Trinity Tx51 User manual

Trinity Tx
Model Numbers: Tx51-151
Version Date: 2013-12-30
INSTALLATION AND OPERATION INSTRUCTIONS FOR
TRINITY Tx BOILER
TABLE OF CONTENTS
1.0 INTRODUCTION................................................................................................................3
2.0 SPECIFICATIONS ..............................................................................................................6
3.0 BOILER LOCATION ..........................................................................................................7
4.0 GENERAL VENTING.......................................................................................................10
5.0 VENT/AIR-INLET TERMINATION CLEARANCES.....................................................24
6.0 CONDENSATE DRAIN....................................................................................................27
7.0 INSTALLING GAS PIPING..............................................................................................29
8.0 LIGHTING THE BOILER.................................................................................................31
9.0 GAS VALVE AND BURNER SET-UP ............................................................................34
10.0 BOILER AND HEATING SYSTEM PIPING...................................................................37
11.0 DOMESTIC HOT WATER (DHW) PIPING –TX151C (COMBI)..................................48
12.0 FIELD WIRING.................................................................................................................52
13.0 CASCADE INSTRUCTIONS............................................................................................55
14.0 WIRING SCHEMATICS...................................................................................................57
15.0 INSTALLATION CHECKLIST ........................................................................................59
16.0 ANNUAL MAINTENANCE AND INSPECTION...........................................................60
17.0 DISPLAY MENU GUIDE.................................................................................................62
18.0 TROUBLESHOOTING .....................................................................................................73
19.0 PARTS LIST ......................................................................................................................76
HAZARD SYMBOLS AND DEFINITIONS
Danger Sign: Indicates a hazardous situation which, if not avoided, will
result in serious injury or death.
Warning Sign: Indicates a hazardous situation which, if not avoided,
could result in serious injury or death.
Caution Sign plus Safety Alert Symbol: Indicates a hazardous situation
which, if not avoided, could result in minor or moderate injury.
Caution Sign without Safety Alert Symbol: Indicates a hazardous
situation which, if not avoided, could result in property damage.
Notice Sign: Indicates a hazardous situation which, if not avoided,
could result in property damage.
This Boiler must be installed by a licensed and trained Heating
Technician or the Warranty is Void. Failure to properly install this
unit may result in property damage, serious injury to occupants, or possibly death.
NTI # 84874
NEW PRODUCT LINE
High Efficiency
Condensing Gas Boiler
H

Trinity Tx│Installation and Operation Instructions Tx Series
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Read Before Proceeding
If you do not follow these instructions exactly, a fire or explosion may result causing
property damage, serious injury or death.
FOR YOUR SAFETY, READ BEFORE OPERATING_
A) This boiler does not have a pilot. It is equipped with an ignition device which automatically lights the
burner. Do not try to light the burner by hand.
B) BEFORE OPERATING smell all around the boiler area for gas. Be sure to smell next to the floor
because some gas is heavier than air and will settle on the floor.
WHAT TO DO IF YOU SMELL GAS:
•Do not try to light any boiler.
•Do not touch any electric switch.
•Do not use any phone in your building.
•Immediately call your gas supplier from a neighbor's phone. Follow the gas supplier's instructions.
•If you cannot reach your gas supplier, call the fire department.
C) Use only your hand to turn the gas “shutoff” valve. Never use tools. If the handle will not turn by hand,
don't try to repair it, call a qualified service technician. Force or attempted repair may result in a fire or
explosion.
D) Do not use this boiler if any part has been under water. Immediately call a qualified service technician
to inspect the boiler and to replace any part of the control system and any gas control which has been
under water.
OPERATING INSTRUCTIONS_
1. STOP! Read the safety information above very carefully.
2. Set the thermostat to lowest setting. Turn off all electric power to the boiler.
3. This boiler does not have a pilot. It is equipped with an ignition device which automatically lights the
burner. Do not try to light the burner by hand.
4. Turn the manual gas valve to the OFF position. Remove front access panel.
5. Wait five (5) minutes to clear out any gas. Then smell for gas, including near the floor. If you smell gas,
STOP! Follow “B” in the safety information above. If you don't smell gas, go to the next step.
6. Turn the manual gas valve ON. Wait an additional five (5) minutes smelling for gas.
7. Replace the front access panel.
8. Set thermostat to highest setting. Turn on all electric power to the boiler.
9. Ignition sequence is automatic. Combustion will occur after a brief fan purge.
10. If ignition does not occur, follow the instructions “To Turn Off Gas To Boiler” and call your service
technician or gas supplier.
TO TURN OFF GAS TO THE BOILER_
1. STOP! Read the safety information above very carefully.
2. Turn off all electric power to the boiler.
3. Turn the manual gas valve to the OFF position.
Crystalline Silica - Certain components confined in the combustion chamber may
contain this potential carcinogen. Improper installation, adjustment, alteration, service or
maintenance can cause property damage, serious injury (exposure to hazardous materials) or death. Refer to
Section 15.0 for information on handling instructions and recommended personal protective equipment.
Installation and service must be performed by a qualified installer, service agency or the gas supplier (who must
read and follow the supplied instructions before installing, servicing, or removing this boiler. This boiler
contains materials that have been identified as carcinogenic, or possibly carcinogenic, to humans).
Void Warranty - This Boiler must have water flowing through it whenever the burner is
on or it will damage the unit and void the warranty. Failure to follow these instructions
may result in serious injury or death.

Tx Series Installation and Operation Instructions │Trinity Tx
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1.0 INTRODUCTION
General Installation Requirements
The installation of your NTI Trinity Tx gas boiler must conform to the requirements of this manual, your local
authority, and the National Fuel Gas Code ANSI Z223.1 and or CAN/CGA B149 Installation Codes. Where
required by the Authority, the installation must conform to the standard for “Controls and Safety Devices for
Automatically Fired Boilers ANSI/ASME CSD-1.
This document pertains to the correct installation and operation of NTI Trinity boiler model Tx. The instructions
detailed in this document supersede any and all previous instructions provided by NTI, written or otherwise.
Each unit is provided with the following:
1. Installation and Operating Instructions,
2. Trinity Users’Manual, and
3. Natural Gas to LP Conversion Kit*
* The conversion kit is required to convert the boiler so it will safely operate with Propane Gas.
Read and understand this entire document prior to proceeding with the installation of the
Trinity Tx. Failure to follow the instructions outlined in this document will result in
property damage, serious injury or death.
Energy Saving Feature - This boiler is equipped with a feature that saves energy by
reducing the boiler water temperature as the heating load decreases. This feature is
equipped with an override which is provided primarily to permit the use of an external energy management
system that serves the same function. THIS OVERRIDE MUST NOT BE USED UNLESS AT LEAST ONE
OF THE FOLLOWING CONDITIONS IS TRUE:
An external energy management system is installed that reduces the boiler water temperature as the heating
load decreases.
This boiler is not used for any space heating.
This boiler is part of a modular or multiple boiler system having a total input of 300,000 BTU/hr or greater.
This boiler is equipped with a tankless coil.
User Responsibilities
This boiler must be installed and serviced by a qualified installer or service technician. This boiler must be
serviced and inspected annually when operating in normal residential applications. Demanding applications or
extreme conditions (i.e. when operating with LP-Propane) may require more frequent service and inspection. As
the User/Owner of this equipment, you are responsible for ensuring the maintenance is performed at the required
intervals (see Section 14 –Annual Maintenance and Inspection).
Failure to have the boiler properly serviced and inspected on a regular basis by a qualified
service technician may result in property damage, serious injury or death.
Failure to keep the Vent and Combustion Air Intake clear of ice, snow, and other debris
may result in property damage, serious injury, or death.
Installer Responsibilities
As the installing technician it is your responsibility to ensure the installation is performed in accordance with this
instruction manual as well as any applicable local or National installation codes. It is also your responsibility to
inform the User/Owner of their obligation with respect to the above description under “User Responsibilities”.
Failure to follow this warning could result in fire, serious injury, or death.

Trinity Tx│Installation and Operation Instructions Tx Series
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Failure to use the appropriate Natural to LP Conversion Kit and Orifice when operating
the Trinity Tx to operate with Propane will result in extremely dangerous burner
operation leading to property damage, serious injury or death. Refer to section titled ATTENTION:
LIQUEFIED PETROLEUM (LP) PROPANE for applicable conversion kit and LP orifice numbers.
ATTENTION: LIQUEFIED PETROLEUM (LP) PROPANE
The Trinity Tx is factory set to operate with Natural Gas. BEFORE OPERATING WITH PROPANE, the
specified LP Conversion Kit and Orifice must be installed to convert the boiler so it will operate safely with
LP Propane. The correct kit and LP orifice is listed below (Each kit comes with conversion instructions).
Liquefied Petroleum (LP) propane gas is heavier than air; therefore, it is imperative that your Trinity Tx boiler
is not installed in a pit or similar location that will permit heavier than air gas to collect. Local Codes may
require boilers fueled with LP gas be provided with an approved means of removing unburned gases from the
room. Check your local codes for this requirement.
Natural to LP Propane Conversion Kit_
Model Number Kit Number LP Orifice
Tx51 84867-1 3.5mm
Tx81 84867-2 3.8mm
Tx101 84867-3 4.2mm
Tx151(C) 84867-4 5.05mm
Boiler Vent / Air-Inlet Piping
The Trinity Tx is certified as a “Category IV” boiler, and requires a “Special Venting
System” designed for pressurized venting. The exhaust gases must be piped directly to
the outdoors using the vent materials and rules outlined in these instructions. Failure to follow these instructions
will result in serious injury or death.

Tx Series Installation and Operation Instructions │Trinity Tx
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IN THE STATE OF MASSACHUSETTS ONLY
(a) For all horizontally vented gas fueled equipment installed in every dwelling, building or structure used in whole or
in part for residential purposes, including those owned and operated by the Commonwealth and where the side wall
exhaust vent termination is less than seven (7) feet above finished grade in the area of the venting, including but not
limited to decks and porches, the following requirements shall be satisfied:
1. INSTALLATION OF CARBON MONOXIDE DETECTORS At the time of installation of the side wall
horizontal vented gas fueled equipment, the installing plumber or gas fitter shall observe that a hard wired
carbon monoxide detector with an alarm and battery back-up is installed on the floor level where the gas
equipment is to be installed and on each additional level of the dwelling, building or structure served by the
equipment. It shall be the responsibility of the property owner to secure the services of qualified licensed
professionals for the installation of hard wired carbon monoxide detectors.
a. In the event that the side wall horizontally vented gas fueled equipment is installed in a crawl space or an
attic, the hard wired carbon monoxide detector with alarm and battery back-up may be installed on the next
adjacent floor level.
b. In the event that the requirements of this subdivision cannot be met at the time of completion of
installation, the owner shall have a period of 30 days to comply with the above requirements; provided,
however, that during said 30 day period a battery operated carbon monoxide detector with an alarm shall
be installed.
2. APPROVED CARBON MONOXIDE DETECTORS Each carbon monoxide detector as required in accordance
with the above provisions shall comply with NFPA 720 and be ANSI/UL 2034 listed and IAS certified.
3. SIGNAGE A metal or plastic identification plate shall be permanently mounted to the exterior of the building
at a minimum height of eight (8) feet above grade directly in line with the exhaust vent terminal for the
horizontally vented gas fueled heating boiler or equipment. The sign shall read, in print size no less than one-
half (1/2) inch in size, “GAS VENT DIRECTLY BELOW. KEEP CLEAR OF ALL OBSTRUCTIONS”
(plate included with boiler).
4. INSPECTION The state or local gas inspector of the side wall horizontally vented gas fueled equipment shall
not approve the installation unless, upon inspection, the inspector observes carbon monoxide detectors and
signage installed in accordance with the provisions of 248 CMR 5.08(2)(a)1 through 4.
(b) EXEMPTIONS: The following equipment is exempt from 248 CMR 5.08(2)(a)1 through 4:
1. The equipment listed in Chapter 10 entitled “Equipment Not Required To Be Vented” in the most current
edition of NFPA 54 as adopted by the Board; and
2. Product Approved side wall horizontally vented gas fueled equipment installed in a room or structure separate
from the dwelling, building or structure used in whole or in part for residential purposes.
(c) MANUFACTURER REQUIREMENTS –GAS EQUIPMENT VENTING SYSTEM PROVIDED: When the
manufacturer of Product Approved side wall horizontally vented gas equipment provides a venting system design or
venting system components with the equipment, the instructions provided by the manufacturer for installation of the
equipment and the venting system shall include:
1. Detailed instructions for installation of the venting system design or the venting system components; and
2. A complete parts list for the venting system design or venting system.
(d) MANUFACTURER REQUIREMENTS –GAS EQUIPMENT VENTING SYSTEM NOT PROVIDED:
When the manufacturer of a Product Approved side wall horizontally vented gas fueled equipment does not provide
the parts for venting the flue gases, but identifies “special venting systems”, the following requirements shall be
satisfied by the manufacturer:
1. The referenced “special venting system” instructions shall be included with the appliance or equipment
installation instructions; and
2. The “special venting system” shall be Product Approved by the Board, and the instructions for that system shall
include a parts list and detailed installation instructions.
(e) A copy of all installation instructions for all Product Approved side wall horizontally vented gas fueled equipment,
all venting instructions, all parts list for venting instructions, and/or all venting design instructions shall remain with
the appliance or equipment at the completion of the installation.

Trinity Tx│Installation and Operation Instructions Tx Series
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2.0 SPECIFICATIONS
Table 2-1 Trinity Tx Specifications
DESCRIPTION
Tx51
Tx81
Tx101
Tx151
Tx151C
CSA Input Modulation1
[MBH]
9.2-46
16.4-82
20.2-101
30.2-151
30.2-151
DOE Heating Capacity1,2
[MBH]
42
75
92
138
138
Net I=B=R Rating1,2
[MBH]
36
65
80
120
120
DOE AFUE2 [%]
93.1
Water Connections –NPT [in.]
1
3/4
Gas Connection - NPT, in.
½
Vent/Air-inletPipeDiameter
[in.] 3
2 or 3
Dimensions H x W x D [in.]
31-1/4 x 18 x 16
Approx. Boiler Weight
with Water [lbs.]
77
79
86
87
98
Approx. Boiler Water Content
[Gallons]
0.5
0.6
0.7
0.8
1
Electrical Rating
120V/1Ph/60Hz/less than 12A
Notes:
1Listed Input and Output ratings are at minimum vent lengths at an altitude of 0-2000ft. Numbers will be lower with
longer venting and/or altitudes greater than 2000ft.
2Ratings based on standard test procedures prescribed by the U.S. Department of Energy.
3Trinity Tx requires a special venting system, use only vent materials and methods detailed in these instructions.
Wall mounting of unit requires two people to lift the boiler into place. Failure to follow
these instructions may result in property damage or personal injury.
High Altitude Operation
The Trinity is designed to operate at its maximum listed capacity in installations located at 0-2000ft above Sea
Level. Since the density of air decreases as elevation increases, maximum specified capacity should be de-rated
for elevations above 2000 ft [610 m] in accordance with Table 2-2.
Table 2-2 De-rate % for High Altitudes
Elevations
2001 ft [610 m]
3000 ft [914 m]
4000 ft [1219 m]
4500 ft [1372 m]
5000 ft [1524 m]
In Canada1
de-rate by 10%
de-rate by 10%
de-rate by 10%
de-rate by 10%
de-rate % may vary
In USA2
-
de-rate by 4%
de-rate by 8%
de-rate by 8%
de-rate by 12%
Notes:
1Canada: Altitudes between 2000-4500 ft [610-1372 m], de-rate by 10%. Consult local authorities for de-rating
capacities for altitudes above 4500 ft [1372 m].
2USA: De-rate capacity by 4% for every 1000 ft [305 m] over 2000 ft [610 m].
Combustion –At elevations above 2000 feet, the combustion of the boiler must be
checked with a calibrated combustion analyzer to ensure safe and reliable operation. It is
the Installers responsibility to check the combustion and to adjust the combustion in accordance with
Section 9.0. Failure to follow these instructions may result in property damage, serious injury, or death.

Tx Series Installation and Operation Instructions │Trinity Tx
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3.0 BOILER LOCATION
In all cases, the Trinity Tx must be installed indoors in a dry location where the ambient temperature must be
maintained above freezing and below 100F [38C]. All boiler components must be protected from dripping,
spraying water, or rain during operation and servicing. Consider the proximity of system piping, gas and
electrical supply, condensate disposal drain, and proximity to vent termination when determining the best boiler
location.
Water or flood damaged components must be replaced immediately with new factory-
approved components as failure to do so may result in fire, serious injury, or death.
Boiler Area Ventilation Air Openings
If boiler area clearances are less than the recommended clearances specified in Table 3-1, the boiler area must be
ventilated (Exception: if the boiler area/room has a volume of 150 ft3or greater, ventilation of the boiler room is
not required). Each ventilation air opening must meet the minimum requirements of 1 in2per 1000 Btu/hr, but
not less than 100 in2. The lower ventilation opening must be located within 6” of the floor while the upper
opening must be located 6” from the top of the space.
If the "Boiler Area" does not meet the recommended clearances listed in Table 3-1, and if
the boiler area has a volume less than 150 ft3, it is considered a Closet or Alcove. In US/
Canada, PVC vent pipe and fittings shall not be used within the closet or alcove; only
approved CPVC, Polypropylene or Stainless Steel vent pipe and fittings can be used. See Table 4-4 for a list of
approved materials. Under all circumstances, the minimum clearances listed in Table 3-1 must be provided.
Closet Installations
For closet installations it is necessary to provide two ventilation air openings as shown in Figure 3-1, each
providing a minimum area equal to 1 in2per 1000 Btu/hr, but not less than 100 in2and within 6” of the top and
bottom of the closet door. See Table 3-1 for minimum clearances.
Alcove Installations
Alcove installations have the same minimum clearances as closet installations, except the front must be
completely open to the room at a distance no greater than 18” [457 mm] from the front of the boiler and the
room is at least three (3) times the size of the alcove. Provided these conditions are met, the boiler requires no
extra ventilation air openings to the space. See Table 3-1for minimum clearances.
Residential Garage Installations
When installed in a residential garage, mount the boiler a minimum of 18” [457 mm] above the floor. Locate or
protect the boiler so it cannot be damaged by a moving vehicle. Check with your local authorities for other
possible regulations pertaining to the installation of a boiler in a garage.
Wall Mounting Installations
The Tx is provided with integrated wall mounting brackets. Refer to Figure 3-2 for instructions and illustrations
on wall mounting.
Table 3-1 Minimum Clearances for Installation and Service
Model No.
Clearances
Dimensions - inches [mm]
Front
Top
Sides
Back
Bottom
Flue Pipe
Trinity Tx
Minimum
24 [610]1
12 [305]
4 [102]
0
9 [229]
1 [25]
Recommended
36 [914]
24 [610]
12 [305]
0
24 [610]
1 [25]
Notes:
1 6” if surface is removable allowing a minimum of 24” [610 mm] clearance (i.e. closet installation). See Ventilation Air
Opening dimensions in Figure 3-1.
Closet/alcove installations in US and Canada require approved CPVC, Polypropylene or
Stainless Steel vent and air-inlet pipe and fittings (see Table 4-4); PVC is not permitted.
Failure to follow these instructions may result in damage or serious injury.

Trinity Tx│Installation and Operation Instructions Tx Series
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Figure 3-1 Closet Installation, Minimum Clearances
(Non-Combi Model Shown)
Ventilation Air Openings
are not required if the
boiler area meets the
Recommended Clearances
listed in Table 3-1.
Bottom ventilation opening
Max. 6” above floor / bottom
Top ventilation opening
Max. 6” below ceiling / top
Sides = 4”
Front = 6”
(if removable)
Removable surface /
closet door
Ventilation air opening
1in2per 1000 Btu/hr,
min. 100in2
Ventilation air opening
1in2per 1000 Btu/hr,
min. 100in2
Min. 1” clearance for hot
water and vent pipes
Bottom = 9”
Top = 12”

Tx Series Installation and Operation Instructions │Trinity Tx
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Figure 3-2 Wall Mounting Instructions
Leave the Top Wall-mount Bracket (A) intact
and remove the Bottom Wall-mount Bracket
(B) that is attached to the bottom-back of the
appliance. Save mounting hardware for Step 4.
Secure Bottom Bracket (B), removed from the
bottom back of the boiler in Step 1, to a solid
wall using field supplied lag screws (anchors
when mounting to a concrete wall) that are
adequate to support the weight of the appliance
(refer to Table 2-1 Specifications). Ensure the
bracket is level and flush to the wall. Mounting
holes to be on the bottom with flange pointed
upward and angled away from the wall.
Mount the appliance to the wall by aligning the
two wall mount brackets, Top Bracket (A)
with the Bottom bracket (B). Slide the top
bracket fastened to the boiler down over the
wall-mounted bracket until it hooks.
Once the appliance is resting securely on the
wall, attach the L-shaped Bracket (C) to the
underside of the appliance using the mounting
hardware removed in Step 1. Next anchor the
L-shaped Bracket (C) to the wall as shown
using field supplied hardware.
Failure to follow instructions may
result in fire, serious injury, or death.
This unit requires two people to lift it
or damage and injury may result.
Top Bracket (A)
Bottom
Bracket (B)

Bottom
Bracket (B)


L-shaped Bracket (C)
shipped with boiler kit box

Wall
Boiler
Ensure Bracket
(A) fully inserts
into Bracket (B)
(B)
(A)

Trinity Tx│Installation and Operation Instructions Tx Series
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4.0 GENERAL VENTING
The Trinity Tx is certified as a “Category IV” boiler requiring a “Special Venting System” designed for
pressurized venting. The Exhaust Vent must be piped to the outdoors, using the vent materials and rules outlined
in this section. Under no conditions may this unit vent gases into a masonry chimney, unless it is vacant, and
utilizes the approved venting material and rules described in this section.
Vent and Air-inlet are to be piped separately. The Trinity Tx cannot share a common vent
or air-inlet with multiple boilers. Failure to comply will result in serious injury or death.
Direct Vent Installation (Best Practice)
When installed as a Direct Vent boiler the combustion air-inlet must also be piped directly to the outdoors using
the methods described in this section and in accordance with the National Fuel Gas Code, ANSI Z223.1 (U.S.) or
CSA B149.1 (Canada) and local requirements.
Installation Using Indoor Combustion Air
When the installation uses Indoor Combustion Air (i.e. piping is not directly connecting the appliance air-inlet
fitting to the outdoors), the combustion air-inlet is drawn from Indoors or Outdoors via the appliance area using
the methods described in this section and in accordance with the National Fuel Gas Code, ANSI Z223.1 (U.S.) or
CSA B149.1 (Canada) and local requirements.
The boiler shall be located so as not to interfere with proper circulation of combustion,
ventilation, and dilution air.
Make up air requirements for the operation of exhaust fans, kitchen ventilation systems,
clothes dryers, and fireplaces shall be considered in determining the adequacy of a space
to provide combustion air requirements. Failure to ensure adequate make up air to all
appliances may result in personal injury or death.
Indoor Combustion Air - Opening Size and Location: The methods detailed below for determining Opening
Size and Location for accessing indoor combustion air, shall be used when the air infiltration rate is adequate, i.e.
greater than 0.4 ACH (air changes per hour) and when the boiler area and communicating spaces have a
minimum volume of 50 cubic ft per 1000 Btu/hr. If the air infiltration rate is known to be less that 0.4 ACH,
refer to the National Fuel Gas Code for further guidance.
1. Combined spaces on the same story –Each opening shall have a minimum free area of 1 in.2/1000 Btu/hr
of the total input rating of all appliances in the space, but not less than 100 in.2. One opening shall
commence within 12 in. of the top, and one opening shall commence within 12 in. of the bottom, of the
enclosure, see Figure 4-1a. The minimum dimension of air openings shall be not less than 3in.
2. Combined spaces in different stories –The volumes of spaces in different stories shall be considered as
communicating spaces where such spaces are connected by one or more openings in doors or floors having a
total minimum free area of 2 in.2/1000 Btu/hr of total input rating of all appliances.
Outdoor Combustion Air –Opening Size and Location: Outdoor combustion air shall be provided through
opening(s) to the outdoors in accordance with the methods detailed below. The minimum dimension of air
openings shall not be less than 3in.
1. Two Permanent Openings Method –Two permanent openings, one commencing within 12in. of the top,
and one commencing within 12in. of the bottom of the enclosure, shall be provided. The openings shall
communicate directly, or by ducts, with the outdoors or spaces that freely communicate with the outdoors, as
follows:
a. Where communicating with the outdoors or where communicating to the outdoors through vertical ducts,
each opening shall have a minimum free area of 1 in.2/4000 Btu/hr of total input rating of all appliances
in the enclosure; see Figures 4-1b and 4-1c.
b. Where communicating with the outdoors through horizontal ducts, each opening shall have a minimum
free area of 1 in.2/2000 Btu/hr of total input rating of all appliances in the enclosure; see Figure 4-1d.