of winter severity, from the high Rockies (Pagosa Springs, Crested Butte, Steamboat: ~-7 °F site-specific design) through the upper Midwest and northern Plains (Bismarck, Duluth, Minneapolis: ~-19 °F site-specific design) to interior Alaska (Fairbanks, Tok: below -40 °F site-specific design). High-elevation Rockies sites operate notably milder than the Plains and Midwest sites in this band, which in turn operate milder than interior Alaska. Coastal-moderated subarctic sites like Anchorage (Jan T_min ≈ 11 °F) classify as MZ-H rather than CZ under this threshold, because their winter conditions are closer to Chicago than to Fairbanks. This is intentional: MZ-H equipment recommendations cover Anchorage-like climates well, and CZ is reserved for the most demanding heating environments.

All cases use site-specific design temperatures derived from each site's climate normals, which captures the within-band spread between high-Rockies sites (~-7 °F design at Pagosa Springs at the case 4 multiplier of 0.15), Plains/Midwest sites (~-17 °F at Bismarck), and interior Alaska (below -30 °F at Fairbanks). The previous methodology's strict-mode use of a band-representative -15 °F is replaced by the site-specific calculation in all cases.

CZ sites at the cold end of the band (interior Alaska, design temperatures below -25 °F) require partner verification regardless of which case is targeted, because the heat-pump performance derate and supplemental sizing are at the limit of the calibrated formula range.

If a site falls between bands, use the colder or more humid band as a conservative assumption. Verify project-specific design temperatures against the latest applicable ASHRAE climatic design data or an equivalent local design source.

3.3 Engineering bands and customer-facing labels

The six engineering bands are the calculation basis for this methodology. Customer-facing pages and tools may consolidate those bands into simpler descriptions for readability, but underlying formulas continue to use the engineering band unless a later methodology revision states otherwise.

4. Geometry and thermal model

4.1 Geometry source

All shell areas, interior volumes, and stem-wall areas come from the Growing Spaces internal geometry workbook, derived from CAD models of each dome size. The dome is a spherical cap of apex height h and base radius R, sitting on a 24-inch cylindrical stem wall. Geodesic frequency varies by size (2V for 15 to 18 ft, 3V for 22 to 33 ft, 4V for 42 ft).

Cap surface area is computed as A_cap ≈ π·(R² + h²). Stem-wall area is A_stem = 2π·R·2.0 ft.

4.2 Conductive U breakdown

The shell is treated as three elements with different thermal properties.

Glazing (transparent polycarbonate). Standard 16 mm RDC (Reinforced Double Co-Extruded) 5-Wall polycarbonate, U = 0.36 BTU·h⁻¹·ft⁻²·°F⁻¹. Light transmission for clear: 65%. SHGC: 0.68.

Insulated north section. Approximately 15 % of the upper cap is replaced with an insulated panel section, R-3 effective, U ≈ 0.33.

Stem wall. Two construction options:

Load tables in 4.6 assume the framed option as the default.

Conductive UA, framed stem wall:

4.3 Infiltration

Infiltration is treated as a separate term, additive to the conductive UA:

Q_inf = 0.018 × ACH × V × ΔT

The 0.018 coefficient is the volumetric heat capacity of air at typical sea-level density.

Load tables use 1.0 ACH as the design baseline.

Infiltration UA at design ACH = 1.0:

4.4 Total UA

4.5 Air-tightness sensitivity

For a 26 ft dome:

Moving from 2.0 ACH (typical aged tape construction) to 0.75 ACH (current-generation seam caps with EPDM gaskets) reduces effective U by roughly 25 %. Because envelope heat loss scales with UA, winter heating load and heating energy scale down proportionally under the same operating assumptions.

4.6 99 % heating-load tables

Q_heat = UA_total × (T_indoor_maintain - T_99 %_outdoor)

Outdoor design temperatures are ASHRAE 99 % values for representative cities. The values shown in 4.6a/b/c are reference envelope loads, useful for partner verification and physics cross-checks. Equipment sizing in the calculator uses site-specific design temperatures per §9.4 rather than the zone-representative values shown here; the CZ rows use -15 °F as a Bismarck-class midpoint for reference, which over-represents high-Rockies sites and under-represents Fairbanks-class extremes.

4.6a 4-season fruiting (50 °F maintain)

Values in kBtu·h⁻¹.

4.6b 4-season cool (40 °F maintain)

4.6c 3-season frost protection (35 °F maintain)

These are envelope loads on a cloudy worst-case design night, before pond, solar gain, or supplemental heat contribute. The reduction from 4-season fruiting to 3-season frost protection is most significant in mild bands (HZ-HD, HZ-HH, MZ-M) where ΔT changes by a large fraction. In colder bands (MZ-D, MZ-H, CZ) the absolute load reduction is smaller because the ΔT change is a smaller fraction of total.

These tables describe the dome's envelope-load characteristics at zone-representative ASHRAE 99 % design conditions for reference and partner verification. Equipment sizing uses the §9.4 unified formula with case-stratified inputs and site-specific design temperatures rather than zone-representative values; the §4.6 envelope loads do not directly drive the calculator's recommendations.

4.7 Solar gain on the heating side

The 99 % heating loads above assume cloudy-day conditions with no solar contribution. Typical winter operation looks very different.

A 26 ft dome at 40° N latitude on a clear winter day at solar noon receives roughly 200 W/m² horizontal irradiance. After 16 mm five-wall PC transmission (~0.62) and with shade cloth retracted, peak solar gain into the dome is on the order of 20 kBtu·h⁻¹ for a 26 ft dome. Daily-integrated solar gain over winter daylight hours is roughly 40 % of the noon peak.

This is the mechanism behind the field-observed passive winter temperature uplift discussed in Section 2.5. During clear winter days, the dome is solar-heated. The pond absorbs excess solar that would otherwise overheat the interior, and releases that heat overnight. Active heating engages only on cold cloudy nights and overnight in deep winter.

For design-day sizing in Section 4.6 and Section 9.6 we ignore solar gain because the worst-case heating event happens on cold cloudy nights.

5. Cooling-load methodology

The cooling load has four components: solar gain through the cap, conduction when outdoor exceeds indoor, latent load from plant evapotranspiration, and latent infiltration in humid climates.

5.1 Solar gain and shade impact

Peak solar load enters as horizontal-projected irradiance through the cap glazing. At 1 % summer design hour:

Q_solar = floor_area × peak_irradiance × τ_PC × shade_factor

Where τ_PC is polycarbonate solar transmission (0.62 for 16 mm five-wall) and shade_factor accounts for shade cloth.

50 % aluminet shade cloth, hung internally. Hung internally, 50 % aluminet absorbs and reflects radiation but the thermal energy that gets absorbed eventually convects into the dome air. Net effect on solar heat gain is roughly 40 % reduction.

Hung externally, the same shade cloth dumps absorbed heat to outdoor air before it can convect into the dome. External hanging cuts solar heat gain by roughly 60 to 65 %.

External hanging requires custom rigging and exposes the cloth to wind, hail, and UV degradation. Methodology assumes internal hanging as the default, with seasonal deployment.

5.2 Conductive cooling load

Q_cond = UA_total × max(0, T_1%_outdoor - T_indoor_max)

Indoor max 90 °F. Material only when outdoor 1 % design exceeds 90 °F.

5.3 Plant evapotranspiration: latent load and sensible cooling benefit

A fully canopied warm-season vegetable or fruit-tree planting with adequate canopy airflow has typical evapotranspiration of 0.10 to 0.18 inches of water per day:

Q_ET_peak ≈ 30 BTU·h⁻¹·ft⁻² of floor area

For a 26 ft dome (520 ft² floor): peak plant latent load ≈ 16 kBtu·h⁻¹.

Dual effect. Plant ET is simultaneously a latent load (water vapor must be removed from dome air) and a sensible cooling benefit (heat-of-vaporization is taken from dome air to convert liquid to vapor). The net effect depends on what removes the vapor:

• Ventilation removes vapor with the airstream. Sensible cooling stays in the dome; latent leaves with exhausted air.
• HP cooling removes vapor by condensation on the indoor coil. Sensible cooling is added to the HP's load.

Plant ET helps when ventilation is the dominant cooling stage and hurts when HP cooling is the dominant stage.

In 3-season operations where the dome is dormant in winter but actively planted in summer, the cooling-side latent load is the same as 4-season operations. ET load doesn't depend on winter operating mode.

5.4 Latent infiltration in humid bands

In HZ-HH and MZ-H, design-day outdoor air carries more moisture per pound than indoor air at 90 °F. Modeled as a fixed peak-hour latent term per dome size, scaled by interior volume relative to the 26 ft baseline. For 26 ft: ~5 kBtu·h⁻¹ at 1.0 ACH design infiltration.

5.5 Peak cooling load table

Combined sensible + latent at 1 % summer design hour, before any passive responses.

6. Pond as bidirectional thermal mass

The above-ground pond absorbs heat when the dome is warmer than the pond and releases heat when the dome is cooler than the pond.

6.1 Heating-side moderation

Hours of design-load coverage at the 99 % heating load (4-season fruiting, 50 °F maintain):

For 4-season cool (40 °F maintain), pond coverage hours scale upward by approximately 20 to 25 %. For 3-season (35 °F maintain), pond coverage scales upward by approximately 30 to 40 % in colder bands and becomes non-binding in mild bands where modeled load drops near zero.

The §9.4 unified sizing method applies pond contribution as a continuous concurrent passive heat source rather than a separate hours-of-coverage term. See Section 9.4.3.

6.2 Cooling-side moderation

In summer, the pond enters morning at its coolest temperature. As solar gain heats dome air through the day, the pond absorbs heat through surface convection.

Approximate cooling absorption capacity at 10 °F afternoon rise:

6.3 Field-validation status for pond moderation

The pond moderation model uses a bulk water heat-capacity approximation. This is appropriate for sizing-level comparisons because the pond's mass is large relative to the daily heat swings being modeled.

Instrumented pond data should eventually be used to refine three assumptions: actual usable temperature swing, stratification within the pond, and heat-transfer rate between dome air and pond water. Until that dataset is published, the pond calculations should be treated as a conservative planning approximation rather than a full transient thermal model.

7. Passive cooling cascade

The cooling cascade transforms raw peak loads from 5.5 into smaller residual loads that any active cooling equipment must carry.

The cascade order:

1. Shade cloth (already accounted for in solar gain).
2. Active mechanical ventilation (when outdoor < indoor).
3. Pond thermal absorption.
4. Direct evaporative cooling (where installed, dry climates only).
5. Heat-pump cooling (for residual).

7.1 Active mechanical ventilation

Useful only when outdoor air is below 90 °F. At 1 fan bank running on a 26 ft dome (~2,900 cfm), mass flow ≈ 13,000 lb·h⁻¹.

Q_vent = ṁ_air × c_p × (T_indoor - T_outdoor)

With a 5 °F approach: roughly 16 kBtu·h⁻¹ sensible. With a 10 °F approach: ~31 kBtu·h⁻¹.

In bands where peak summer outdoor stays below 90 °F (MZ-M, CZ), one fan bank handles sensible cooling at peak. In bands where peak outdoor exceeds 90 °F (HZ-HD, HZ-HH, MZ-D, MZ-H), ventilation does not help at the design hour.

7.2 Direct evaporative cooling

Effectiveness depends on wet-bulb depression at design conditions:

T_supply = T_DB - 0.80 × (T_DB - T_WB)

At Phoenix 1 % design (110 °F DB, 70 °F WB): supply at 78 °F, ~37 kBtu·h⁻¹ sensible cooling delivered.

At Denver 1 % design (93 °F DB, 60 °F WB): supply at 67 °F, ~80 kBtu·h⁻¹ available.

In humid climates, adding moisture to already-humid air worsens the latent problem and narrows wet-bulb depression too much for useful sensible cooling. Direct evap is effective only in dry climates.

7.3 Net HP cooling load with evap installed

26 ft dome, evap installed in HZ-HD and MZ-D only:

7.4 Net HP cooling load without evap

For HZ-HD and MZ-D specifically, without evap the HP must handle the full sensible cooling load:

7.5 SHR considerations for HP-driven cooling bands

In HZ-HH and MZ-H, the residual HP cooling load is heavily latent. Heat pumps operate at a Sensible Heat Ratio (SHR) that depends on coil temperature, airflow, and entering humidity. At low SHR, effective sensible capacity per ton of nameplate is reduced compared to dry-coil rating.

For methodology sizing purposes, this document applies a 15 to 25 % derate on nameplate cooling capacity in HZ-HH and MZ-H. This is a representative range used to set capacity classes; manufacturer-published SHR data and bin-hour analysis at the project's design wet-bulb should be used for final equipment selection.

7.6 Net HP cooling table by dome size (with evap installed where applicable)

Residual after cascade including pond absorption and SHR derate, at 1 % design hour. Round to nearest kBtu·h⁻¹.

8. Airflow and ventilation strategy

8.1 Small domes (15 and 18 ft) - passive stack ventilation

Geometric vent open areas at typical θ_max = 30°:

Stack flow at design ΔT = 10 °F:

Q_stack ≈ 60 × Cd × (A/√2) × √(2g × h × ΔT / T_avg)

Using Cd = 0.65, h ≈ 7 to 8 ft, T_avg ≈ 520 °R, this yields roughly 240 to 360 cfm, or about 10 ACH at design ΔT.

Small domes also include a single intake fan in the standard kit. Stack ventilation is the primary ventilation strategy at this size; the intake fan supplements air movement and is sized to match typical operating conditions. See §8.2 for fan capacity sizing methodology.

8.2 Larger domes (22 ft and up) - single-speed mechanical ventilation

Single-speed intake and exhaust fans arranged in pairs.

ACH targets: Low ~20, Medium ~35 to 40, High ~55 to 60.

Passive vents are included as standard on 22 ft and 26 ft domes (4 heat-activated vents, 2 top + 2 bottom) alongside the single intake fan. 33 ft and 42 ft domes ship with mechanical ventilation only; their standard kit includes paired intake and exhaust fans (2 + 2 for 33 ft; 3 + 3 for 42 ft) sized to handle the full ventilation load without passive vent contribution.

8.3 Doors as supplemental low intake

Opening dome doors materially increases low-side intake area. Doors typically add 18 to 32 ft² of low-side opening.

8.4 Undersoil recirculation system

Each dome includes an undersoil ventilation system, comprising corrugated ducting buried below the planting beds.

The undersoil system functions primarily as a soft internal recirculation system. It pulls air from near the pond at one end of the dome, runs that air through the protected ducts under the planting area, and deposits it gently on the opposite side of the dome. Benefits: gentle air circulation, distribution of pond-moderated air, reduced winter stratification. Geothermal effect is real but small and not modeled.

8.5 Interlocks (when active heat pump is installed)

When the heat pump is heating, cooling, or drying:

• Outside-air ventilation fans: OFF.
• Recirculation (undersoil and indoor head fan): ON LOW or as scheduled.
• Evaporative cooler (if installed): LOCKED OUT.

Economizer enable:

• T_out ≤ T_in − 2 °F, AND
• RH_out ≤ 80 % OR h_out < h_in − 3 BTU/lb.

When economizer is ON, HP_COOL is inhibited and ventilation fans stage per ACH targets.

8.6 Optional additional fan upgrade for warm-summer climates

An additional fan is offered as an optional upgrade for 18 through 33 ft domes in warm-summer climates (HZ-HD, HZ-HH, and MZ-D). On 18 ft domes, this supplements the single intake fan in the standard kit. On 18 ft domes, the optional fan supplements the single intake fan in the standard kit. On 22 ft and 26 ft, where the standard kit includes a single intake fan, the optional fan adds capacity (typically as the optional exhaust upgrade in the product line, but customer or installer may configure differently). On 33 ft, the optional fan supplements the 2 intake + 2 exhaust standard configuration. The added fan can be configured as intake or exhaust depending on dome layout, prevailing wind, and existing fan placement. Benefits scale with summer severity and are most pronounced in dry-summer climates (HZ-HD, MZ-D), where higher airflow rates support evap saturation and pond convective heat absorption. In humid-summer climates (HZ-HH), the additional fan operates primarily in economizer windows when outdoor enthalpy is below indoor; the §11.3 interlock matrix locks out outside-air ventilation during HP cooling and dry-mode operation, so the additional fan does not work against active dehumidification.

The Greenhouse Climate Calculator surfaces this as an optional item for the qualifying zone-and-size combinations. The recommendation is intentionally configuration-neutral; intake or exhaust selection is a project-level decision based on site-specific factors not captured in the methodology.

9. Heat-pump performance

9.1 NEEP-anchored COP

Heat-pump performance is anchored to the NEEP cold-climate ASHP database, filtered for single-zone non-ducted split systems with R-454B refrigerant. Averaged across several units at standard test points:

Source: NEEP cold-climate ASHP database, ashp.neep.org. The values above are representative anchors for methodology development. Final equipment selection should verify the specific unit's rated capacity, COP, defrost behavior, and low-ambient operation at the project design condition.

9.2 Greenhouse-adjusted COP

For 40 °F or 35 °F maintain, heating lift drops by 10 to 15 °F across all bands and design-point COP rises correspondingly.

For CZ sites at the cold end of the band (Fairbanks-like), heating COP at design drops below 1.5 and effective HP capacity is well below nameplate.

9.3 Why 15 and 18 ft envelopes are challenging for active heating

Three factors:

1. Acoustics. Typical 12 kBtu wall-mount minisplit heads are sized for residential rooms of comparable interior volume but produce noticeable noise and turbulence in the smaller dome envelopes.
2. Cycling. At small heating loads (roughly 0 to 12 kBtu·h⁻¹ depending on band and mode), even a 1-ton inverter unit cycles aggressively in shoulder seasons.
3. Capacity-to-load mismatch. Available HP nominal sizes (12 kBtu minimum) exceed the load by 2 to 6x in many bands, leading to oversized equipment.

9.4 Unified heating-equipment sizing method

This section defines how the calculator sizes heating equipment for all four customer cases described in §10.2. A single formula applies across cases; case-specific inputs (target temperature, design temperature, and pond contribution) reflect each customer's operating commitment and tolerance for temperature drift during the cold-tail design event.

The physical basis is the envelope heat-loss equation from §4.6 extended with explicit passive credit from the §6.1 pond. Equipment selection on top of the calculated load (heat pump, supplemental, or paired) is governed by the optimization rule in §9.4.7.

9.4.1 Sizing formula

Heating equipment for all four cases is sized via:

Q_required = max(floor, UA × (T_target − T_design) − Q_pond_credit)

with case-stratified inputs:

annualRangeF = julAvgHighF − janAvgLowF.

UA from §4.4. Q_pond_credit from §9.4.3. Floor: 4 kBtu·h⁻¹. Supplemental sizes are rounded up to the nearest 2 kBtu·h⁻¹ increment (4, 6, 8, 10).

The 0.15 multiplier on annual range captures continentality for case 4 only: continental sites with large annual swings have deeper cold tails relative to their January average; maritime sites with small swings have shallow cold tails. The multiplier is calibrated against operating practice at the Pagosa Springs demonstration dome, where the case 4 design temperature lands on -7 °F (matching ASHRAE 99 % heating for that site).

Cases 1-3 do not apply the multiplier because the gardener-tolerance customer accepts dome temperature drift below T_target during the cold-tail design event. Equipment for those cases is sized for typical cold weather (January average low), not the worst few hours per year.

9.4.2 Target temperature by case

The target temperature is the binding lower bound below which the customer's case does not accept dome temperature drift. T_target steps with case ambition:

The monotonic stepping ensures equipment recommendations scale predictably with case ambition: a more demanding case never produces less equipment than a less demanding case at the same site and dome size.

9.4.3 Pond continuous contribution by dome size

Computed from §6.1 as full pond storage at 15 °F swing divided by 14-hour night:

Cases 1-3 apply the full Q_pond_continuous value as a continuous concurrent passive heat source at design conditions. Case 4 sets Q_pond_credit = 0 to represent the design event of multi-day overcast cold conditions in which pond charge has been exhausted.

The 14-hour assumption represents a typical mid-latitude winter night (sunset to sunrise). At extreme latitudes the night is longer and per-hour pond contribution decreases proportionally; this is a §9.4.6 calibration consideration rather than a per-site adjustment.

9.4.4 Calculated reference values, 26 ft Q_required

Q_required for representative cells, in kBtu·h⁻¹:

"Passive" indicates Q_required ≤ 0 at design conditions; the dome's passive systems carry the load alone with no active heating equipment recommended. "PV" indicates the cell triggers partner verification per §9.4.6.

Equipment recommendations on top of Q_required are produced by the calculator's optimization rule (heat pump alone, supplemental alone, or paired) and are not detailed in this methodology because the relevant variables vary too widely across customers to model precisely. The Greenhouse Climate Calculator surfaces the recommendation directly.

9.4.5 Worked example: 26 ft CZ at Pagosa Springs, case 2 (4-season cool, gardener tolerance)

Inputs:

• ZIP 81147 Pagosa Springs climate normals: Jan T_min 3.5 °F, Jul T_max 75.3 °F
• Annual range: 75.3 − 3.5 = 71.8 °F
• Case 2 T_design (cases 1-3 use janAvgLow without the multiplier): 3.5 °F
• Case 2 T_target: 38 °F
• UA from §4.4 (26 ft): 405 BTU·h⁻¹·°F⁻¹
• Q_pond_continuous from §9.4.3: 9.6 kBtu·h⁻¹

Calculation:

• UA × (T_target − T_design) = 405 × (38 − 3.5) = 405 × 34.5 = 13,973 BTU·h⁻¹ = 13.97 kBtu·h⁻¹
• Net of pond: 13.97 − 9.6 = 4.37 kBtu·h⁻¹
• Round up to nearest 2 kBtu increment: 6 kBtu·h⁻¹
• Floor at 4 kBtu does not bind.

Output: 6 kBtu supplemental heater. No heat pump in case 2 at this site (Q_required is below the optimization threshold; supplemental delivers alone).

Compare to operating practice at the Pagosa Springs demonstration dome, which runs case 2 cool-season production on roughly 5 kBtu·h⁻¹ of supplemental capacity. The 6 kBtu calculator output rounds up from a 4.37 kBtu calculated value, sized for design-event worst-hour operation rather than typical operating average. The calibration matches operating reality within rounding tolerance.

Compare to case 4 strict at the same dome and site:

• Case 4 T_design: 3.5 − 0.15 × 71.8 = -7.27 °F
• Case 4 T_target: 48 °F
• Q_pond_credit: 0 (depleted)
• UA × (T_target − T_design) = 405 × 55.27 = 22,384 BTU·h⁻¹ = 22.4 kBtu·h⁻¹
• Net of pond: 22.4 − 0 = 22.4 kBtu·h⁻¹
• Round up: 24 kBtu·h⁻¹

Case 4 output: heat pump and supplemental package targeting 24 kBtu·h⁻¹ delivered capacity at -7 °F site-specific design. The case 4 to case 2 ratio (24 vs 6 kBtu·h⁻¹, roughly 4×) reflects the customer-commitment difference, not a continentality calibration adjustment.

9.4.6 Field validation status and assumptions

The §9.4 method is anchored to the same physical model as §4.6 (UA × ΔT), with case-stratified assumptions:

• Cases 1-3 — full pond credit. Pond is fully charged at the start of the design night (15 °F swing per §6.1) and provides continuous Q_pond_continuous credit at design conditions. Customer accepts dome temperature drift below T_target during the cold-tail event.
• Case 4 — depleted pond. Pond charge has been exhausted by extended cloud cover preceding the design event. Q_pond_credit = 0 is the conservative assumption for productive year-round operation.
• 0.15 annual-range multiplier (case 4 only). Calibrated against operating practice at the Pagosa Springs demonstration dome and cross-checked against ASHRAE 99 % heating values for representative sites. Produces case 4 design temperatures within ~3 °F of ASHRAE 99 % for non-extreme sites and underestimates Fairbanks-class extremes by ~10 °F (acceptable because partner verification covers those sites).

Sites in chronically overcast climates (Pacific Northwest coastal, far-north winter dark periods) may want larger case 4 equipment than §9.4.1 produces; this is a partner-verification consideration.

Heat-pump performance derate past -15 °F outdoor design temperature is at the limit of the calibrated range used in the calculator's optimization rule. Sites with case 4 T_design below -15 °F (Bismarck and colder) trigger partner-verification flags in calculator output.

Field validation should track:

• Actual pond temperature at start and end of the design night
• Heater run-time and duty cycle on cold cloudy nights
• Indoor temperature minimum and frequency of excursions below T_target by case
• Solar charging effectiveness on partly-cloudy days

Until that dataset is published, the §9.4 method is a planning model.

9.4.7 Equipment selection on top of Q_required

The calculator selects between supplemental-only, heat-pump-only, and heat-pump-plus-supplemental packages using a rough optimization that balances:

• Heat-pump nominal capacity available in standard tonnage classes (12, 18, 24, 36, 48 kBtu·h⁻¹) and capacity derate at site-specific design temperature
• Supplemental delivery limits (single-unit standalone capacity capped at 10 kBtu·h⁻¹ to fit safe configurations: 120 V resistive units in pairs, or unvented gas heaters within plant-radiant safety envelopes)
• Inverter heat-pump modulation behavior at shoulder-season loads
• Equipment capital cost and operating efficiency at site-typical run hours

The optimization is internal to the calculator and not exposed in detail because the relevant variables (utility rates, fuel availability, customer run-time preferences, planned operating schedule) vary too widely across customers to model precisely. The calculator's output is a starting point for project planning, not a final equipment specification.

10. Binding constraint analysis

The central engineering question for any active climate equipment is whether heating or cooling drives equipment sizing in a given band, and what tolerance the customer accepts for short excursions outside the design band.

10.1 Side-by-side peak loads (4-season fruiting, 26 ft reference)

For 4-season cool and 3-season modes, heating peaks reduce while cooling peaks stay constant. This shifts heating-driven bands closer to balanced or cooling-driven status, which is reflected in smaller heat-pump and supplemental sizing for cases 1-3 compared to case 4.

At the cold end of CZ, the case 4 heating load exceeds heat-pump nameplate at design; supplemental heat carries the deficit, and the calculator surfaces a partner-verification flag. See §9.4 for the unified heating-equipment sizing method that produces these recommendations.

10.2 Operating tolerance spectrum

The 50 to 90 °F operating envelope, or the appropriate heating edge for the selected operating mode, assumes short excursions of about one hour at a time. Customer operating goals span a tolerance spectrum that distinguishes how much drift below the productive maintain target is acceptable. The spectrum has four cases:

Case 1 — drift-accepted 3-season operation. Customer grows vegetables, herbs, and other warm-season crops in their natural seasons (spring through fall). Dome rests in winter. The maintain target (35 °F) is for frost protection of the pond, water systems, beds, and growing systems; the customer accepts drift below this target on the worst hours per year as long as the dome stays above the critical temperature (33 °F). This is the most common Growing Spaces operating profile.

Case 2 — drift-accepted 4-season cool operation. Customer grows cool-season crops (greens, brassicas, root vegetables, herbs) through winter; warm-season crops in their natural season. The maintain target (40 °F) supports active cool-season production. The customer accepts drift between maintain and critical (33 °F) on the coldest cloudy nights, during which production may slow but plants survive (cool-season crops tolerate brief 32 °F excursions). The common year-round option.

Case 3 — drift-accepted 4-season warm-season survival. Customer maintains warm-season plants (tomatoes, peppers, citrus, and similar) through winter, with the goal of plant survival rather than active winter production. The productive maintain target (50 °F) is the customer's preference for active production; the customer accepts drift between maintain and critical (33 °F) during deep winter, during which plants survive but typically do not actively produce. The customer is explicitly trading winter production for reduced equipment scope. Warm-season plants experience chilling injury during drift hours as part of this trade.

Case 4 — strict productive winter harvest. Customer wants productive year-round warm-season crop production with no temperature drift accepted during the cold-tail design event. Equipment is sized via §9.4 with case 4 inputs: T_target = 48 °F (a 2 °F margin below the 50 °F warm-season chilling threshold), T_design at janAvgLow − 0.15 × annualRange, and pond credit set to zero (depleted-pond design event). This is the most demanding common case. A small but real customer audience.

The Greenhouse Climate Calculator distinguishes these cases through the operating-mode and tolerance inputs. The calculator's default (Strict mode toggle off) returns case 1, 2, or 3 sizing per §9.4, depending on the operating mode chosen. The Strict mode toggle returns case 4 sizing per §9.4 with case 4 inputs (T_target = 48 °F, T_design at janAvgLow − 0.15 × annualRange, Q_pond_credit = 0). When Strict mode is toggled on, the calculator UI locks the operating mode to 4-season fruiting and forces summer cooling on, because case 4 only applies to year-round productive operation. Most Growing Spaces customers fall in cases 1, 2, or 3.

For most owners and growing goals, the dome operates well inside the design band on most days, and active equipment is engaged only during the worst hours of the worst weeks. For some combinations of band and mode (HZ-HD, HZ-HH, MZ-M across all relaxed cases; MZ-D and MZ-H 4-season cool relaxed), the dome can hold acceptable conditions through entire seasons without active equipment beyond the standard kit.

11. Controls, sensors, and set-points

11.1 Staging logic

Typical sequence for a mixed or cold zone, parameterized by operating mode.

Compressor short-cycle lockouts: minimum off-time of 5 minutes on smaller domes.

For cases 1-3, supplemental staging targets the case-specific T_target (33 °F for case 1, 38 °F for case 2, 43 °F for case 3) as the lower bound. For case 4, staging targets 48 °F with no drift accepted.

11.2 Sensor placement

• Interior temperature and humidity sensors near the north-center strut, roughly 5 ft above grade, in a small radiation shield.
• Exterior reference sensor on the north side of the structure, shaded from direct sun, clear of roof runoff.
• Minisplit indoor head on the east wall around 6 ft above slab.

11.3 Interlock matrix

11.4 Seasonal shade cloth deployment

12. Energy modeling framework

12.1 Three scenarios

1. Full-mechanical baseline. HP carries all loads outside the band. Vents and fans stay closed. No pond.
2. Passive, no pond. Passive vents, fans, shade, and evap (where installed) handle as much load as possible. HP covers the rest.
3. Passive with pond and PV-driven fans. Adds bidirectional pond moderation, solar-gain offset on heating loads, and PV-offset fan kWh.

12.2 Method

1. Degree-day or degree-hour methods with band-specific HDD to a 50 °F base (or 40 °F or 35 °F base for other operating modes) and CDD to a 90 °F base.
2. Apply seasonal heat-pump COP.
3. Apply passive uplift factors for ventilation, shade, evap (where installed), and pond as applicable per band.
4. Apply solar-gain offset on heating side as a band-specific reduction in HDD-equivalent.
5. Apply PV fan offsets in scenario 3.

12.3 Order-of-magnitude annual electrical energy

26 ft dome at 50 °F maintain (4-season fruiting), illustrative scenario 3 outputs:

For 4-season cool: scenario-3 energy reduces by 20 to 35 % across mild bands and 10 to 20 % in cold bands. For 3-season: scenario-3 energy reduces by 35 to 60 % across mild bands and 15 to 30 % in cold bands. In HZ-HD and MZ-M, 3-season energy approaches summer-only minimums.

The CZ figure above uses the calculator's representative -15 °F design point (strict mode). CZ sites at the cold end of the band (Fairbanks-like, 99 % design colder than −30 °F) can use roughly 2 to 3x this energy, with the increase concentrated in supplemental heat rather than HP electrical draw.

For cases 1-3 (drift accepted, §10.2), annual energy is materially lower than the case 4 figures above because equipment runs at lower duty cycle and capacity. Field-validation work will refine case-specific energy estimates.

These values are order-of-magnitude outputs of the framework. They are useful for comparing bands and operating modes, but they are not utility-cost estimates or performance guarantees.

13. Limits of this model

• Single steady-state heat-loss model. Transient effects are not modeled.
• No floor / ground-coupling term. Ground losses are lumped into conductive UA.
• Solar gain modeling is coarse. Used as horizontal-projected peak hour incident scaled by transmission and shade.
• Pond cooling absorption uses a simple bulk-temperature-rise model.
• Plant ET assumes "fully canopied" baseline. Sparser plantings have lower latent loads.
• Wind effects. Infiltration ACH does not include wind-driven uplift.
• Elevation. All values assume sea-level air density.
• ASHRAE design values are representative climatic design values. Verify project-specific values against the latest applicable ASHRAE climatic design data or equivalent local design source.
• SHR derate for HP cooling in humid bands is approximate.
• The CZ band covers a wide design-condition range (-7 to -47 °F at 99 %). All cases use site-specific design temperatures derived from climate normals (§9.4). Sites at the cold end of the band (Fairbanks-class and colder) require partner verification regardless of which case is targeted, because heat-pump performance derate and supplemental sizing are at the limit of the calibrated formula range.
• §9.4 uses calibration assumptions specific to each case: - Cases 1-3 assume full pond charge at the start of the design night (15 °F swing per §6.1), 14-hour winter night length, and January average low as design temperature without the cold-tail multiplier. - Case 4 assumes depleted pond, 0.15 annual-range multiplier on T_design, and the same 14-hour pond night assumption. - The 0.15 multiplier replaces the v1.5 value of 0.20, recalibrated against the Pagosa Springs demonstration dome's operating practice (5 kBtu·h⁻¹ case 2 supplemental capacity matches the formula's 4.4 kBtu calculated load within rounding) and ASHRAE 99 % heating cross-references at representative sites. The previous v1.5 calibration produced systematic over-sizing in case 2 and case 3 that has been resolved by removing the cold-tail multiplier from cases 1-3 entirely. - All assumptions may need refinement as field-validation data accumulates per §9.4.6.
• Light availability is not modeled. This methodology covers temperature, humidity, and ventilation. Winter light availability is a separate constraint that limits warm-season crop productivity at high latitudes regardless of how well the dome holds the temperature band. For productive winter harvest of warm-season fruiting crops above approximately 40° N, supplemental lighting may matter as much as or more than supplemental heat. The calculator's equipment recommendations are correct on temperature but should be combined with separate planning for light if the operating goal is winter warm-season fruiting at high latitudes.
• Operating mode is a sizing parameter, not a usage guarantee. Owners can shift modes seasonally without equipment changes; calculator outputs represent the baseline design target.
• Multi-day overcast pond depletion modeling: Currently handled by the case 4 binary depleted-pond assumption
• Heat-pump performance derate calibration past -15 °F: Currently handled by partner-verification flag
• 15 / 18 ft outside-CZ short-cycle behavior: reassessment under the new outputs
• Bin-hour energy modeling: currently handled by §12 order-of-magnitude approach

14. Application in Growing Spaces climate tools

This methodology is the technical reference for Growing Spaces climate sizing logic. It supports a customer-facing calculator and a customer-facing decision guide, both of which apply the formulas and assumptions in this document. The technical methodology owns formulas and assumptions; the implementation tools own user inputs, product logic, and presentation.

14.1 Greenhouse Climate Calculator

The Greenhouse Climate Calculator is the primary customer-facing implementation of this methodology. It takes site (ZIP code), dome size, and operating-mode inputs; classifies the site to one of the six climate bands using the rules in Section 3; applies the sizing logic in this methodology; and returns a recommended climate package for the dome.

The calculator implements the §9.4 unified sizing method with case-stratified inputs. The user selects an operating mode (3-season, 4-season cool, or 4-season fruiting) and optionally toggles Strict mode on. The combination of operating mode and Strict toggle determines which case (1-4) the calculator sizes for.

Strict mode is implemented as a checkbox in the calculator's advanced options. When Strict is toggled on, the operating-mode selector visually locks to 4-season fruiting and the summer-cooling checkbox locks on; this matches the engine invariant that case 4 (productive year-round operation with no drift accepted) is meaningful only for the 4-season fruiting operating mode and requires active summer cooling. Toggling Strict off restores user control over operating mode and summer cooling.

The calculator's heat-pump-versus-supplemental optimization is not exposed in the methodology because the underlying variables vary too widely across customers to model precisely. The output is a starting point for project planning, not a final equipment specification.

The calculator applies Growing Spaces product logic in addition to the engineering methodology. Product availability, pricing, installation constraints, electrical constraints, low-ambient equipment performance, humidity-control requirements, and support review may affect the final recommendation. The calculator output is a starting point for project planning, not a final equipment specification.

14.2 Heating & Cooling Guide

The Heating & Cooling Guide is a customer-facing decision aid that explains the same sizing logic in plain language. It does not redefine the calculations. It translates engineering bands into simpler climate descriptions, walks the reader through operating-mode trade-offs, and provides language for productive conversations with local HVAC contractors. It links back to this methodology for technical details.

14.3 Direct use by partners and HVAC professionals

Partners and HVAC professionals working from this document directly should:

1. Determine which case (1-4) the project targets per §10.2.
2. The case selection determines T_target, T_design, and Q_pond_credit per §9.4.1.
3. Apply the unified formula with case-stratified inputs to produce Q_required.
4. Equipment selection on top of Q_required (heat pump nominal class, supplemental capacity, or paired package) follows the optimization in §9.4.7 with project-specific adjustments for utility rates, fuel availability, and customer operating preferences.
5. Use the cooling-load methodology in Section 5 and the passive cascade in Section 7.
6. Confirm whether evaporative cooling is included in the project configuration.
7. Compare heating residuals and cooling residuals to determine the binding sizing condition.
8. Verify actual equipment against manufacturer data at the project design condition, including low-ambient capacity, defrost behavior, COP, condensate management, and controls.
9. Revisit assumptions for sites outside the representative climate bands, especially high-altitude, high-wind, very humid, very hot, or very cold locations.

If this methodology is adapted to a non-Growing Dome greenhouse, substitute the actual envelope U-values, shell area, infiltration assumptions, thermal mass, ventilation strategy, crop density, and operating targets. Do not carry Growing Dome pond, fan, shade, or geometry assumptions into another structure without adjustment.

Appendix A. Source notes

Source notes should be reviewed annually, or when climate data sources, ASHRAE design data, heat-pump datasets, refrigerants, dome geometry, fan packages, or product logic materially change.

• Dome geometry: Growing Spaces internal geometry workbook, derived from CAD models.
• Pond capacities: Growing Spaces 2025 Owner's Manual and size-specific installation documentation.
• Polycarbonate: Manufacturer published data (Gallina USA via A&C Plastics). 16mm RDC 5-Wall, U-Factor 0.36, R-Factor 2.778, weight 0.522 lb/ft², clear light transmission 65%, SHGC 0.68.
• ASHRAE 99 % heating and 1 % cooling design temperatures: Representative values are embedded in Section 3.2. Project-specific work should verify against the latest applicable ASHRAE climatic design data or equivalent local design source. ASHRAE Handbook of Fundamentals, Chapter 14 (Climatic Design Information).
• Growing Spaces climate zone custom classification informative sources: PNNL/DOE Building America Climate Region Guide (free PDF). IECC climate zone map (Building America Solution Center). ASHRAE Climate Zones overview. USDA Plant Hardiness Zone Map.
• Design Conditions: ANSI/ASHRAE Standard 169-2020 Addendum covers climate zone classifications and 9,237 station-specific design conditions.
• Climate data pipeline: zippopotam.us API, open-meteo.com API, NASA POWER API. NASA Power Methodology & API Documentation
• Heat-pump performance: NEEP cold-climate ASHP database, filtered for representative single-zone non-ducted split systems. Final equipment selection should verify the selected model's rated performance. PNNL "Performance Results from DOE Cold Climate Heat Pump Specification" (PDF)
• Greenhouse heat-loss formulas: Standard greenhouse engineering methods, including extension and agricultural greenhouse references from Bartok / UConn, Purdue CEA, and ASHRAE Applications material. Thank you John Bartok.
• Direct evaporative cooling effectiveness: UAF Cooperative Extension, "Controlling the Greenhouse Environment" (PDF)
• Shade cloth performance: Manufacturer data for 50 % aluminet or equivalent reflective shade cloth.
• Plant evapotranspiration: Range from greenhouse production literature for fully canopied warm-season vegetable and fruit-tree crops. FAO Paper 56 - Crop Evapotranspiration (Allen, Pereira, Raes, Smith, 1998)
• Infiltration coefficient: Standard 0.018 BTU·ft⁻³·°F⁻¹ for sea-level air. ASHRAE Handbook of Fundamentals, Chapter 16 (Ventilation and Infiltration) and Bartok, "Determining greenhouse heat loss," Greenhouse Management (Aug 2019)
• §9.6 calibration: 0.2 multiplier on annual range and 14-hour pond night length anchored to operating practice at the Pagosa Springs demonstration dome (1989-present).

Appendix B. Worked examples

B.1 26 ft Pagosa Springs CZ, 4-season cool, gardener tolerance (§9.4.5)

Inputs:

• ZIP 81147 Pagosa Springs climate normals: Jan T_min 3.5 °F, Jul T_max 75.3 °F
• Annual range: 75.3 − 3.5 = 71.8 °F
• Case 2 T_design (cases 1-3 use janAvgLow without the multiplier): 3.5 °F
• Case 2 T_target: 38 °F
• UA from §4.4 (26 ft): 405 BTU·h⁻¹·°F⁻¹
• Q_pond_continuous from §9.4.3: 9.6 kBtu·h⁻¹

Calculation:

• UA × (T_target − T_design) = 405 × (38 − 3.5) = 405 × 34.5 = 13,973 BTU·h⁻¹ = 13.97 kBtu·h⁻¹
• Net of pond: 13.97 − 9.6 = 4.37 kBtu·h⁻¹
• Round up to nearest 2 kBtu increment: 6 kBtu·h⁻¹
• Floor at 4 kBtu does not bind.

Output: 6 kBtu supplemental heater. No heat pump in case 2 at this site (Q_required is below the optimization threshold; supplemental delivers alone).

Compare to operating practice at the Pagosa Springs demonstration dome, which runs case 2 cool-season production on roughly 5 kBtu·h⁻¹ of supplemental capacity. The 6 kBtu calculator output rounds up from a 4.37 kBtu calculated value, sized for design-event worst-hour operation rather than typical operating average. The calibration matches operating reality within rounding tolerance.

Compare to case 4 strict at the same dome and site:

• Case 4 T_design: 3.5 − 0.15 × 71.8 = -7.27 °F
• Case 4 T_target: 48 °F
• Q_pond_credit: 0 (depleted)
• UA × (T_target − T_design) = 405 × 55.27 = 22,384 BTU·h⁻¹ = 22.4 kBtu·h⁻¹
• Net of pond: 22.4 − 0 = 22.4 kBtu·h⁻¹
• Round up: 24 kBtu·h⁻¹

Case 4 output: heat pump and supplemental package targeting 24 kBtu·h⁻¹ delivered capacity at -7 °F site-specific design. The case 4 to case 2 ratio (24 vs 6 kBtu·h⁻¹, roughly 4×) reflects the customer-commitment difference, not a continentality calibration adjustment.

Appendix C. Field validation framework

Growing Spaces intends to validate this methodology against instrumented dome data over time. A complete field log should include the following fields.

This appendix defines the validation format. It does not yet claim statistical validation across all dome sizes, climate bands, operating modes, and mechanical configurations.

The §9.4 method introduces calibration parameters that should be specifically tracked: pond charge state at start of design night, actual winter night length at site latitude, the 0.15 annual-range multiplier applied to case 4 T_design, and the validity of the case 4 depleted-pond assumption against actual multi-day overcast pond depletion observed at instrumented sites. Future validation may differentiate calibration by latitude, build generation, or pond installation state.

Last updated: May 6, 2026. Version 1.5. Methodology owner: Growing Spaces Engineering. This document supersedes prior climate and HVAC methodology drafts including v1.4.