ASTM F558-21

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F558 − 18 F558 − 21 An American National Standard
Standard Test Method for
Measuring Air Performance Characteristics of Vacuum
Cleaners
This standard is issued under the fixed designation F558; the number immediately following the designation indicates the year of original
adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript
epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This test method covers procedures for determining air performance characteristics of commercial and household upright,
canister, stick, hand-held, utility, and combination-type vacuum cleaners having provisions for attaching a hose and incorporating
a series universal motor. This test method can be applied to the carpet cleaning mode of operation.
1.2 These tests and calculations include determination of suction, airflow, air power, maximum air power, and input power under
standard operating conditions (see Note 1). The nozzle mounted on plenum testing is an ideal air performance measurement and
is not intended to represent the actual air performance during carpet or floor cleaning.
NOTE 1—For more information on air performance characteristics, see Refs (1-6).
1.3 The foot-pound-inch system of units is used in this standard. The values in parentheses are given for information only.
1.4 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all
of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate
safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. A specific
precautionary statement is given in Note 2.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E1 Specification for ASTM Liquid-in-Glass Thermometers
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
E2251 Specification for Liquid-in-Glass ASTM Thermometers with Low-Hazard Precision Liquids
F431 Specification for Air Performance Measurement Plenum Chamber for Vacuum Cleaners
2.2 AMCA Standard:
210-85 Laboratory Methods of Testing Fans for Rating
This test method is under the jurisdiction of ASTM Committee F11 on Vacuum Cleaners and is the direct responsibility of Subcommittee F11.22 on Air Performance.
Current edition approved Oct. 1, 2018Feb. 1, 2021. Published October 2018February 2021. Originally approved in 1978. Last previous edition approved in 20172018 as
F558 – 17a.F558 – 18. DOI: 10.1520/F0558-18.10.1520/F0558-21.
The boldface numbers in parentheses refer to the list of references appended to this test method.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Available from Air Movement and Control Association, 30 West University Dr., Arlington Heights, IL, 60004.60004, http://www.amca.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F558 − 21
2.3 IEC Standard:
IEC 62885-2 Surface Cleaning Appliances – Part 2: Dry Vacuum Cleaners for Household or Similar Use – Methods for
Measuring the Performance
3. Terminology
3.1 Definitions:
3.1.1 air power, AP, W, n—in a vacuum cleaner, the net time rate of work performed by an air stream while expending energy to
produce an airflow by a vacuum cleaner under specified air resistance conditions.
3.1.2 automatic bleed valve, n—any device a part of a vacuum cleaner’s design which automatically introduces an intentional leak
within the vacuum cleaner’s system when manufacturer specified conditions are met.
3.1.3 corrected airflow, Q, cfm, n—in a vacuum cleaner, the volume of air movement per unit of time under standard atmospheric
conditions.
3.1.4 input power, W, n—the rate at which electrical energy is absorbed by a vacuum cleaner.
3.1.5 model, n—the designation of a group of vacuum cleaners having the same mechanical and electrical construction with only
cosmetic or nonfunctional differences.
3.1.6 population, n—the total of all units of a particular model vacuum cleaner being tested.
3.1.7 repeatability limit (r), n—the value below which the absolute difference between two individual test results obtained under
repeatability condition may be expected to occur with a probability of approximately 0.95 (95 %).
3.1.8 repeatability standard deviation (S ), n—the standard deviation of test results obtained under repeatability conditions.
r
3.1.9 reproducibility limit (R), n—the value below which the absolute difference between two test results obtained under
reproducibility conditions may be expected to occur with a probability of approximately 0.95 (95 %).
3.1.10 reproducibility standard deviation (S ), n—the standard deviation of test results obtained under reproducibility conditions.
R
3.1.11 sample, n—a group of vacuum cleaners taken from a large collection of vacuum cleaners of one particular model which
serves to provide information that may be used as a basis for making a decision concerning the larger collection.
3 3 3
3.1.12 standard air density, ρ , lb/ft , n—atmospheric air density of 0.075 lb/ft (1.2014 Kg/m ).
std
3.1.12.1 Discussion—
This value of air density corresponds to atmospheric air at a temperature of 68°F (20°C),68 °F (20 °C), 14.696 psi (101.325 kPa),
and approximately 30 % relative humidity.
3.1.13 suction, inch of water, n—in a vacuum cleaner, the absolute difference between ambient and subatmospheric pressure.
3.1.14 test run, n—the definitive procedure that produces the singular result of calculated maximum air power.
3.1.15 test station pressure, B , inch of mercury,n—for a vacuum cleaner, the absolute barometric pressure at the test location
t
(elevation) and test time.
3.1.15.1 Discussion—
It is not the equivalent mean sea level value of barometric pressure typically reported by the airport and weather bureaus. It is
sometimes referred to as the uncorrected barometric pressure (that is, not corrected to the mean sea level equivalent value). Refer
to 5.5 for additional information.
Available from the IEC Web store, webstore.iec.ch, or American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036.10036,
http://www.ansi.org.
F558 − 21
3.1.16 unit, n—a single vacuum cleaner of the model being tested.
4. Significance and Use
4.1 The test results allow the comparison of the maximum potential air power available for cleaning tasks when tested under the
conditions of this test method. The test results do not indicate the actual air power present during the cleaning process due to the
effects of the various tools in use and surfaces being cleaned. During the nozzle on plenum chamber air performance testing, the
brushroll is unloaded and this condition is not representative of the brushroll being in contact with carpet or other surfaces being
cleaned.
5. Apparatus
5.1 Plenum Chamber—See Specification F431 or IEC 62885-2, Section 5.8.3.
5.2 Water Manometers, or equivalent instruments. One to measure from 0 to 6 in. (152.4 mm) in increments of 0.01 in. (0.254
mm), and one with increments of 0.1 in. (2.54 mm) for use in making measurements above 6 in. (152.4 mm). A single instrument
having a resolution of 0.01 in. (0.254 mm) over the entire required range may be used instead of two separate instruments.
5.3 Wattmeter, to provide measurements accurate to within 61 %.
5.4 Voltmeter, to provide measurements accurate to within 61 %.
5.5 Barometer, with an accuracy of 60.05 in. of mercury (1.27 mm of mercury), capable of measuring and displaying absolute
barometric pressure, scale divisions 0.02 in. (0.51 mm) or finer.
5.5.1 Mercury barometers, in general, measure and display the absolute barometric pressure. Some corrections may be needed for
temperature and gravity. Consult the owner’s manual.
5.5.2 When purchasing an aneroid or electronic barometer, be sure to purchase one which displays the absolute barometric
pressure, not the mean sea level equivalent barometric pressure value. These types of barometers generally have temperature
compensation built into them and do not need to be corrected for gravity.
5.6 Sharp-Edge Orifice Plates—See specifications in Specification F431.
5.7 Thermometer—Solid-stem, ambient thermometer having a range from 1818 °F to 89°F89 °F (or –8–8 °C to +32°C)+32 °C)
with graduations in 0.2°F (0.1°C),0.2 °F (0.1 °C), conforming to the requirements for thermometer 63°F (17.2°C)63 °F (17.2 °C)
as prescribed in Specification E1. As an alternative, thermometers S63F or S63C, as prescribed in Specification E2251, may be
used. In addition, thermometric devices such as resistance temperature detectors (RTDs), thermistors or thermocouples of equal
or better accuracy may be used.
5.8 Psychrometer—Thermometers graduated in 0.2°F (0.1°C).0.2 °F (0.1 °C).
5.9 Voltage-Regulator System, to control the input voltage to the vacuum cleaner. The regulator system shall be capable of
maintaining the vacuum cleaner’s rated voltage 61 % and rated frequency having a wave form that is essentially sinusoidal with
3 % maximum harmonic distortion for the duration of the test.
6. Sampling
6.1 A minimum of three units of the same model vacuum cleaner, selected at random in accordance with good statistical practice,
shall constitute the population sample.
6.1.1 To determine the best estimate of maximum air power for the population of the vacuum cleaner model being tested, the
arithmetic mean of the maximum air power of the sample from the population shall be established by testing it to a 90 % confidence
level within 65 %.
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6.1.2 Annex A2 provides a procedural example for determining the 90 % confidence level and when the sample size shall be
increased (see Note 2).
NOTE 2—See Annex A2 for method of determining 90 % confidence level.
7. Test Vacuum Cleaners
7.1 New Test Vacuum Cleaners:
7.1.1 Preconditioning a New Test Vacuum Cleaner—Run the vacuum cleaner in at rated voltage 61 % and rated frequency with
filters in place.
7.1.1.1 Preconditioning a Rotating Agitator Type Vacuum Cleaner—In a stationary position, operate the vacuum cleaner for 1 h
with the agitator bristles not engaged on any surface.
7.1.1.2 Preconditioning a Straight-Air Canister Vacuum Cleaner—Operate the vacuum cleaner for 1 h with a wide-open inlet
(without hose).
7.2 Used Test Vacuum Cleaners:
7.2.1 Recondition a used test vacuum cleaner; prior to the initial test run as follows:
7.2.1.1 Thoroughly remove excess dirt from the vacuum cleaner. Without using tools for disassembly, clean the entire outer
surface, brushes, nozzle chamber, ductwork, inside of the chamber surrounding the primary filter, and inside hose and wands.
7.2.1.2 For vacuum cleaners using disposable filters as the primary filters, use a new disposable primary filter from the
manufacturer for each test. Install it as recommended by the vacuum cleaner manufacturer.
7.2.1.3 For vacuum cleaners using water as the primary filter, empty the receptacle and refill as recommended by the manufacturer.
7.2.1.4 For vacuum cleaners using non-disposable dirt receptacles, empty in accordance with the manufacturer’s instructions and
clean the receptacle until its weight is within 0.07 oz (2 g) of its original weight and install it as recommended by the vacuum
cleaner manufacturer.
NOTE 3—It is preferable to conduct this test method on new test vacuum cleaners prior to any other ASTM test methods to avoid contamination that could
cause performance variations.
7.3 Test Vacuum Cleaner Settings—If various settings are provided, set the motor speed setting or suction regulator using the
manufacturer’s specifications as provided in the instruction manual for normal operation. If a different setting is used, make a note
of the deviation in the test report.
8. Procedure
8.1 Preparation for Test:
8.1.1 Prepare the test vacuum cleaner(s) in accordance with Section 7.
8.1.2 Set the manometers to zero and check all instruments for proper operation.
8.1.3 Record the test station pressure and the dry-bulb and wet-bulb temperature readings within 6 ft (1.8 m) of the test area. Read
the barometric pressure to the nearest 0.02 in. of mercury (0.51 mm of mercury), and the dry-bulb and wet-bulb temperatures to
the nearest 0.2°F0.2 °F (or 0.1°C)0.1 °C)
8.1.3.1 The test area shall be free of major fluctuating temperature conditions due to air conditioners or air drafts that would be
indicated by a thermometer at the immediate test area.
8.1.4 Connect a manometer or equivalent instrument to the plenum chamber.
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8.1.5 Connect a power analyzer.
8.2 Setup—Attachment Hose:
8.2.1 Connect the hose assembly to the plenum chamber hose adapter and seal only this connection. See Fig. 1.
8.2.1.1 The end of the hose assembly should be inserted inside the hose connector adapter and be perpendicular to the plenum
chamber.
8.2.1.2 The end of the hose assembly shall not project into the plenum chamber.
8.2.2 The hose should be supported and kept straight and horizontal. Maintain the vacuum cleaner in its normal operating
orientation. If the hose is not intended to enter the vacuum cleaner horizontally, gradually bend the hose with a single bend from
the intake port to the plenum chamber. Any restraining method should allow the hose coupling to seal at the cleaner. See Fig. 2.
8.3 Test Setup—Carpet Cleaning Mode:
8.3.1 Mount the cleaner plate as shown in Fig. 1e of Specification F431 to the plenum chamber.
8.3.2 Make an adapter by any convenient method which adapts the test vacuum cleaner’s nozzle opening to the opening in the
cleaner plate.
8.3.3 Maintain the largest cross-sectional area possible throughout the adapter. This will prevent impeding the airflow between the
plenum chamber and the test vacuum cleaner’s nozzle.
8.3.4 It is recommended that the hole for the adapter/plenum chamber interface be located as close, if not directly below, the dirt
pickup duct for the test vacuum cleaner’s nozzle.
8.3.5 The interface between the adapter and the test vacuum cleaner’s nozzle is to be airtight. This may be achieved by any
convenient means.
8.3.6 If the vacuum cleaner incorporates edge cleaning slots along the side edge(s), or slots along the front and rear edge of the
bottom plate, or both, these slots should be sealed by any convenient means such as clay, tape, and so forth.
8.3.7 Do not eliminate leaks resulting from test vacuum cleaner’s construction, except at the adapter/nozzle interface as described
above.
8.3.8 An example of an adapter is shown in Fig. 3. This adapter uses a closed-cell foam gasket material or molded low durometer
urethane material shaped to fit the contour of the test cleaner’s nozzle opening with sufficient surface area for sealing.
8.3.9 Attach the nozzle adapter to the plenum chamber’s cleaner plate, taking care to center the adapter’s opening over the hole
in the cleaner plate.
FIG. 1 Diagram of Hose and Adapter Connection
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FIG. 2 Schematic for Air Performance Test
8.3.10 The interface between the adapter and the plenum chamber should be airtight. The use of foam, clay, tape, or any other
convenient means may be used to make this interface airtight.
8.3.11 Mount the test vacuum cleaner to the nozzle adapter by any convenient means.
8.3.12 The test vacuum cleaner, when mounted to the plenum chamber, should be set on the plenum chamber/adapter in the user
position. If needed, the test vacuum cleaner’s rear wheels should be supported to keep the cleaner’s foot parallel with the plenum
chamber’s surface.
8.3.13 For test cleaners incorporating a pivoting handle, support the test vacuum cleaner’s handle at 31.5 in. (800 mm) above the
nozzle/adapter surface.
8.3.14 For those vacuum cleaners which have a non-pivoting handle, support the test vacuum cleaner’s handle at a height such
that the cleaner’s nozzle is parallel to the surface of the nozzle adapter.
8.3.15 Secure the test vacuum cleaner to the plenum chamber to prevent the test vacuum from possibly moving and breaking the
airtight seal during the test.
8.3.16 If the vacuum cleaner has a brush roll or other mechanism for agitating the floor surface during cleaning, it shall be
activated for the duration of the test.
8.4 Test Procedure:
8.4.1 Any automatic bleed valve which affects the air performance of the vacuum cleaner shall not be defeated.
8.4.2 Operate the vacuum cleaner with no orifice plate inserted in the plenum chamber inlet at nameplate rated voltage 61 % and
frequency 61 Hz prior to the start of the test run to allow the unit to reach its normal operating temperature. For vacuum cleaners
with dual nameplate voltage ratings, conduct testing at the highest voltage. Do this before each test run.
8.4.3 The vacuum cleaner is to be operated at its nameplate rated voltage 61 % and frequency 61 Hz throughout the test. For
vacuum cleaners with dual nameplate voltage ratings, conduct the test at the highest voltage.
8.4.3.1 Allow the vacuum cleaner to operate at the open orifice for 11 min to 2 min between test runs.
8.4.4 While operating the vacuum cleaner per 8.4.3, insert orifice plates sequentially into the orifice plate holder of the plenum
chamber starting with the largest size orifice and following it with the next smaller orifice plate. Use the following orifice plates:
2.000, 1.500, 1.250, 1.000, 0.875, 0.750, 0.625, 0.500, 0.375, 0.250, and 0 in. (50.8, 38.1, 31.7, 25.4, 22.2, 19.0, 15.8, 12.7, 9.5,
and 6.3 mm). The following optional orifice plates may also be used: 2.500, 2.250, 1.750, 1.375, and 1.125 in. (63.5, 57.2, 44.5,
34.9, and 28.6 mm).
8.4.5 For each orifice plate, record the suction, h, and input power, P, in that order. All readings should be taken within 10 s of
the orifice insertion. Allow the vacuum cleaner to operate at the open orifice for 15 seconds minimum before inserting the next
orifice.
8.4.5.1 Read the suction to the nearest graduation of the instrument. Readings should be taken as soon as the manometer reaches
a true peak. (When using a fluid type manometer, the liquid level may peak, drop, and peak again. The second peak is the true
F558 − 21
FIG. 3 Nozzle Adapter
peak reading. A person conducting the test for the first time shall observe at least one run before recording data. See Specification
F431 for instructions on how to minimize the overshoot (first peak) of the liquid level.)
9. Calculation
9.1 Correction of Data to Standard Conditions:
9.1.1 Air Density Ratio—The density ratio, D , is the ratio of the air density at the time of test ρ , to the standard air density,
r test
3 3 3
ρ = 0.075 lb/ft (1.2014 kg/m ). It is used to correct the vacuum and wattage readings to standard conditions. Find ρ (lb/ft
std test
or kg/m ) from standard psychometric charts or ASHRAE tables and calculate D as follows:
r
ρ
test
D 5 (1)
r
ρ
std
FIG. 4 Vacuum Cleaner Test Arrangement
F558 − 21
where:
ρ = the air density at the time of test, lb/ft , and
test
3 3
ρ = the standard air density, 0.075 lb/ft (1.2014 kg/m ).
std
9.1.1.1 As an alternative, the following equation is intended to be used for correcting ambient conditions where the barometric
pressure exceeds 27 in mercury and the dry-bulb and wet-bulb temperatures are less than 100°F (37.8°C);100 °F (37.8 °C); and
may be used as an alternate method of calculating D (see Appendix X1 for derivation and accuracy analysis).
r
[17.68 B – 0.001978 T + 0.1064 T
t w w
D =
r
+ 0.0024575 B (T – T ) – 2.741]
t d w
T + 459.7
d
where:
B = test station pressure at time of test, in. of mercury,
t
T = dry-bulb temperature at time of test, °F, and
d
T = wet-bulb temperature at time of test, °F.
w
9.1.2 Corrected Suction—Corrected suction, h , is the manometer reading, h, times the correction factor, C as follows:
s s
h 5 C h (2)
s s
9.1.2.1 For series universal motors (see Ref (6)) the correction factor, C , is calculated as follows:
s
C 5 110.667 12 D (3)
~ !
s r
9.1.2.2 This test method does not have any formulas available for correcting input power for any other type of motor (permanent
magnet, induction, etc.).
9.1.3 Corrected Input Power—Corrected input power, P , expressed in watts, is the wattmeter reading, P, times the correction
s
factor, C , as follows:
p
P 5 C P (4)
s p
9.1.3.1 For series universal motors the correction factor, C , is calculated as follows:
p
C 5 110.5 12 D (5)
~ !
p r
9.1.3.2 This test method does not have any formulas available for correcting input power for any other types of motor (permanent
magnet, induction, etc.)
9.2 Corrected Airflow—Calculate the corrected airflow, Q, expressed in cubic feet per minute (see Note 4 and Appendix X2) as
follows:
=
Q 5 21.844D K h (6)
1 s
where:
Q = corrected flow, cfm,
D = orifice diameter, in.,
K = constant (dimensionless), orifice flow coefficients for orifices in the plenum chamber. See Table 1 for values for each
orifice. See Ref (1) for the derivation of these flow coefficients.
h = corrected suction, in. of water.
s
NOTE 4—For the corrected airflow expressed in liters per second, use the following equation:
Q 5 10.309 D K =h
1 s
F558 − 21
TABLE 1 Orifice Flow Coefficient Equations (K )
NOTE 1—K was determined experimentally using an ASTM plenum
chamber (see Specification F431) and an ASME flowmeter (see Ref (1)).
NOTE 2—Equations for K in terms of B and h are given in Appendix
1 t
X6.
A
Orifice Diameter, in. (mm) Orifice Flow Coefficient Equation
0.5575r20.5955
0.250 (6.3)
K 5
r21.0468
0.5553r20.5754
0.375 (9.5)
K 5
r21.0263
0.5694r20.5786
0.500 (12.7)
K 5
r21.0138
0.5692r20.5767
0.625 (15.8)
K 5
r21.0104
0.5715r20.5807
0.750 (19.0)
K 5
r21.0138
0.5740r20.5841
0.875 (22.2)
K 5
r21.0158
0.5687r20.5785
1.000 (25.4)
K 5
r21.0146
0.5675r20.5819
1.125 (28.6)
K 5
r21.0225
0.5717r20.5814
1.250 (31.7)
K 5
r21.0152
0.5680r20.5826
1.375 (34.9)
K 5
r21.0235
0.5719r20.5820
1.500 (38.1)
K 5
r21.0165
0.5695r20.5839
1.750 (44.5)
K 5
r21.0235
0.5757r20.5853
2.000 (50.8)
K 5
r21.0157
0.5709r20.5878
2.250 (57.2)
K 5
r21.0279
0.5660r20.59024
2.500 (63.5)
K 5
r21.0400
A
B 0.4912 2h 0.03607
s d s d
t
r 5
B 0.4912
s d
t
where:
B = test station pressure at time of test, in. of mercury, and
t
h = uncorrected suction (manometer reading), in. of water.
TABLE 2 Repeatability and Reproducibility
Test Type Coefficient of Repeatability Coefficient of Reproducibility
Variation, Limit, Variation, Limit,
CV % r CV % R
r R
End of Hose 2.190 6.132 6.533 18.292
Nozzle 4.795 13.426 19.265 53.942
where:
Q = corrected flow, L/s,
D = orifice diameter, m,
K = constant (dimensionless), and
h = corrected suction, Pa.
s
9.3 Air Power—Calculate the air power, AP, in watts, as follows:
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AP 5 0.117354 Q h (7)
~ !~ !
s
where:
AP = air power, W,
Q = corrected flow, cfm, and
h = corrected suction, inch of water.
s
NOTE 5—See Appendix X3 for derivation.
9.4 Maximum Air Power—Determine the maximum air power using the method in Annex A1.
10. Report
10.1 For each vacuum cleaner sample from the population being tested, report the following information:
10.1.1 Manufacturer’s name and product model name or number, or both.
10.1.2 Type of cleaner; that is, upright, canister, etc.
10.1.3 The corrected input power, corrected vacuum, corrected airflow, and air power for each orifice used.
10.1.4 Measured or calculated maximum air power, whichever is greater.
10.1.5 Indicate the method of testing, end of hose or nozzle on plenum.
11. Precision and Bias
11.1 The following precision statements are based on interlaboratory tests involving eight laboratories and four units.
11.2 The statistics have been calculated as recommended in Practice E691.
11.3 The following statements regarding repeatability limit and reproducibility limit are used as directed in Practice E177.
11.4 The End of Hose Coefficients of Variation of repeatability and reproducibility of the measured results have been derived from
nine sets of data, where each of two sets have been performed by a single analyst within each of the eight laboratories on separate
days using the same test unit.
11.5 The Nozzle Coefficients of Variation of repeatability and reproducibility of the measured results have been derived from
seven sets of data, where each of two sets have been performed by a single analyst within each of the seven laboratories on separate
days using the same test unit.
11.6 Repeatability (Single Operator and Laboratory, Multiday Testing)—The ability of a single analyst to repeat the test within
a single laboratory.
11.6.1 The expected coefficient of variation of the measured results within a laboratory, CV % , has been found to be the respective
r
values listed in Table 2.
11.6.2 The 95 % repeatability limit within a laboratory, r, has been found to be the respective values listed in Table 2, where r
= 2.8 (CV % ).
r
11.6.3 With 95 % confidence, it can be stated that within a laboratory a set of measured results derived from testing a unit should
be considered suspect if the difference between any two of the three values is greater than the respective value of the repeatability
limit, r, listed in Table 2.
Complete data on the round-robin test is available from ASTM Headquarters. Request RR:F11-1010. Contact ASTM Customer Service at service@astm.org.
F558 − 21
11.6.4 If the absolute value of the difference of any pair of measured results from three test runs performed within a single
laboratory is not equal to or less than the respective repeatability limit listed in Table 2, that set of results shall be considered
suspect.
11.7 Reproducibility (Multiday Testing and Single Operator Within Multilaboratories)—The ability to repeat the test within
multiple laboratories.
11.7.1 The expected coefficient of variation of reproducibility of the average of a set of measured results between multiple
laboratories, CV % , has been found to be the respective values listed in Table 2.
R
11.7.2 The 95 % reproducibility limit within a laboratory, R, has been found to be the respective values listed in Table 2, where
R = 2.8 (CV % ).
R
11.7.3 With 95 % confidence, it can be stated that the average of the measured results from a set of three test runs performed in
one laboratory, as compared to a second laboratory, should be considered suspect if the difference between those two values is
greater than the respective values of the reproducibility limit, R, listed in Table 2.
11.7.4 If the absolute value of the difference between the average of the measured results from the two laboratories is not equal
to or less than the respective reproducibility limit listed in Table 2, the set of results from both laboratories shall be considered
suspect.
11.8 Bias—No justifiable statement can be made on the accuracy of this test method for testing the properties listed. The true
values of the properties cannot be established by acceptable referee methods.
12. Keywords
12.1 airflow; air performance; air power; suction; suction power; vacuum cleaner
ANNEXES
(Mandatory Information)
A1. MATHEMATICAL METHOD FOR DETERMINING MAXIMUM AIR POWER POINT
A1.1 The following, second degree polynomial equation, is assumed to provide the best mathematical approximation of the air
power versus airflow relationship.
NOTE A1.1—See Ref (4) for additional information.
Y 5 A 1A X1A X (A1.1)
1 2 3
where:
Y = air power (AP),
X = airflow (Q), and
A , A , andA , = arbitrary constants.
1 2 3
A1.1.1 Use X and Y values obtained from only five specific orifices selected as follows:
A1.1.1.1 Using the test data, determine the orifice size that produced the highest air power value.
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A1.1.1.2 Use the air power and airflow values at this orifice, and the next two smaller and the next two larger orifices in the
following computations:
A1.1.1.3 If the highest air power value calculated from the observed data is at the 2.0 in. (50.8 mm) orifice or larger, then use the
air power and airflow values from the five largest orifices.
A1.2 To determine the values of A , A , and A , use the X and Y values obtained from the five specified orifices and solve the
1 2 3
following set of normalized equations:
Y 5 NA 1A X 1A X (A1.2)
( i 1 2 ( i 3 ( i
2 3
X Y 5 A X 1A X 1A X (A1.3)
( i i 1 ( i 2 ( i 3 ( i
2 2 3 4
X Y 5 A X 1A X 1A X (A1.4)
( i i 1 ( i 2 ( i 3 ( i
where:
N = 5 (number of orifices selected),
i = 1 to N, and
X and Y = the values obtained during testing (X Y , X Y , . . . X Y ) at the five orifices specified in A1.1.1.
i i 1 1 2 2 N N
A1.3 Setting the derivative of Eq A1.1 equal to zero and solving for X will determine the value of X where Y is at its maximum
m
value f(Y ) as follows:
max
dy d
5 A 1A X1A X 5 0 (A1.5)
@ #
1 2 3
dx dx
dy
5 A 12A X 5 0
2 3
dx
Substitute X as the value of X at Y and solve for X :
m max m
A
X 52 (A1.6)
m
2A
Substituting this value of X , and A , A , and A , into A1.1 will determine the value of Y (AP ) as follows:
m 1 2 3 max max
Y 5 A 1A X 1A X (A1.7)
max 1 2 m 3 m
A1.4 Calculate the goodness of fit, R (correlation coefficient) as follows:
Y 2 Y
~ !
( i OBS i CAL
R 5 12 (A1.8)
Y 2 Y
~ !
( i OBS OBS
where:
Y 5 A 1A X 1A X (A1.9)
i CAL 1 2 i OBS 3 i OBS
and:
Y 5 Y (A1.10)
OBS ( i OBS
N
and:
i = 1 to N orifices used in 8.2,
OBS = observed data,
CAL = calculated data, and
F558 − 21
Y = is the air power (AP) obtained from the calculations in 9.3 for the corresponding value X (airflow, Q) at any of
i OBS iOBS
the N orifices selected.
A1.4.1 If R is not greater than or equal to 0.900, the test must be performed again and the new set of data shall be used. If after
repeating the test, the R value is still less than 0.9, the maximum measured or calculated value shall be reported.
A2. DETERMINATION OF 90 % CONFIDENCE INTERVAL
A2.1 Theory:
A2.1.1 The most common and ordinarily the best estimate of the population mean, μ, is simply the arithmetic mean, x¯, of the
individual scores (measurements) of the units comprising a sample taken from the population. The average score of these units will
seldom be exactly the same as t
...