7.4-i

APPENDIX 7.4. FURNACE FAN CURVES

TABLE OF CONTENTS

7.4.1 GENERAL AIR SPEED AND AIRFLOW RELATIONSHIP ................... 7.4-1

7.4.2 BLOWER FAN CURVES ............................................. 7.4-2

7.4.2.1 Fan Laws ..................................................... 7.4-3

7.4.2.2 Motor Speed .................................................. 7.4-3

7.4.2.3 Shaft Power ................................................... 7.4-4

7.4.2.4 System Effect Factor ............................................ 7.4-4

7.4.3 FAN CURVES FOR GENERIC MODEL FURNACES ....................... 7.4-4

LIST OF TABLES

Table 7.4.1 Coefficients for Static Pressure as a Function of Airflow .................. 7.4-6
7.4-1

APPENDIX 7.4. FURNACE FAN CURVES

Furnace energy consumption includes motor electricity from the motor of the indoor air blower. 

The furnace blower electricity use depends on air flow through the furnace and the pressure rise across

the furnace. A fan curve is a graphical representation of the pressure rise, called static pressure,

compared to the airflow through the fan or blower.

A furnace fan has three operational modes: cooling (when central air conditioning is present),

normal heating, and low-fire heating. This appendix describes the Department’s methods for

determining the generic model furnace fan curves for the cooling operation mode. For the normal

heating or low-fire heating operation, DOE fit the basic model fan curves directly to develop equations

of static pressure versus air flow across the furnace.

Blower manufacturers provide blower fan curves for both static pressure and shaft power as

functions of airflow. The furnace fan curve shows the static pressure compared to airflow through the

furnace. The Department combined the blower fan curves with assumptions about the furnace airflow

and motor performance to derive furnace fan curves for generic model furnaces.

7.4.1 GENERAL AIR SPEED AND AIRFLOW RELATIONSHIP

Blowers are the component inside the furnace that moves the air through the furnace. All the air

that moves through the furnace also goes through the blower. 

Many furnace components, such as the heat exchangers, the inlet and outlet openings, and the

geometry of the enclosure, partially obstruct or restrict the airflow. The decrease in the pressure rise

due to putting a blower into the furnace enclosure is called the system effect factor (SEF). SEF is a

pressure loss which represents the effect of fan inlet restrictions, fan outlet restrictions, or other

conditions influencing fan performance when installed in the system.1 The difference between the blower

pressure and the external static pressure across the furnace at the same airflow is due to the SEF. The

SEF varies as the square of the air velocity.

For any given furnace model, the air velocity at the blower is directly proportional to airflow

through the furnace. Thus, the pressure across the furnace can be calculated as:

Pfurn(Q) = Pblower(Q, N ) − SEF × Q

2
7.4-2

where:

P = furnace static pressure (in.w.g.), furn

P = static pressure across blower alone (in.w.g.), blower

Q = airflow (cfm),

N = motor speed (rpm), and

SEF = system effect factor.

7.4.2 BLOWER FAN CURVES

The Department chose four blowers from Lau Industries, a manufacturer that supplies blowers

to the furnace industry, to match with four virtual model furnace blowers2 (see Chapter 7, section 7.2,

for a discussion of virtual model furnaces). The Department first determined equations for the blower

fan curves. The Department fit third- and fourth-order polynomial equations of air flow to the pressure

and shaft power curves of these blowers. (See Appendix 7.5, Blower Fan Curves, for more details.)

P(Q Ntest) cpc p

Q

, = + ×











 + 0 1

1000

c p

Q

c p

Q

c p

Q

2

1000

2

3

1000

3

4

1000

4

×











 + ×











 + ×













where:

 P = static pressure (in.w.g.),

Ntest = motor speed at the test speed (rpm), and

cp0,cp1,cp2,cp3,cp4 = empirical coefficients.

The Department also determined shaft power for the blower as:

H(Q Ntest ) ch ch

Q

ch

Q

ch

Q

ch

Q

, = + ×











 + ×











 + ×











 + ×











0 1 

1000 21000

2

3

1000

3

4

1000

4

where:

H = shaft power (W), and

ch0,ch1,ch2,ch3,ch4 = empirical coefficients.
7.4-3

7.4.2.1 Fan Laws

Using the relationships between blower speed, airflow, static pressure, and shaft power, DOE

determined1 the equation for the fan curves for speeds other than those at which they were tested. 

These relationships are known as fan laws and can be written as:

( ) ( )

N

N

Q

Q

N

N

P

P

N

N

H

H

1

2

1

2

2

1

2

1

2

3

1

2

1

2

= = =

Using the blower equations and the fan laws, the blower pressure and shaft power can be

determined for any speed and airflow.

P Q N P Q

N test

N

N

Ntest

( , ) = ,











 ×













2

H Q N H Q

N test

N

N

Ntest

( , ) = ,











 ×













3

7.4.2.2 Motor Speed

The permanent split capacitor (PSC) motors used in the baseline furnaces do not operate at

constant speed. The difference between actual operating speed and the synchronous speed of an

induction motor is referred to as slip. For six-pole induction motors, the synchronous speed is 1200

rpm. At the rated speed of these motors of 1075 rpm, so the slip is 125 rpm. 

S = Nsync − N

where:

S = motor slip (rpm),

Nsync = synchronous blower speed (rpm), and

N = motor speed (rpm).

For a broad operating range, the slip on induction motors is proportional to the load. For

blower motors the load is the shaft power of the blower.3

S

S

H

H

1

2

1

2

=
7.4-4

where:

H = shaft power (hp or W).

7.4.2.3 Shaft Power

The shaft power to turn the blower must equal the shaft power produced by the motor, so the

previous equation can be written as:

( )

( )

( )

Hblower Q N Hmotor rated

Nsync N

Srated

, _= ×

−

where:

Hmotor_rated = is the rated motor output, and

Srated = the motor slip at its’ rated output power.

For any airflow, the speed can be adjusted iteratively until the equation is solved. 

7.4.2.4 System Effect Factor

The Department assumed that furnaces are designed so the blower motors operate at rated

power at the nominal maximum air flow with 0.5 in.w.g. static pressure. Following this assumption, the

Department adjusted the speed until the shaft power of the blower (at the nominal maximum airflow)

matched the rated power output of the motor.

Once DOE found the motor speed necessary to produce the nominal maximum airflow through

the furnace at 0.5 in.w.g. external static pressure (Qnom), the SEF was determined as:

( ) ( )

( )

SEF

Pblower Qnom N Pfurn Qnom

Qnom

=

, −

2

7.4.3 FAN CURVES FOR GENERIC MODEL FURNACES

For each airflow, across the full range of airflows for each virtual model furnace, the speed was

then iteratively adjusted until the blower shaft power matched the motor shaft power.

Once the speed was known for each airflow, the external static pressure across the furnace

was calculated as:
7.4-5

P ( ) ( )

furn Q Pblower = Q, N − SEF × Q

2

For each of the four airflow capacities of virtual model furnaces, the Department repeated this

process for several values of airflow to determine motor speed and external static pressures during

cooling operation. The Department fit a polynomial equation of P as a function of Q through these

points to get the fan curve for each airflow capacity of virtual model furnaces. The form of the

equations is:

P ( ) furn Q C C

Q

C

Q

C

Q

= + ×











 + ×











 + ×











0 1 

1000 21000

2

3

1000

3

To develop equations of static pressure across the furnace for normal heating or low-fire

heating operation modes, DOE fit the pressure from the basic model fan curves directly to air flow. 

Table 7.4.1 presents the coefficients for static pressure as a function of airflow for the virtual furnace

models.
7.4-6

Table 7.4.1 Coefficients for Static Pressure as a Function of Airflow 

C0 C1 C2 C3

Cooling

5ton 1.916151 -0.87805 0.317813 -0.11646

4ton 0.631601 1.183158 -0.90841 0.073442

3ton 0.259783 2.2545 -2.11025 0.332181

2ton 1.452571 -1.26789 0.41408 -0.39707

Single-stage heating or high fire 2-stage heating

5ton 1.6533 -1.5622 1.6788 -0.7274

4ton 2.7447 -6.1898 7.4999 -3.1809

3ton 0.0778 2.8833 -2.5288 0

2ton 0.9753 1.0443 -2.9451 0

Low-fire heating

5ton 0.511338 1.356782 -1.0186 0

4ton -0.08841 3.268466 -2.57168 0

3ton -0.56392 5.35246 -5.04481 0

2ton 0.861904 1.106394 -3.14531 0
7.4-7

REFERENCES

1. Air Movement and Control Association International Inc., Fans and Systems, in AMCA

Publication 201-90. 1990: Arlington Heights, IL. 

2. Lau Industries Inc., e-mail from Michael J. Neely, Research and Development Engineer, to Jim

Lutz, personal communication. August 29, 2002.

3. Nadel, S., M. Shepard, S. Greenberg, G. Katz, and A. T. d. Almeida, Energy-Efficient

Motor Systems: A Handbook on Technology, Program, and Policy Opportunities. In

Series on Energy Conservation and Energy Policy, C. Blumstein, Editor. 1992, American

Council for an Energy-Efficient Economy: Washington, DC. p. 76-77.