ASHRAE Journal Supplement - AMCA InMotion - November 2024 - 29

Combining these substitutions with an assumption
of standard air density (which matches CFEI calculation
assumptions), we can rewrite the equation for referencefan
shaft power as:
Hi,ref =
(cfm + 26,500) (Pt + 0.0027)
6,343 × 0.42
The following equation for fan total pressure is not in
ANSI/AMCA Standard 208-18 but is needed to complete
our calculations:
Pt =
cfm
(1,097.8 × πD2/4
)
2 × 0.075
We now have all of the tools we need to rearrange
and simplify the equation for reference-fan shaft
power purely in terms of fan airflow and diameter:
cfm
(cfm + 26,500)
Hi,ref =
((1,097.8 × πD2/4
6,343 × 0.42
)
ηtrans,ref = 0.96 ×(Hi,ref+2.2
Hi,ref
)
0.05
Eq. 5.5
Similarly to what we did with the equation for reference-fan
shaft power, we can simplify the equation for
reference transmission effi ciency as a function of only
fan airfl ow and diameter:
ηtrans,ref= 0.96 ×
(
Ht,ref =
Ht,ref =
0.96×
(
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
cfm
)
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
cfm
6,343 × 0.42
2
)
6,343 × 0.42
2
)
)
+2.2
0.05
)
The fi nal piece of the puzzle involves Equation 5.6 for
reference motor output power (Ht,ref) from ANSI/AMCA
Standard 208-18:
ηtrans,ref
Hi,ref
Eq. 5.6
Using what we have learned to this point, let's rewrite
the equat ion for reference motor output power:
2
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
cfm
)
6,343 × 0.42
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
cfm
)
)
6,343 × 0.42
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2
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
cfm
6,343 × 0.42
2
)
)
+2.2
0.05
)
FEPact =
)
2
)
× 0.075 + 0.0027
Building on our success, we will use Equation 5.5
for reference transmission effi ciency from ANSI/AMCA
Standard 208-18:
A
B
C
D
E
Next, we need to write Equation 5.7 for reference motor
effi ciency using Table 5.1 from ANSI/AMCA Standard
208-18 (Table 3):
ηmtr,ref = A ∙ [log10 (Ht,ref) × 0.7457]4 + B ∙ [log10 (Ht,ref) ×
0.7457]3 + C ∙ [log10 (Ht,ref) × 0.7457]2 + D ∙ [log10 (Ht,ref)
× 0.7457]+ E
Eq. 5.7
Ht,ref<185 kW
(<250 BHP)
-0.003812
0.025834
-0.072577
0.125559
0.850274
Ht,ref≥185 kW
(≥250 BHP)
0.962
TABLE 3. ANSI/AMCA Standard 208-18 Table 5.1,
Reference Motor Effi ciency Coeffi cients.
Combining equations 5.2 and 5.7 and substituting the
longer equation for reference motor effi ciency, we now
have an equation for reference-fan electrical input power
as a function of only fan airfl ow and diameter. The exact
algebra is trivial and left as an exercise for a particularly
enthusiastic reader. The full equation is omitted for
practical purposes, as the substitution of reference motor
effi ciency in combination with the equations above is
exceedingly tedious.
FEPref =
0.96×
(
CFEI =
(cfm + 26,500) ((1097.8 × πD2/4 × 0.075 + 0.0027
6,343 × 0.42
)
We have a few simple equations left:
FEPref
FEPact
where:
FEPact = fan electrical input power, actual
We can rearrange this to come up with:
FEPref
CFEI
Combining this result with earlier equations, we are
able to calculate reference-fan electrical input power
using a manufacturer-reported CFEI value (dependent
2024 AMCA inmot ion 29
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
)
)
)
0.05
× ηmtr,ref
+2.2
× 745.7
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ASHRAE Journal Supplement - AMCA InMotion - November 2024

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