**(This is a normative appendix and is part of this standard.)**

**C1. MINIMUM INFORMATION**

The following minimum information shall be specified for the *proposed design*.

**C1.1 At the Building Level.**

The floor area, broken down by

*space-conditioning categories*, shall be specified.

**C1.2 At the Exterior Surface Level.**

The classification, gross area,

*orientation*,

*U-factor*, and exterior conditions shall be specified. For

*mass walls*only:

*HC*and insulation position. Each surface is associated with a

*space-conditioning category*as defined in Section C1.1.

**C1.3 For Fenestration.**

The classification, area,

*U-factor*,

*SHGC*, VT, overhang

*PF*for

*vertical fenestration*, and width, depth, and height for

*skylight wells*shall be specified. (See Figure C1.3 for definition of width, depth, and height for

*skylight wells*.) Each

*fenestration*element is associated with a surface (defined in Section C1.2). and has the

*orientation*of that surface. For

*dynamic glazing*, the

*SHGC*and

*VT*shall be equal to that determined in accordance with C3.5 for the base envelope design.

FIGURE C1.3 Skylight well dimensions.

**C1.4 For Opaque Doors.**

The classification, area,

*U-factor*,

*HC*, and insulation position shall be specified. Each

*opaque door*is associated with a surface (defined in Section C1.2). and has the

*orientation*of that surface.

**C1.5 For Below-Grade Walls.**

The area, average depth to the bottom of the

*wall*, and

*C-factor*shall be specified. Each

*below-grade wall*is associated with a

*space-conditioning category*as defined in C1.1 .

**C1.6 For Slab-On-Grade Floor.**

The perimeter length and

*F-factor*shall be specified. Each

*slab-on-grade floor*is associated with a

*space-conditioning category*as defined in Section C1.1.

**C2. OUTPUT REQUIREMENTS**

Output reports shall contain the following information.

**C2.1**

Tables summarizing the minimum information described in Section C1.

**C2.2**

The

*envelope performance factor*differential broken down by envelope component. The differential is the difference between the

*envelope performance factor*of the proposed building and the

*envelope performance factor*of the base envelope design. Envelope components include the

*opaque roof*,

*skylights*,

*opaque above-grade walls*including

*vertical fenestration*and

*opaque doors*,

*below-grade walls, floors*, and

*slab-on-grade floors*.

**C3. BASE ENVELOPE DESIGN AND PROPOSED DESIGN SPECIFICATION**

**C3.1**

The base envelope design shall have the same building floor area,

*building envelope floor area*,

*slab-on-grade floor*perimeter, below-

*grade*floor area,

*gross wall area*,

*opaque door area*, and

*gross roof area*as the

*proposed design*. The distribution of these areas among

*space-conditioning categories*shall be the same as the

*proposed design*.

**C3.2**

The

*U-factor*of each

*opaque*element of the base envelope design shall be equal to the criteria from Tables 5.5-1 through 5.5-8 for the appropriate climate for each

*construction*classification.

*The HC*of

*mass wall*elements in the base envelope design shall be identical to the

*proposed design*.

*Mass walls*in the base envelope design shall have interior insulation, when required.

**C3.3**

The

*vertical fenestration area*of each

*space-conditioning category*in the base envelope design shall be the same as the proposed building or 40% of the

*gross wall area*, whichever is less. The distribution of

*vertical fenestration*among

*space-conditioning categories*and surface

*orientations*shall be the same as the

*proposed design*. If the

*vertical fenestration area*of any

*space-conditioning category*is greater than 40% of the

*gross wall area*of that

*space-conditioning category*, then the area of each

*fenestration*element shall be reduced in the base envelope design by the same percentage so that the total

*vertical fenestration area*is exactly equal to 40% of the

*gross wall area*.

**C3.4**

For

*enclosed spaces*required to comply with Section 5.5.4.2.3, the

*skylight area*in the base envelope design shall be 3% of the

*roof*area of that

*enclosed space.*For

*enclosed spaces*required to comply with Section 5.5.4.2.3, the total

*daylight area under skylights*in both the base envelope design and the proposed envelope design shall be a minimum of half the floor area. For all other

*spaces*the

*skylight area*of each

*space*category in the base envelope design shall be the same as the proposed envelope design or 5% of the

*gross roof area*, whichever is less. This distribution of

*skylights*among

*spaceconditioning categories*shall be the same as the

*proposed design*. If the

*skylight area*of any

*space*category is greater than 5% of the

*gross roof area*of that

*space-conditioning category*, then the area of each

*skylight*shall be reduced in the base envelope design by the same percentage so that the total

*skylight area*is exactly equal to 5% of the

*gross roof area*.

**C3.5**

The

*U-factor*for

*fenestration*in the base envelope design shall be equal to the criteria from Tables 5.5-1 through 5.5-8 for the appropriate climate, except the

*U-factor*for

*skylights*in

*enclosed spaces*required to comply with Section 5.5.4.2.3 shall be equal to the criteria listed in the Exception to Section 5.5.4.3. The SHGC for

*fenestration*in the base envelope design shall be equal to the criteria from Tables 5.5-1 through 5.5-8. For portions of those tables where there are no requirements, or for

*enclosed spaces*required to comply with Section 5.5.4.2.3 , the

*SHGC*shall be equal to 0.46 for all

*vertical fenestration*, 0.77 for plastic

*skylights*on a curb, and 0.72 for all other

*skylights*with a curb and without. The VT for

*fenestration*in the base envelope design shall be the VT factor from Table C3.5 times the

*SHGC*criteria as determined in this subsection. or

*enclosed spaces*required to comply with Section 5.5.4.2.3, the VT for

*skylights*in that

*enclosed space*shall be 0.40.

TABLE C3.5 VT Factor for the

Base Envelope Design

Climate Bin | Vertical Fenestration | Glass Skylights | Plastic Skylights |

1(A, B) | 1.00 | 1.27 | 1.20 |

2(A, B) | 1.00 | 1.27 | 1.20 |

3(C) | 1.00 | 1.27 | 1.20 |

3(A, B) | 1.27 | 1.27 | 1.20 |

4(A, B, C) | 1.27 | 1.27 | 1.20 |

5(A, B, C) | 1.27 | 1.27 | 1.20 |

6(A, B) | 1.27 | 1.27 | 1.20 |

7 | 1.00 | 1.00 | 1.20 |

8 | 1.00 | 1.00 | 1.20 |

**C3.6**

The

*roof*of the base envelope design and the

*roof*of the proposed envelope design shall both comply with either section 5.5.3.1.1 (a) or (b).

**C3.7**

*Unconditioned spaces*of the base envelope design and the proposed envelope design shall comply with Section 5.5.4.2.3.

**C4. ZONING AND BUILDING GEOMETRY**

No information about thermal zones needs to be entered to perform the calculations, but when the calculations are performed the building shall be divided into thermal zones according to the following procedure.

**C4.1**

Determine the ratio (

*Rc*) of the

*gross floor area*to the

*gross wall area*for each

*space-conditioning category*. The index “c” refers to the

*space-conditioning category*, either

*non-residential conditioned*,

*residential conditioned*, or

*semiheated*.

**C4.2**

Create a perimeter zone for each unique combination of

*space-conditioning category*and

*wall orientation*. The

*floor area*of each perimeter zone shall be the

*gross wall area*of the zone times

*Rc*or 1.25, whichever is smaller.

**C4.3**

For

*space-conditioning categories*where

*Rc*is greater than 1.25, interior zones shall be created and used in the trade-off procedure. The

*floor area*of the interior zone shall be the total floor area for the

*space-conditioning category*less the floor area of the perimeter zones created in Section C4.2 for that

*space-conditioning category*.

**C4.4**

*Roof area*,

*floor area*,

*below-grade wall area*, and

*slab-on-grade floor*perimeter associated with each

*space-conditioning category*shall be prorated among the zones according to

*floor area*.

**C4.5**

*Skylights*shall be assigned to the interior zone of the

*space-conditioning category*. If the

*skylight area*is larger than the

*roof area*of the interior zone, then the

*skylight area*in the interior zone shall be equal to the

*roof area*in the interior zone and the remaining

*skylight area*shall be prorated among the perimeter zones based on

*floor area*.

**C5. MODELING ASSUMPTIONS**

The following are modeling assumptions for the purposes of this appendix only and are not requirements for building

**C5.1**

The

*residential conditioned*and

*nonresidential conditioned space-conditioning categories*shall be modeled with both heating and cooling

*systems*for both the base envelope design and the

*proposed design*. The

*thermostat setpoints*for

*residential*and

*nonresidential spaces*shall be 70°F for heating and 75°F for cooling, with night

*setback*temperatures of 55°F for heating and 99°F for cooling.

**C5.2**

The

*semiheated space*categories shall be modeled with heating-only

*systems*for both the base envelope design and the

*proposed design*. The

*thermostat setpoint*shall be 50°F for all hours.

**C5.3**

Both the base envelope design and the proposed design shall be modeled with the same heating, ventilating, and air-conditioning (HVAC)

*systems*. The

*system*shall consist of a packaged rooftop

*system*serving each thermal zone. Cooling shall be provided by a direct expansion air conditioner (EER = 9.5, COP

*= 2.78). Heating shall be provided by a gas furnace (AFUE = 0.78).*

_{cooling}**C5.4**

The electrical

*systems*shall be the same for both the base envelope design and the

*proposed design*. The

*LPD*shall be 1.20 W/ft

^{2}for

*nonresidential conditioned spaces*, 1.00 W/ft

^{2}for

*residential conditioned spaces,*and 0.50 W/ft

^{2}for

*semiheated spaces*. The

*equipment*power density shall be 0.75 W/ft

^{2}for

*nonresidential conditioned spaces*, 0.25 W/ft

^{2}for

*residential conditioned spaces*, and 0.25 W/ft

^{2}for

*semi-heated spaces*.

*Continuous daylight dimming*shall be assumed in all

*spaces*and be activated at 50 fc for

*nonresidential conditioned spaces*and

*residential conditioned spaces*and 30 fc for

*semiheated spaces*.

**C5.5**

Surface

*reflectances*for daylighting calculations shall be 80% for ceilings, 50% for

*walls*, and 20% for floors.

**C5.6**

The

*U-factor*entered for surfaces adjacent to crawl

*-*spaces, attics, and parking garages with mechanical or natural

*ventilation*shall be adjusted by adding R-2 to the

*thermal resistance*to account for the buffering effect.

**C5.7**

Heat transfer for

*below-grade walls*shall be based on the temperature difference between indoor and outdoor temperature conditions and a heat transfer path at the average

*wall*depth below

*grade*.

**C6. EQUATIONS FOR ENVELOPE TRADE-OFF CALCULATIONS**

*building envelope*trade-off calculations.

**C6.1 Inputs.**

Building descriptions shall be converted to equation variables using Table C6.1.

TABLE C6.1 Input Variables

Variable | Description | I-P Units |

Area_{surface} | Area of surface | ft^{2} |

Area_{zone} | Gross floor area of zone as defined in Section C.5 | ft^{2} |

C-factor | C-factor for below-grade walls | Btu/h•ft^{2}•°F |

CDD50 | CDDs | Base 50°F•day |

CDD65 | CDDs | Base 65°F•day |

CDH80 | Cooling degree-hours | Base 80°F•hour |

Depth | Depth of bottom of below-grade wall | ft |

DI | Artificial lighting design illuminance from Section C.5.4 | footcandles |

DR | Daily range (average outdoor maximum-minimum in hottest month) | °F |

EPD | Miscellaneous equipment power density from Section C.5.4 | W/ft^{2} |

F-factor | F-factor for slab-on-grade floors | Btu/h•ft•°F |

HC | Wall heat capacity | Btu/ft^{2}•°F |

HDD50 | HDDs | Base 50°F•day |

HDD65 | HDDs | Base 65°F•day |

Length | Length of slab-on-grade floor perimeter | ft |

LPD | LPD from Section C.5.4 | W/ft^{2} |

R-Value | Effective R-value of soil for below-grade walls | h•ft^{2}•°F/Btu |

U-factor | U-factor | Btu/h•ft^{2}•°F |

VS | Annual average daily incident solar radiation on vertical surface | Btu/ft^{2}•day |

**C6.2 Envelope Performance Factor.**

The

*EPF*of a building shall be calculated using Equation C-1 using its actual

*orientation*, rotating the entire building 90, 180, and 270 degrees, then averaging the results.

EPF = FAF × [ΣHVAC+ ΣLighting_{surface} ]_{zone} | (C-1) |

ΣHVAC_{surface} | = | sum of HVAC for each surface calculated using Equation C-2 |

ΣLighting_{zone} | = | sum of lighting for each zone calculated using Equation C-3 |

**C6.3 HVAC.**

The HVAC term for each

*exterior*or

*semi-exterior*surface in the building shall be calculated using Equation C-2.

HVAC= 0.0939 × COOL + 1.22 × HEAT_{surface} | (C-2) |

COOL | = | cooling factor for the surface calculated according to the appropriate equation in C-14, C-19, or C-22 |

HEAT | = | heating factor for the surface calculated according to the appropriate equation in C-16, C-18, or C-23 |

**C6.4 Lighting.**

The lighting term for each zone in the building as defined in Section C4 shall be calculated using Equation C-3.

Lighting= _{zone} LPDadj× AREA_{zone} × 2700 ×0.939_{zone} | (C-3) |

LPDadj_{zone} | = | lighting power density for the zone adjusted for daylighting potential using Equation C-9 |

**C6.5 Solar and Visible Aperture**

**C6.5.1 Solar and Visible Aperture of Vertical Fenestration.**

The visible aperture (VA), solar aperture for cooling (SA

*), and solar aperture for heating (SA*

_{c}*) of each*

_{h}*vertical fenestration*shall be calculated using Equations C-5, C-6, and C-7.

VA = Area× VT_{vf} × (1 + PCC1 × PF + PCC2 × PF_{vf} ^{2}) | (C-5) |

SA = Area_{c}× 1.163 × SHGC × (1 – PCC1 × PF + PCC2 × PF_{vf} ^{2}) | (C-6) |

SA = Area_{h}× 1.163 × SHGC × (1 + PCH1 × PF + PCH2 × PF_{vf} ^{2}) | (C-7) |

Area_{vf} | = | glazing area of the vertical fenestration |

SHGC | = | the solar heat gain coefficient of the vertical fenestration assembly |

VT_{vf} | = | the visible transmittance of the vertical fenestration assembly |

PF | = | the projection factor for the overhang shade on the vertical fenestration |

PCH1, PCH2, PCC1, and PCC2 | = | overhang projection coefficients for the vertical fenestration orientation from Table C6.5.1 |

TABLE C6.5.1 Overhang Projection Coefficients

Orientation | PCC1 | PCC2 | PCH1 | PCH2 |

North | –0.5 | 0.22 | 0 | 0 |

East, South, West | –0.97 | 0.38 | 0 | 0 |

**C6.5.2 Visible Aperture of Skylights.**

The VA of a

*sky-light*shall be calculated using Equation C-8.

VA = Area× VT_{sky} × 10_{sky} ^{(–0.250 × (5 × D × (W + L) / (W × L))} | (C-8) |

Area_{sky} | = | fenestration area of the skylight assembly |

VT_{sky } | = | the visible transmittance of the skylight assembly |

D | = | average depth of skylight well from fenestration to ceiling |

W | = | width of skylight well |

L | = | length of skylight well |

**C6.6 Adjusted Lighting Power (**

*LPD*adj).The adjusted lighting power for each zone shall be calculated using Equation C-9.

LPDadj= _{zone} LPD × (1 – Kd)_{zone} | (C-9) |

*= daylight potential fraction calculated using Equation C-10.*

_{zone}*skylight*s and

*vertical fenestration*, the larger of the Kd calculated independently for each shall be used to calculate

*LPD*adj.

(C10) |

Area_{fen} | = | total fenestration area of the vertical fenestration or skylight assemblies in the zone |

VA | = | total visible aperture of the vertical fenestration or skylights in the zone, as calculated in Equation C-5 |

Area_{surface} | = | gross wall area of the zone for vertical fenestration or gross roof area of the zone for skylights |

and the coefficients 1 through 4 are defined in Table C6.6.

TABLE C6.6 Coefficients for Calculating Kd

Coefficient | Skylight | Vertical Fenestration |

Φ1 | 0.589 | 0.737 |

Φ2 | 5.18E–07 | –3.17E-04 |

Φ3 | –220 | –24.71 |

Φ4 | 2.29 | 0.234 |

**C6.7 Delta Load Factors for Mass Walls in the Exterior Building Envelope.**

Adjustments to cooling and heating loads for use in Equations C-14 and C-16 due to the mass properties of each

*mass wall*component shall be calculated using Equations C-11 and C-12.

(C-11) |

CMC | = | cooling delta load factor |

Area_{mw} | = | net opaque area of this mass wall |

A_{c} | = | CDH80/10000 + 2 |

B | = | DR/10 + 1 |

HC | = | wall heat capacity |

DR | = | average daily temperature range for warmest month |

CP_{1} | = | C_{5} |

CP_{2} | = | C_{15}/B^{3} + C_{16}/(A_{C}^{2}B^{2}) + C_{17} |

CP_{3} | = | |

CP_{4} | = | C_{12}(A_{C}^{2}B^{2}) + C_{13}/B^{3} + C_{14} |

U | = | area average of U-factors of mass walls in thezone |

CP_{5} | = | C_{18} |

CP_{6} | = | |

LN | = | natural logarithm |

CP_{7} | = | |

CP_{8} | = |

_{1}through C

_{22}depend on insulation position in the

*wall*and are taken from Table C6.7A.

(C-12) |

HMC | = | heating delta load factor |

HC | = | wall heat capacity |

Area_{mw} | = | net opaque area of this mass wall |

HP_{1} | = | H_{6} |

A_{H} | = | HDD65/100 + 2 |

HP_{2} | = | H_{14}LN(AH_{H}) + _{15} |

LN | = | natural logarithm |

HP_{3} | = | |

U | = | area average of U-factors of mass walls in the zone |

HP_{4} | = | |

HP_{5} | = | H_{16} |

HP_{6} | = | H_{7}A + H_{H}_{8} |

HP_{7} | = | H_{17}/A_{H}^{3} + H_{18} |

HP_{8} | = | H_{9}/A_{H}^{3}+ H_{10} |

_{1}through H

_{18}depend on the position of the insulation in the

*wall*and are taken from Table C6.7B. If the

*U-factor*of

*mass wall*is greater than 0.4 Btu/(h•ft

^{2}•°F), then the

*U-factor*shall be set to 0.4 Btu/(h•ft

^{2}•°F). If the

*U-factor*of the

*mass wall*is less than 0.05 Btu/(h•ft

^{2}•°F), then the

*U-Factor*shall be set to 0.05 Btu/(h•ft

^{2}•°F). If the

*wall HC*of the

*mass wall*is greater than 20 Btu/(ft

^{2}•°F), then

*HC*= 20 Btu/(ft

^{2}•°F) shall be used.

TABLE C6.7A Cooling Delta Load Coefficients

Insulation Position | |||

Variable | Exterior | Integral | Interior |

C_{1} | 220.7245 | 139.1057 | 181.6168 |

C_{2} | –0.0566 | –0.0340 | –0.0552 |

C_{3} | –118.8354 | –10.3267 | –34.1590 |

C_{4} | –13.6744 | –20.8674 | –25.5919 |

C_{5} | 0.2364 | 0.2839 | 0.0810 |

C_{6} | 0.9596 | 0.3059 | 1.4190 |

C_{7} | –0.2550 | 0.0226 | 0.4324 |

C_{8} | –905.6780 | –307.9438 | –1882.9268 |

C_{9} | 425.1919 | 80.2096 | 443.1958 |

C_{10} | –2.5106 | 0.0500 | 0.4302 |

C_{11} | –43.3880 | –5.9895 | –28.2851 |

C_{12} | –259.7234 | –11.3961 | –63.5623 |

C_{13} | –33.9755 | 0.3669 | 20.8447 |

C_{14} | 20.4882 | 30.2535 | 9.8175 |

C_{15} | –26.2092 | 8.8337 | 24.4598 |

C_{16} | –241.1734 | –22.2546 | –70.3375 |

C_{17} | 18.8978 | 29.3297 | 9.8843 |

C_{18} | –0.3538 | –0.0239 | –0.1146 |

C_{19} | 156.3056 | 63.3228 | 326.3447 |

C_{20} | –74.0990 | –16.3347 | –77.6355 |

C_{21} | 0.4454 | –0.0111 | –0.0748 |

C_{22} | 7.4967 | 1.2956 | 5.2041 |

TABLE C6.7B Heating Delta Load Coefficients

Insulation Position | |||

Variable | Exterior | Integral | Interior |

H_{1} | 0.0000 | 0.0000 | 0.0000 |

H_{2} | –0.0015 | –0.0018 | –0.0015 |

H_{3} | 13.3886 | 15.1161 | 19.8314 |

H_{4} | 1.9332 | 2.1056 | 1.4579 |

H_{5} | –11.8967 | –13.3053 | –15.5620 |

H_{6} | 0.4643 | 0.1840 | 0.0719 |

H_{7} | 0.0094 | 0.0255 | 0.0264 |

H_{8} | –0.1000 | 0.0459 | 0.7754 |

H_{9} | –1223.3962 | –622.0801 | 0.2008 |

H_{10} | –0.9454 | –0.5192 | -0.6379 |

H_{11} | –0.0001 | –0.0001 | 0.0000 |

H_{12} | 3.8585 | 4.1379 | 2.4243 |

H_{13} | 7.5829 | 6.2380 | 7.9804 |

H_{14} | –0.7774 | –0.7711 | –0.1699 |

H_{15} | 9.0147 | 7.7229 | 8.5854 |

H_{16} | 0.2007 | 0.2083 | –0.0386 |

H_{17} | 206.6382 | 105.9849 | 3.1397 |

H_{18} | 0.2573 | 0.1983 | 0.1863 |

**C6.8 Walls and Vertical Fenestration in the Exterior Building Envelope.**

Equations C-14 and C-16 shall be used to calculate COOL and HEAT for

*exterior walls*and

*vertical fenestration*in the

*exterior building envelope*except

*walls*next to crawlspaces, attics, and parking garages with natural or mechanical

*ventilation*.

*Walls*next to crawlspaces, attics, and parking garages with natural or mechanical

*ventilation*shall use the equations in Section C6.10 and they shall not be included in calculations in Section C6.8. Zones shall be constructed according to Section C4 and the HEAT and COOL for the combination of all

*exterior walls*and

*vertical fenestration*in the zone shall be calculated using Equations C-14 and C-16, which include interactive effects. For a zone having a cardinal

*orientation*(north, east, south, or west), Equations C-14 and C-15 shall be applied directly. For zones with northeast, north-west, southwest, and southeast

*orientation*s, EC shall be determined by finding the average of the values for the two closest cardinal

*orientations*; for instance, COOL for a

*wall*facing northeast is calculated by taking the average of COOL for a north-facing

*wall*and COOL for an east-facing

*wall*.

**C6.8.1 Effective Internal Gain.**

The effective internal gain to zone G shall be calculated using Equation C-13.

G = EPD + LPDadj_{zone} | (C-13) |

LPDadj_{zone} | = | lighting power density adjusted for daylighting, from Equation C-9 |

**C6.8.2 Cooling Factor.**

The cooling factor for the surfaces in the zone shall be calculated using Equation C-14.

COOL = 1000/(1200 × 12.24) × [CLU + CLUO + CLXUO + CLM + CLG + CLS + CLC] | (C-13) |

CLU | = | Area × _{opaque}U × [CU1 × CDH80 + CU2 × CDH80_{ow}^{2 }+ CU3 × (VS × CDH80)^{2} + CU4 x DR] |

CLUO | = | Area × UO × [CUO1 × EA_{grosswall}_{C} × VS × CDD50 + CUO2 × G + CUO3 × G^{2} × EA_{C}^{2}× VS × CDD50 + CUO4 × G^{2} × EA_{C}^{2}× VS × CDD65] |

CLXUO | = | Area / UO × [CXUO1 × EA_{grosswall}_{C} × VS × CDD50 + CXUO2 × EA_{C} × (VS × CDD50)^{2} + CXUO3 × G × CDD50 + CXUO4 × G^{2} × EA_{C}^{2} × VS × CDD50 + CXUO5 × G^{2} × CDD65] |

CLM | = | Area × SCMC × [CM1 + CM2 × EA_{opaque}_{C} × VS × CDD50 + CM3 × EA_{C} × VS × CDD65 + CM4 × EA_{C}^{2} × VS × CDD50 + CM5 × G^{2} × CDD65 + CM6 × G × CDD50 + CM7 × G × CDD65 + CM8 × G × EA_{C} × VS × CDD50] |

CLG | = | Area × {G × [CG1 + CG2 × CDD50 + CG3 × EA_{grosswall}_{C} × (VS × CDD50)^{2} + CG4 × EA_{C}^{2} × VS × CDD50 + CG5 × CDD65 + CG6 × CDD50^{3} + CG7 × CDD65^{3}] + G^{2} × [CG8 × EA_{C} × VS × CDD50 + CG9 × EA_{C}^{2} × VS × CDD50]} |

CLS | = | Area × {EA_{grosswall}_{C} × [CS1 + CS2 × VS × CDD50 + CS3 × (VS × CDD50)^{2} + CS4 × VS × CDD65 + CS5 × (VS × CDD65)^{2}] + EA_{C}^{2} × [CS6 + CS7 × (VS × CDD65)^{2}]} |

CLC | = | Area × [CC1 × CDD50 + CC2 × CDD50_{grosswall}^{2}+ CC3 × CDH80 + CC4 × CDH80^{2} + CC5 × CDD65 + CC6 × (VS × CDD65)^{2} + CC7 × VS × CDD50 + CC8 × (VS × CDD50)^{2} + CC9 × (VS × CDH80)^{2} + CC10 × VS + CC11 × DR + CC12 × DR^{2} + CC13] |

Area_{grosswall} | = | total gross area of all walls and vertical fenestration in the zone, including opaque and fenestration areas |

Area_{opaque} | = | total opaque area of all walls in the zone |

U_{ow} | = | area average of U-factors of opaque walls (including those of mass construction) in the zone |

VS | = | annual average daily incident solar energy on surface |

DR | = | average daily temperature range for the warmest month |

UO | = | area average of U-factor of opaque walls and vertical fenestration in the zone |

SCMC | = | sum of the CMC from Equation C-11 for each mass wall in the zone |

G | = | effective internal gain to space, from Equation C-13 |

EA_{C} | = | effective solar aperture fraction for zone calculated using Equation C-15 |

(C-15) |

ΣSA_{c} | = | the sum of SA from Equation C-6.6 for all _{c }vertical fenestration in the zone. |

*orientation*of the surface and shall be found in Table C6.8.2.

TABLE C6.8.2 Cooling Coefficients for the Exterior Wall Equation

Variable | Orientation of Surface | |||

North | East | South | West | |

CU1 | 0.001539 | 0.003315 | 0.003153 | 0.00321 |

CU2 | –3.0855E-08 | –8.9662E-08 | –7.1299E-08 | –8.1053E-08 |

CU3 | 7.99493E-14 | 3.7928E-14 | 1.83083E-14 | 3.3981E-14 |

CU4 | –0.079647 | 0.163114 | 0.286458 | 0.11178 |

CM1 | 0.32314 | 0.515262 | 0.71477 | 0.752643 |

CM2 | 1.5306E-06 | 1.38197E-06 | 1.6163E-06 | 1.42228E-06 |

CM3 | –2.0432E-06 | –1.6024E-06 | –2.1106E-06 | –1.9794E-06 |

CM4 | –7.5367E-07 | –7.6785E-07 | –6.6443E-07 | –7.4007E-07 |

CM5 | –1.0047E-06 | 0 | 8.01057E-06 | 3.15193E-06 |

CM6 | 3.66708E-05 | 3.56503E-05 | 4.48106E-05 | 2.96012E-05 |

CM7 | –6.7305E-05 | –6.4094E-05 | –0.000119 | –7.6672E-05 |

CM8 | –2.3834E-08 | –4.7253E-08 | –4.9747E-08 | 0 |

CUO1 | –6.5109E-06 | –8.3867E-06 | –8.89E-06 | –7.5647E-06 |

CUO2 | –1.040207 | –1.507235 | –1.512625 | -1.238545 |

CUO3 | –4.3825E-06 | –2.7883E-06 | –2.3135E-06 | –4.1257E-06 |

CUO4 | 0.000012658 | 8.09874E-06 | 7.36219E-06 | 1.06712E-05 |

CXUO1 | 1.03744E-06 | 1.19338E-06 | 1.18588E-06 | 1.23251E-06 |

CXUO2 | –1.3218E-13 | –1.3466E-13 | –1.1625E-13 | –1.3E-13 |

CXUO3 | 2.75554E-05 | 2.02621E-05 | 2.02365E-05 | 2.36964E-05 |

CXUO4 | 9.7409E-08 | 1.175E-07 | 9.39207E-08 | 1.36276E-07 |

CXUO5 | –1.1825E-05 | –9.0969E-06 | –9.0919E-06 | –1.1108E-05 |

CG1 | 0.891286 | 0.583388 | 0.393756 | 0.948654 |

CG2 | 0.001479 | 0.001931 | 0.002081 | 0.001662 |

CG3 | –5.5204E-13 | –2.8214E-13 | –2.8477E-13 | –4.5572E-13 |

CG4 | 2.52311E-06 | 3.70821E-06 | 4.30536E-06 | 5.91511E-06 |

CG5 | –0.001151 | –0.001745 | –0.001864 | –0.00153 |

CG6 | 1.95243E-12 | 0 | –2.9606E-12 | 3.16358E-12 |

CG7 | –8.3581E-12 | 1.01089E-11 | 3.30027E-11 | 0 |

CG8 | 1.41022E-06 | 7.53875E-07 | 7.133E-07 | 9.70752E-07 |

CG9 | –2.3889E-06 | –1.6496E-06 | –1.6393E-06 | –1.9736E-06 |

CS1 | 46.9871 | 33.9683 | 18.32016 | 29.3089 |

CS2 | 3.48091E-05 | 3.74118E-05 | 0.000034049 | 5.02498E-05 |

CS3 | 0 | 0 | 2.71313E-12 | 0 |

CS4 | –1.6641E-05 | 6.94779E-06 | –2.8218E-05 | –2.7716E-05 |

CS5 | 8.42765E-12 | 0 | –3.0468E-12 | 2.91137E-12 |

CS6 | –56.5446 | 0 | 26.9954 | 14.9771 |

CS7 | –1.3476E-11 | –5.881E-12 | –6.5009E-12 | –7.8922E-12 |

CC1 | 0.002747 | 0 | 0.010349 | 0.001865 |

CC2 | 0 | 3.18928E-07 | –3.0441E-07 | 0 |

CC3 | –0.000348 | 0.000319 | 0.00024 | 0.000565 |

CC4 | 1.22123E-08 | –7.7532E-08 | –2.7144E-08 | –5.4438E-08 |

CC5 | 0.012112 | 0.011894 | 0.013248 | 0.009236 |

CC6 | 1.04027E-12 | –6.2266E-13 | –2.0518E-12 | 0 |

CC7 | –1.2401E-05 | –7.0628E-06 | –1.6538E-05 | –6.0269E-06 |

CC8 | 0 | 0 | 8.20869E-13 | 0 |

CC9 | –3.758E-14 | 6.06235E-14 | 1.97598E-14 | 3.89425E-14 |

CC10 | 0.030056 | 0.023121 | 0.0265 | 0.01704 |

CC11 | 0 | 0 | –0.271026 | –0.244274 |

CC12 | 0.002138 | 0.001103 | 0.006368 | 0.007323 |

CC13 | –12.8674 | –13.16522 | –18.271 | –10.1285 |

**C6.8.3 Heating Factor.**

The heating factor for the surfaces in the zone shall be calculated using Equation C-16.

HEAT=10/(1200 × 0.608488) × [HLU + HLUO + HLXUO + HLM + HLG + HLS + HLC] | (C-15) |

HLU | = | Area × U_{opaque}_{ow}× [HU1 × HDD50 + HU2 × (VS × HDD65)^{2}] |

HLUO | = | Area × UO × [HUO1 × HDD50 + HUO2 × HDD65 + HUO3 × EA_{grosswall}_{H} × VS × HDD65] |

HLXUO | = | Area × {(1/UO) × [HXUO1 × EA_{grosswall}_{H}× (VS × HDD50)^{2} + HXUO2 × EA_{H} × (VS × HDD65)^{2}] + (1/UO^{2}) × [HXUO3 × EA_{H}^{2} × VS × HDD65]} |

HLM | = | Area × SHMC × [HM1 + HM2 × G × UO × HDD65 + HM3 × G_{opaque}^{2} × EA_{H}^{2}× VS × HDD50 + HM4 × UO× EA_{H} × VS × HDD65 + HM5 × UO × HDD50 + HM6 × EA_{H} × (VS × HDD65)^{2} + HM7 × EA_{H}^{2} × VS × HDD65/UO] |

HLG | = | Area × {G × [HG1 × HDD65 + HG2 × UO× HDD65 + HG3 × EA_{grosswall}_{H}× VS × HDD65 + HG4 × EA_{H}^{2}× VS × HDD50] × G^{2} × [HG5 × HDD65 + HG6 × EA_{H}^{2}× VS × HDD65]} |

HLS | = | Area × {EA_{grosswall}_{H} × [HS1 × VS × HDD65 + HS2 × (VS × HDD50)^{2}] + EA_{H}^{2} × [HS3 × VS × HDD50 + HS4 × VS × HDD65]} |

HLC | = | Area × [HC1 + HC2 × HDD65 + HC3 × HDD65_{grosswall}^{2} + HC4 × VS^{2} + HC5 × VS × HDD50 + HC6 × VS × HDD65 + HC7 × (VS × HDD50)^{2}] |

VS | = | annual average daily incident solar energy on surface |

SHMC | = | sum of the HMC from Equation C-12 for each mass wall in the zone |

EA_{H} | = | effective solar aperture fraction for zone calculated using Equation C-17. |

(C-17) |

*SA*= the sum of

_{h}*SA*from Equation C-7 for all

_{h}*vertical fenestration*in the zone

*.*

*orientation*of the surface and shall be found in Table C6.8.3. Terms not defined for Equation C-16 are found under Equation C-14.

TABLE C6.8.3 Heating Coefficients for the Exterior Wall Equation

Variable | Orientation of Surface | |||

North | East | South | West | |

HU1 | 0.006203 | 0.007691 | 0.006044 | 0.006672 |

HU2 | –1.3587E-12 | –5.7162E-13 | –2.69E-13 | –4.3566E-13 |

HM1 | 0.531005 | 0.545732 | 0.837901 | 0.616936 |

HM2 | 0.000152 | 0.000107 | 0.000208 | 0.00015 |

HM3 | –5.3183E-07 | –1.0619E-07 | –6.8253E-07 | –2.6457E-07 |

HM4 | –7.7381E-07 | –1.4787E-06 | 2.11938E-06 | –4.5783E-07 |

HM5 | –0.000712 | –0.000484 | –0.001042 | –0.000625 |

HM6 | 3.34859E-13 | 4.95762E-14 | 7.7019E-14 | 7.37105E-14 |

HM7 | 2.39071E-07 | 2.75045E-07 | –3.8989E-07 | 0 |

HUO1 | 0.004943 | 0.008683 | 0.009028 | 0.008566 |

HUO2 | 0.013686 | 0.011055 | 0.010156 | 0.01146 |

HUO3 | –1.1018E-05 | –8.6896E-06 | –7.3232E-06 | –8.9867E-06 |

HXUO1 | 1.2694E-12 | 7.85644E-14 | –2.8202E-13 | 3.04904E-14 |

HXUO2 | –7.3058E-13 | –8.109E-14 | 7.45599E-14 | –7.4718E-14 |

HXUO3 | 1.9709E-07 | 1.94026E-07 | 9.87587E-08 | 1.95776E-07 |

HG1 | –0.001051 | –0.000983 | –0.000981 | –0.000948 |

HG2 | –0.001063 | –0.00093 | –0.000815 | –0.000975 |

HG3 | 2.99013E-06 | 2.62269E-06 | 2.4188E-06 | 2.49976E-06 |

HG4 | 7.49049E-07 | –1.1106E-06 | –2.1669E-06 | –8.5605E-07 |

HG5 | 0.000109 | 0.000093431 | 9.75523E-05 | 8.62389E-05 |

HG6 | –5.5591E-07 | –3.158E-07 | –2.61E-07 | –2.9133E-07 |

HS1 | –2.1825E-05 | –2.0922E-05 | –2.1089E-05 | –2.0205E-05 |

HS2 | 3.39179E-12 | 1.905E-12 | 1.48388E-12 | 2.18215E-12 |

HS3 | –6.5325E-06 | –2.2341E-05 | –1.8473E-05 | –2.4049E-05 |

HS4 | 2.23087E-05 | 2.41331E-05 | 2.45412E-05 | 2.30538E-05 |

HC1 | –0.106468 | –5.19297 | –3.66743 | –5.29681 |

HC2 | 0.00729 | 0.007684 | 0.007175 | 0.007672 |

HC3 | –2.976E-07 | –3.0784E-07 | –2.6419E-07 | –3.0713E-07 |

HC4 | 2.01569E-06 | 6.3035E-06 | 3.32112E-06 | 6.43491E-06 |

HC5 | 1.29061E-05 | 4.77552E-06 | 3.25089E-06 | 4.83233E-06 |

HC6 | –1.2859E-05 | –6.1854E-06 | –4.6309E-06 | –6.251E-06 |

HC7 | 2.75861E-12 | 8.20051E-13 | 4.38148E-13 | 8.09106E-13 |

**C6.9 Skylights in the Exterior Building Envelope.**

HEAT and COOL shall be calculated for

*skylights*in

*nonresidential conditioned*and

*residential conditioned*zones using Equations C-17 and C-18.

HEAT=Area × HDD65 ×(H_{sky}_{2} × U + H_{sky}_{3} × SHGC/0.86) | (C-17) |

COOL = Area × C_{sky}_{2} × CDD50 × SHGC/0.86 | (C-18) |

Area_{sky} | = | fenestration area of the skylight assembly |

SHGC | = | the solar heat gain coefficient of the skylight assembly |

U_{sky} | = | U-factor of skylight assembly |

The coefficients used in the equations depend on the *space *type and shall be taken from Table C6.9.

TABLE C6.9 Heating and Cooling

Coefficients for Skylights

Coefficient | Nonresidential | Residential |

C_{2} | 1.09E-02 | 1.64E-02 |

H_{2} | 2.12E-04 | 2.91E-04 |

H_{3} | –1.68E-04 | –2.96E-04 |

**C6.10 Calculations for Other Exterior and Semi-Exterior Surfaces.**

For all

*exterior*and

*semi-exterior*surfaces not covered in Sections C6.8 and C6.9, the cooling factor, COOL, and heating factor, HEAT, shall be calculated using the procedure in this section.

**C6.10.1 U-Factor for Below-Grade Walls.**

The effective

*U-factor*of

*below-grade walls*shall be calculated using Equation C-20. R

_{soil}shall be selected from Table C6.10.1 based onthe average depth of the bottom of the

*wall*below the surface of the ground.

U-factor = 1 / ((1/C-factor) + 0.85 + R_{soil}) | (C-20) |

_{soil}=effective R-value of the soil from Table C6.10.1

TABLE C6.10.1 Effective R-Value of Soil

for Below-Grade Walls

Depth, ft | R_{soil} (h•ft^{2}•°F/Btu) |

1 | 0.86 |

2 | 1.6 |

3 | 2.2 |

4 | 2.9 |

5 | 3.4 |

6 | 4.0 |

7 | 4.5 |

8 | 5.1 |

9 | 5.6 |

10 | 6.1 |

**C6.10.2 Adjustment for Other Protected Elements of the Exterior Envelope.**

The adjusted

*U-factor*for

*exterior envelope*surfaces, which are protected from outdoor conditions by crawlspaces, attics, or parking garages with natural or mechanical

*ventilation*, shall be adjusted using Equation C-21 before calculating HEAT and COOL.

U_{adj} = 1 / ((1 / U-factor) + 2) | (C-21) |

TABLE C6.10.2 Heating and Cooling Coefficients for Other Exterior and

Semi-Exterior Surfaces

Building Envelope Classification | Exterior | Semi-Exterior | |||||||

Space-Conditioning Type | Nonresidential | Residential | All | ||||||

Surface Type | Ccoef1 | Ccoef2 | Hcoef | Ccoef1 | Ccoef2 | Hcoef | Ccoef1 | Ccoef2 | Hcoef |

Roof | 0.001153 | 5.56 | 2.28E-04 | 0.001656 | 9.44 | 3.37E-04 | 0 | 0 | 8.08E-05 |

Wall, above-grade, and opaque doors | 6.04E-04 | 0 | 2.28E-04 | 1.18E-03 | 0 | 3.37E-04 | 0 | 0 | 7.56E-05 |

Wall, below-grade | 2.58E-04 | 0 | 2.29E-04 | 6.80E-04 | 0 | 3.35E-04 | N/A | 0 | 7.85E-05 |

Mass floor | 6.91E-04 | 0 | 2.39E-04 | 1.01E-03 | 0 | 3.60E-04 | 0 | 0 | 7.14E-05 |

Other floor | 7.09E-04 | 0 | 2.43E-04 | 9.54E-04 | 0 | 3.66E-04 | 0 | 0 | 7.14E-05 |

Slab-on-grade floor | 0 | 0 | 2.28E-04 | 0 | 0 | 3.37E-04 | 0 | 0 | 6.80E-05 |

Vertical fenestration | N/A | 0 | N/A | N/A | 0 | N/A | 0 | 0 | 7.56E-05 |

Skylights | N/A | 0 | N/A | N/A | 0 | N/A | 0 | 0 | 8.08E-05 |

**C6.10.3 Calculation of COOL and HEAT.**

COOL and HEAT shall be calculated for each surface using Equations C-21 and C-22 and coefficients from Table C6.10.2, which depend on surface classification and

*space-conditioning category*.

COOL = Size × Factor × (Ccoef1 × CDD50 + Ccoef2) | (C-21) | ||

HEAT = Size × Hcoef × Factor × HDD65 | (C-22) |

Size | = | area of surface or length of exposed slab-on-grade floor perimeter in the building |

Ccoef1, Ccoef2 | = | coefficients, from Table C6.10.2 |

Hcoef | = | coefficient from Table C6.10.2 |

Factor | = | U-factor except U_{adj} calculated using Equation C-21 for protected surfaces and for slab-on-grade floors, perimeter |