One Person's Opinion: The Case For Tchebycheff (November 1999)
The purpose of this article is to prevent any further T&B reports that unknowingly state misleading and incorrect results that always jeopardize the hvac systems' ability to operate safely and as designed.
Cutting Corners Has A CostSome time before 1952, a group of engineers established techniques for measuring airflow in hvac rectangular ducts and round ducts. Those methods were called "equal area" and "log-linear" respectively, and they are still exclusively in use. In the 1970s and 1980s, two separate organizations were established that use these methods in their business of testing and balancing airflow systems. The companies are the American Air Balance Council (AABC) and the National Environmental Balance Bureau (NEBB) and are the only nationally recognized agencies that test and certify airflow measurements.
Then, in 1977, a mathematician named Tchebycheff (pronounced "che-bu'-chef) developed interesting methods for measuring airflow in rectangular and round ducts. His methods became published in the International Organization for Standardization #3966, and those methods are simply called the "log-Tchebycheff" methods.
About 10 years later, the AABC and NEBB adopted and included Tchebycheff's methods into their standards as an option to the equal area method. However, no contracted AABC or NEBB company has ever used the log-Tchebycheff method for rectangular duct; all acknowledge that the result will be different, but those differences are thought to be insignificant.
In January 1998, I discovered two things and confirmed a third:
- The results of the equal area method will always be in error, from -3% to a consistent -7%, all the way up to -25%.
- The log-Tchebycheff method for rectangular ducts will yield correct results.
- The log-Tchebycheff and log-linear methods for round ducts produce the same, correct results.
It is important to address a perceived weakness of using the log-Tchebycheff method for rectangular ducts. It is thought log-Tchebycheff requires significantly more velocity readings and more work than the equal area method. However, with regard to that 1998 research, the sum of the log-Tchebycheff readings is 214, and the sum of the equal area method readings is 209.
The reason the log-Tchebycheff method works is simply because it takes into account the lower air velocity readings along the interior duct wall surfaces and the duct corners, which are then averaged with those higher-velocity readings of the interior. The equal area method only measures and averages the higher air velocity readings of the interior and, consequently, results in an incorrect, higher cfm airflow than actually exists. This is also stated in ANSI/ASHRAE 111-1988 with the same conclusions.
Consequences In The FieldLast year, I built a fan-duct assembly to analyze the established, conventional methods of measuring airflow. The results indicated that the equal area method is flawed and will always result in incorrect airflow.
At the same time, results indicated that the log-Tchebycheff will provide accurate results. The following are some typical problems and facts that will occur when the airflow in rectangular duct is measured and set while using the equal area transverse method.
- The airflow in all systems that have been certified, tested, and balanced to design airflow will always operate with less air than recorded, and no one will know it.
- The operational, field-tested EER of cooling equipment will always be less than specified and consequently will be in violation of the energy code.
- The operational, field-tested COP of hvac equipment will always be less than specified and consequently be in violation of the energy code.
- The operational, field-tested AFUE of oil- and gas-fired burners that are mechanically supplied combustion air will always be less than specified and will be in violation of the energy code. Also, due to complete combustion, there will be carbon of some concentration emitted to the space.
- All manual dampers in ducted systems will always need excessive throttling, wasting energy.
- Duct leakage in metal or fiberglass duct will always be incorrectly reported with an unacceptable operational leakage to 25%.
- Fan efficiency will be less than specified and will always be in violation of the energy code.
- The operational smoke evacuation control systems will always be less than specified and in violation of the code by not meeting the minimum 6-min air change requirement.
- Toilet exhaust systems will be less than specified and will always be in violation of the code.
- Grease exhaust systems will be less than the 1,500 fpm specified and always in violation of the code.
- The outdoor air ventilation makeup air will always be less than specified and in violation of the code. This will directly cause the building to become negatively pressurized, infiltrating unconditioned air into the occupied spaces. The indoor air quality will be susceptible to mold and mildew and be responsible for unacceptable levels of carbon dioxide.
A typical problem is as follows. The design of a rectangular duct is to be 60,000 cfm. The equal area method will field balance the airflow exactly at 60,000 cfm. However, the log-Tchebycheff method would measure the quantity to be 55,000 cfm, which is marginally acceptable at -8.3%. No one is aware that it is not 60,000 cfm, nor are they aware of the magnitude of the error.
A more important example: The design of a rectangular duct is to be 60,000 cfm. The equal area method can be field balanced and set for 55,000 cfm (-8.3%) that is within the acceptable 10% industry standard of tolerance. However, the log-Tchebycheff method will correctly field-measure 50,000 cfm. If anyone knew it was 50,000 cfm (and -16.6% below design), which no one does, it would be unacceptable and rejected.
Another typical certified T&B report of one of my previous projects is as follows, stating a problem that does not exist:
- The air handler #5 of 100% outside air unit at 5,830 cfm is supplying a very good 104% of design airflow directly to the space, but the main duct is transversed by the equal area method to be 125%.
- The air handler #7 of 100% outside air unit at 3,800 cfm is supplying a very good 107% of design airflow directly to the space, but the main duct is transversed by the equal area method to be 119%.
- The exhaust fan #8 of 2,875 cfm is exhausting a very good 98% of design air-flow directly from the space, but the main duct is transversed by the equal area method to be 143%.
- The exhaust fan #10 of 5,830 cfm is exhausting a very good 99% of design airflow directly from the space, but the main duct is transversed by the equal area method to be 156%.
Keep in mind that these same duct systems were pressure-tested during construction and certified by that same T&B contractor as not exceeding 1.5% leakage. The common dilemma about this is, what if the T&B agency transversed the main duct first, set the airflow to what they really believed to be the design quantity, and then actually became predictably short of airflow within the space?
I later reviewed five previous project T&B reports that certified that airflows were within the ±10% industry standard, but they are in fact in excess of that -10% of design and would not have been accepted. The log-Tchebycheff method will yield accurate airflow results.
Despite Success, Little SupportThe professional publications that endorse the log-Tchebycheff method include International Organization for Standardization 3966; AMCA Standard 500-D-98; ANSI/AMCA Standard 210-85; AMCA publication 501-93; ASHRAE 1997 Fundamental Handbook; and ANSI/ ASHRAE Standard 111-88.
To my knowledge, there is only one T&B agency in the U.S. that exclusively uses the log-Tchebycheff method for rectangular duct: HABCO, Inc. (East Aurora, NY). Since implementing the log-Tchebycheff method into our construction documents, there have been no disputes and no claims for additional cost to the project, either during bidding or after the contract is awarded. And since that time, I have not had any post-construction airflow distribution or air pressure problems.
A statement, not easily accepted among my engineering friends, that is an absolute fact is, "the most important professional involved with an hvac project is the AABC and NEBB-certified test and balance agency. My perfectly designed, constructed, and installed system will not work until they are done."