HighPlains
Posts: 2712
Joined: 3/2/2003
From: Over da rainbow,
KS, USA
Status: offline
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quote:
there is a lot of theory in propeller designing and the "proof is in the pudding".
This is true. A terrific amount of study was done on the subject, mostly in the 30’s and 40’s but a limited amount still goes on even today. Yet the result of all of it is efficiency in the range of 80-85%. The prop designer has a great number of tradeoffs to make. Pitch and diameter most are aware of, but toss into the mix the pitch curve (actual pitch of the prop from the hub to the tip), airfoil selection, and blade width. Other requirements have to do with the distribution of mass in the blades relative to the plane of rotation, modes of vibration and stiffness, and material strength.
Usually the airfoil is picked more for strength towards the hub, while the airfoils on the outer portions of the blade does most of the work. With most props washed out at the hub (lowered pitch), sport and racing props differ at the tips. Many sport props are also washed out at the tips, while racing props typically have the highest pitch at the tips. For a sport prop, this washout at the tip gives better acceleration on takeoffs and more rpm in the air.
So if we assume that any well chosen, well made prop has roughly the same efficiency, say 82%, then selecting a prop comes down to matching it to both airframe and power available from the engine. This means finding the optimum size to allow the engine to unload to a point where it makes the maximum power. Fortunately, this peak power rpm is usually fairly flat over a narrow rpm range. Generally, once you get very close, then changes of a couple tenth’s of inch in pitch or diameter is about all you can make, and atmospheric conditions start to dominate which prop over a very limited range will work best.
Knowing the airspeed that a certain power output achieves with a well matched prop then allows calculation of how much power is required to achieve another speed. Simply stated, power required is a simple cubic function, so doubling the power only increases speed by 26%. So when a 6 lb. airplane flys level at 135 mph while hitting 170 at a 45 degree dive, we can calculate how much power is available from both gravity and the engine. It turns out in this single case, that engine power (82%) and gravity power are roughly equal. With the airplane diving it moving at 250 feet/sec, and the downward component of this is (sine 45) x 250 ft/sec, or 177 feet of altitude per second. Multiply this by 6 lbs. and you have 1060 ft^2-lbs/sec. Divide that by 550 ft^2-lb/sec and you have 1.9 hp added by the dive. Since this is roughly equal to what the engine is putting out, we figure the engine power by 1.9/0.82 (prop efficiency) and end up with an engine output power of 2.3 hp.
Now to see if 200 mph is possible when in the 6 lb configuration, we need to increase the available power by 63% over what was available at 170. This works out to 6.2 hp (my bad earlier, I used 2 hp from the engine in a rough estimate). Subtracting the 1.9 from 6.2 means that gravity has to provide 4.3 hp. This is 2365 ft^2-lbs/sec, and 200 mph is 293.3 ft/sec. So dividing out gives 8.06 lbs., thus at 6 lbs, the airplane will not be able to reach 200 mph regardless what propeller is used.
< Message edited by HighPlains -- 1/7/2008 12:15:02 AM >
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Why the Speedboy Patriot went 170 mph - 
