ASHRAE Journal Supplement - AMCA InMotion - November 2024 - 30

on operating speed). When looking at the energy use of
a fan run at 100-percent speed, CFEI100 should be used;
when looking at the energy use of the same fan run at
40-percent speed, CFEI40 should be used. As a result,
we are able to calculate the actual fan electrical input
power of an operating point if given the fan's airfl ow and
diameter and the CFEI of the desired operating point:
0.96×
FEPact =
(
∆Costfan ≤
cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
cfm 2
)
2
)
)
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
6,343 × 0.42
cfm
cfm
)
2
)
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
6,343 × 0.42
CFEI
Calculating Payback
Determining payback is comparably straightforward once
actual fan electrical input power is calculated. Payback
periods vary dramatically, depending on geographic location
(local electricity prices) and manufacturer costs. In
general terms, however, a simple equation can help guide us:
∆FEPact × t
1,000
× Costelectricity
where:
∆Costfan = the difference in cost between gear-driven
and direct-drive motor
∆FEPact = the difference in FEPact between gear-driven
and direct-drive motor
t = time
Rearranging, we get:
× 1,000
(
Costelectricity
∆Costfan
∆FEPact
)
≤ t
Gear-Driven
Fan
Initial cost (USD)
Local energy cost (USD)
CFEI100
CFEI40
Airfl ow 40 percent (cfm)
Airfl ow 100 percent (cfm)
Fan diameter (ft)
Runtime (hours per day)
$4,000
$0.20/kWh
1.06
1.32
100,000
250,000
24
16
TABLE 4. Example fan specifi cations.
30
2024 AMCA inmot ion
Direct-Drive
Fan
$5,000
$0.20/kWh
1.22
1.57
100,000
250,000
24
16
Running at 100-percent speed 16 hours (two eighthour
shifts) a day 220 days a year, our fi ctional directdrive
fan would have a just-under-six-year payback
period over our fictional gear-driven motor. This,
of course, simplifies the financials by assuming a
fi xed electricity cost, no maintenance/failures, and a
calculation purely in today's dollars without regard
to infl ation.
Adding a little complexity, a better approach
would be to assume 100-percent speed during the
hottest fi ve months of the year and 40-percent speed
the remainder of the year. Inserting the diameter,
airfl ow, and CFEI40 numbers from Table 4 into our
formula for ∆FEPact, we get a difference of only 39 W
between the two fans run at 40-percent speed. The
∆Costfan remains $1,000.
We now can introduce a weighted average for energy
consumption based on expected operating speed:
× 1000
(
(
∆Costfan
Costelectricity
)
(5 months × ∆FEPact,100%)+(7 months × ∆FEPact,40%)
12 months
0.20 USD/kWh × 1,000 W/kW
1,000 USD
)
(5 months × 255 W)+(7 months × 39 W)
12 months
38,760 hours ×
1 day
16 hours
×
1 year
220 days
= 38,760 runtime
hours
= 11 years
We have effectively doubled the payback period by
running the fan at slower speeds for most of the year.
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≤ t
)
)
× 745.7
0.05
× ηmtr,ref
+2.2
19,608 hours ×
1 day
16 hours
×
1 year
220 days
= 5.6 years
Table 4 shows specifi cations for a fi ctional fan with a
gear-driven motor and a fi ctional fan with a direct-drive
motor we will use in our calculations.
Inserting the diameter, airfl ow, and CFEI100 numbers
from Table 4 into our formula for ∆FEPact, we get a difference
of 255 W between the two fans. The table also gives
us a ∆Costfan of $1,000.
(
0.20 USD/kWh × 1,000 W/kW
225 W
1,000 USD
)
= 19,608 runtime hours
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ASHRAE Journal Supplement - AMCA InMotion - November 2024

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