The situation clearly called for serious air-handling technology. I had been impressed by a floor fan I had seen at a local dance hall, and purchased one for the club's use. This fan did improve matters somewhat in our dance/sauna room but not as much as I expected. I investigated the matter further, and after a few measurements I sent the following letter to the fan's manufacturer (names have been removed to protect the guilty).
Dear Sir or Madam:
I purchased one of your floor fans this Summer to ventilate a dance hall. I had estimated the volume of air circulation required, and selected your 12,500 cfm model (Whole House fan, Model TG-1887W 120 V 60 Hz 270 W 2.6 A serial number 93-TG4-002713) on that basis. The fan was helpful in cooling the room, but it did not provide as much cooling as I had estimated. This prompted me to attempt to measure the airflow generated by the fan directly (all the comments which follow refer to the "high" speed setting.)
I have measured air velocity about 5 cm from the face of the fan and this velocity is plotted as a function of radial distance from the fan center on the enclosed graph. From this data a number of values may be calculated, including the air flow volume (1.0 cubic meters per second), reaction force or thrust (8.6 N) and air kinetic energy/sec (40 watts). This measurement is disturbing since the measured air flow is considerably less than the advertised value of 12,500 cfm (5.9 cubic meters/second). However, I have independently measured the fan thrust at 9.5 N which is in agreement within 10% of the value calculated from my velocity data. I also measured the electrical current consumed by the fan to be 2.6 A as specified. For the stated 270 W electric power, the overall efficiency [air kinetic/electric] is then 15% which is what might be expected for a typical consumer motor and fan blade design. I conclude that my measurements are approximately correct and the actual fan performance is 1/6 of the advertised value.
It might also be pointed out that, given only the diameter of the blades on this fan (18" = 46 cm) and the power used (270 W), it is fundamentally impossible to achieve the stated air flow of 5.9 cubic meters per second. If the air velocity is uniform across the cross-section (unrealistic, but the minimum-power requirement case), a velocity of 36 m/s (80 mph) is required to achieve 5.9 cubic meters/sec. This becomes absurd when the implications are considered. The power in such an air flow is 4.6 kW, which is 17 times as much (!) as the fan uses. At the existing 15% efficiency of your fan design, 30 kW of electrical energy would be required. This hypothetical fan would also be quite dangerous as it hops around the room, since the reaction force of 255 N (57 pounds-thrust) is roughly four times the fan's weight.
If we work in the other direction and assume the fan motor and blade are both 100% efficient, we obtain 14 m/s flow, which corresponds to 2.3 cubic meters per second, still less than half the quoted value. With the existing 270 W motor and fan blade design with 15% overall efficiency, a fan blade diameter of 1.5 meters (4' 11") would be required for 5.9 cubic meters/s (12,500 cfm).
I would appreciate hearing from you in detail how you measured the air movement capacity of this fan. Thank you very much.
I mailed the letter and awaited details of how the fan company had arrived at their numbers. Perhaps my measurements were in error. Several weeks passed without any reply-- maybe the letter had been misplaced. I sent another copy, this time adding a new cover letter.
Enclosed please find a copy of the letter I sent to your company three weeks ago. I have not received any reply so I suspect the letter may have been misdirected or misplaced. Accordingly, I am taking the precaution of sending this letter by registered mail, return receipt requested.
Per the enclosed letter, I have had difficulty in finding agreement between the stated capacity of your floor fan, model TG-1887W, and my own measurements detailed therein. As the letter sets forth, the three independent measurements I have made of the fan output agree on a value which is approximately 1/6 (that is, 17%) of the 12,500 cfm capacity advertised on side of the fan box. Further, based on theoretical grounds I have concluded that the model TG-1887W fan cannot simultaneously achieve an output of 12,500 cfm while also obeying the laws of physics that I am familiar with.
Together with several members of my research group, I have considered the problem of reconciling the measured fan output with the advertised performance. We have arrived at a few possible scenarios:
1) You measured the fan output at some extreme elevation where the pressure is less than 1/16 sea level and the fan would have enough energy (at least in theory) to impart 36 m/s velocity to this low-density air. However, the efficiency of your fan blade design at very low pressures poses an interesting problem, which we have not yet examined, and your product packaging does not mention or suggest use of the product in near vacuum.
2) You might have used a toroidal test chamber, in which the air was accelerated in several stages through the fan blades to achieve a peak velocity greater than any single pass. I imagine the chamber walls would have to be quite smooth to avoid severe losses, and even so I would expect significant boundary layer drag. In any case I have not previously heard of such a test, or found it described in any ASHRAE standards documents to which I have access.
3) You are employing some nonstandard definition of CFM, interpreted not as cubic feet per minute but rather as some novel unit. For example, I calculate that the fan moves a quantity of air equivalent to 3874 cubic furlongs per millennium, and perhaps some other combination of units would agree with 12,500 to a reasonable approximation.
I remain in some doubt that any of these speculations correctly describe the measurements you have performed on the fan. I am curious how you did obtain your fan rating number and I would appreciate the favour of a reply.
Shortly after I sent the second letter, I received a call from the director of engineering at the company in question. He did not have a great deal of information to convey. He seemed relieved when, in response to his first question, I said that I did not represent a law firm. He said he had asked around the company, and no one could remember how the advertised number had been determined. I volunteered that I was surprised that they even advertised a specific CFM value, as the average consumer probably wasn't familiar with these measurements. He replied that yes, in fact the packaging had recently been redesigned and the CFM number had been replaced with information felt to be of more use to the customer.
What was this information, I wondered.
He replied that the package now specifies the color of the fan. It comes in white, teal or black.
I thanked him for his time.
Addendum: this story is completely true. From what I can
determine online now in 2001, the company in question is no longer in business.