letters to the editor

Engineered Systems, March, 2000

More on Tchebycheff

This article is in reference to "The Case for Tchebycheff" by Ernest MacFerran (November 1999, page 54).

Mr. MacFerran's article brings to light some interesting issues. However, the article contains a number of inaccuracies that need to be addressed.

The article represents the Air Movement and Control Association International, Inc. (AMCA) as exclusively endorsing the logTchebycheff method of determining the number and location of duct traverse points in a rectangular duct in AMCA International's standards and publications. While we appreciate being cited as an authoritative reference, the following corrections are presented to set the record straight.

AMCA Publication 501-93 Application Manual for Air Louvers makes no reference to traverse points in a rectangular duct.

AMCA Standard 500-D -98 Laboratory Methods for Testing Dampers for Rating"does show the log-Tchebycheff method for a rectangular duct in a labora tory setting where the velocity profile of the airstream is fully developed. For round ducts, the log-linear method is given.

ANSI/AMCA Standard 210-85 is Laboratory Methods for Testing Fans for Rating." This standard shows the use of the log-linear method for use with a round duct in some of the test setups. The standard makes no reference to traverse points in a rectangular duct. Airflow measurements through the rectangular cross-section of chambers are accomplished with flow nozzles.

The simple fact of the matter is that AMCA International does not "exclusively endorse" any specific method for determining the number and location of duct traverse points for a Pilot traverse. For AMCA's test standards, AMCA uses methods that have proven to be satisfactorily accurate over the years. These methods include the log-Tchebycheff, log-linear, and equal area.

Some may wonder why AMCA International would not choose to endorse log- Tche bycheff with more enthusiasm, based on the data presented in Mr. MacFerran's article. There are two reasons why we would not. The first reason is that we do not necessatily agree that, when the results of two test methods do not agree, one set of results is "tight" and other set of results is necessatily "wrong." It is entirely possible, that both sets of results are "wrong."

The second reason is that underlying the logTchebycheff method is the assumption that the velocity profile of the airstream flowing through a rectangular duct "well-behaved" and has the familiar "D" shape of a fully developed airstream. For ducts below 24 [ft.sup.2], the logTchebycheff method may require too few measurement points. Therefore, if the original assumption that the velocity profile is "well-behaved" and has the familiar "D" shape is incorrect, and also the number of traverse points is insufficient, the test results will surely suffer.

The results presented by Mr. MacFerran are based on a 16-point equal area traverse versus a traverse made using traverse points determined per log-Tchebycheff. We agree that the 16-point traverse is inadequate with respect to the number of points; more points would undoubtedly have resulted in better test results for the equal area traverse. To show the relative merits of either method, in this case, would require that the results of BOTH the equal area traverse and the log-Tchefbycheff traverse be compared against a known contract airflow, such as might be obtained by flow nozzle(s) in a laboratory environment.

AMCA International obviously has no quarrel with the idea that use of the logTchebycheff method results in an adequate number and location of traverse points in a rectangular duct, given that the airstream has a well-behaved velocity profile. But we believe that Mr. MacFerran has jumped to conclusions in the presentation of both his data and his arguments.

For field-testing, both AMCA Publication 203-90 Field Performance Measurement of Fan Systems and AMCA Standard 803-87 Industrial Process/Power Plant Fans: Site Performance Test Standard make recommendations with respect to the number and location of duct traverse points. For a round duct, the log-linear method is recommended. For a rectangular duct, a modified equal area method is recommended: a minimum of 24 points are required for a rectangular duct having a crosssectional area of 24 [ft.sup.2] or less, down to a duct area of 10[ft.sup.2]. ASHRAE's recommendation in its 1997 Handbook Fundamentals is consistent with this prescription. AMCA 803-87 and Publication 203-90 specify no additional lower limit with respect to duct size or area. (It should also be remembered that, as duct size increases, low air velocity along the duct walls has an increasingly smaller effect on the average air velocity through the duct. The resulting accuracies of the three methods then tend to converge, given that an adequate numb er of traverse locations are used.) AMCA Standard 803-87 also imposes strict limits on the quality of the velocity profile across a plane of measurement.

Most fan service technicians and fan engineers who conduct field tests will err towards an excess number of test points rather than too few. Where log-Tchebycheff might specify nine points for a duct 15 in. by 15 in., it would not be uncommon for a fan engineer to use up to 25 points based on the modified equal area method. Further, the velocity profile of the airstream would be checked at the outset to determine whether the airflow profile is stable enough to permit an accurate determination of airflow before the method for determining the number/location of traverse points is even considered.