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power factor, The

Model Airplane News, Sep 1999 by Gierke, Dave

FOR AS LONG as I can remember, engine manufacturers have advertised horsepower ratings for their products. Unfortunately, this activity has degenerated into a meaningless game of one-upmanship, possessing little-if any-technical merit.

As I complained about this sad state of affairs to my neighbor and partner in aeronautical investigation, Frank Vassallo (remembered by readers of this column as "Professor Physics"), he politely but impatiently allowed me to finish my ranting before he exclaimed: "Dave, the model aviation community has suffered long enough!" Wagging his forefinger for emphasis, he continued, "In the neverending quest for truth, it's time to arm your readership with a simple, yet elegant, weapon from the uncompromising discipline of physics: the power factor."

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"Wow, professor!" I exclaimed. "You mean there's something that can help curious modelers learn the truth about engine horsepower?"

"Yes, Dave; there's a simple relationship between engine power and propeller rpm."

"What's the relationshi, professor?" "Not so fast, Dave. You're not getting off that easy! I'll provide an illustration. When I've finished, you tell me the relationship. Fair enough?"

"Oh, no, here we go agin-Classroom Dynamics 101." (Professor Physics always enjoys a lively game of "Know your concepts.")

The professor snatched a calculator from my workbench and scrutinized it closely, probably suspicious that it was the TV remote control he had mistakenly attempted to use a few years ago. He finally rejected it and pulled out instead a well-worn slide rule from its holder on his belt. After flashing through some calculations, he proceeded to outline the problem on the portable chalkboard he keeps in my shop for impromptu teaching sessions such as this.

"OK, Dave: here's the situation. We have two engines: a sport .35 equipped with a muffler and a racing .40 fitted with a tuned pipe. We've run them both on the same propeller, an APC* 9x6. Both were operated at wide-open throttle with the needle valve carefully peaked for maximum rpm." With a hint of a smile, the professor continued, "The little sport engine spun the APC at a respectable 10,000rpm. At this speed, the dynamometer** tells us that it's producing 0.25bhp. Conversely, the hot racing engine developed 2.00bhp while turning 20,000rpm." With a sardonic grin, he asked, "What is the relationship between power and rpm?"

**Note: over the years, I've tested hundreds of model airplane engines on a homebuilt instrument known as a dynamometer. From its operation, the accumulated torque and rpm data allow the calculation of brake horsepower (bhp). The term "brakeS indicates that an absorption unit (dynamometer) of one type or another was used to load the engine during an actual test. Occasionally, a manufacturer will supply a torque and bhp graph from its own "dyno," but this is rare. Because the first production gas engines were applied to freeflight model airplanes in the 1930s, the task of providing such information has been left to high-performance engine enthusiasts and magazine columnists.

Although uncomfortable when put on the spot by the professor, I tried to act as though I enjoyed the challenge. "Let's see; the rpm increased by 10,000, and the horsepower improved by 1.75." I could feel the perspiration forming on my brow. "Ah, let's see ... as the rpm doubles, the power increases eight times."

"That's correct. Now, the relationship; what is it?"

I gazed at the numbers on the dusty board, anxiously searching for a delaying tactic. Just as I was about to excuse myself to mow the lawn, a thought flashed through my mind: wait a minute, I've seen this before. It's a ... that's it! "I've got it!" I shouted, "It's a cube relationship! Power increases as the cube of the rpm!" "Good," said the professor, "But take it easy; this isn't a revelation. In fact, it's quite simple." As the professor erased the board with one hand, he scribbled the general power factor equation with the other:

Power = constant x rpm^sup 3^

"Now that I know the answer, that really was a simple problem, professor. But how does the power factor help modelers unscramble the horsepower-rating mess? After all, your example used dyno horsepower data for both engines."

"I'm getting to that, Dave. Let's use some new rpm and horsepower numbers for the same engines using the APC 9x6 propeller." As his chalk clattered on the slate, he muttered, "The .35 engine produces 0.22bhp at 9,000rpm, and the .40 turns 18,900rpm. OK; can you solve this one?"

"I don't know; you didn't give the horsepower for the .40."

"That's the point, Dave! If you know the rpm for each engine on the same prop and the horsepower for one of them, the power factor allows you to predict the unknown horsepower." With hands on hips and looking somewhat annoyed, he continued, "Here's the version of the power factor equation that everyone can use to ferret out the horsepower frauds," as the chalk again danced across the board.

"By multiplying the constant-known bhp-by the cube of the rpm ratiounknown hp rpm divided by the known bhp rpm-the unknown horsepower can always be determined." Again, the professor's chalk rattled across the board.

power factor, The

Model Airplane News, Sep 1999 by Gierke, Dave

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