Reynolds Wizardry/ tapered blades....

[darrellwittke]

I ran across these formula's on scienceworld.com. I wonder if I have grasped the relevance correctly in regards to tapered blade tips.

Drag coefficient (Cd) is defined by Cd = Fd (drag force) /divided by 1/2 p (where p is density of air) and U squared (where U is speed) and L squared (where L is size scale of body.)

I noticed that L is exponential and on the bottom of the equation, thereby offering huge paybacks if the number can be reduced. The same for U, or speed, however.

Therefore, can it be said that reducing the blade tip size/scale (as in tapered blades) allows the blades to produce more lift at lower speeds? I theorize that, at higher speeds, the somewhat modest size scale reduction is quickly offset by the (U) or speed exponential increase.

Would this not explain the "tons of lift" reported by Paul B., possibly also the lack of "speed stability?" In other words, the tapered rotors are sensitized to rotor speed and when cruising in forward flight, they get past their "sweet spot"?

Hope this is clearer than mud, just thinking and would like to understand.

Reynolds numbers, as explained by Wikipedia, is a number to correlate inertial forces with viscosity, most often used to differentiate laminar flow to turbulent flow. Most, if not all, gyro rotors with their 300 plus mph tip speed should be laminar flow, if I am not mistaken. It is also a red herring, having little to do with the above postulation, I believe.

Thanks in advance to any/all who answer.

[Al_Hammer]

Darrell, I see this thread isn't going to win any awards for popularity :D


Drag is linearly proportional to the blade area. Drag= 1/2 p V2 A Cd, and lift is also proportional to area, so I don't think changing the tip area will gain you anything from this vantage point.
Tapering the overall planform of the blade, or of the tip, can increase performance according to studies, and helps from a structural standpoint, although it adds manufacturing complexity.

The proper blade tip shape can help reduce tip vortex effects. It seems this is as important as any gains in efficiency from overall blade taper. The tip vortex interferes with the following blade.

study of blade tip shapes:
http://www.enae.umd.edu/AGRC/Aero/AHS2002_Martin.pdf

study of blade taper:
http://techreports.larc.nasa.gov/ltrs/PDF/tm4345.pdf

[darrellwittke]

I see the second report reports the torque required for 3:1 50% and 75% tapered blades is less than the rectangular or regular blades.

I still don't quite understand the mechanism of action (Please remember I can't read sheet music.) Is it the reduction in wetted area and if so, how is this different than the size/scale (L) posted in the first formula?

In re-reading your post, Al, I understand it is wetted area. Something basic is off in my understanding. You say drag is linearly proportional to size and lift is also proportional to size. My understanding is that lift is exponentially proportional to speed, so it follows if you reduce the size you increase speed (because of drag reduction) which effects lift exponentially. In other words, you get more lift by reducing size because speed goes up, something for nothing, which flies in the face of common sense and physics. Is this correct?

On the tip vortices, great graphics! A picture is so illuminating to me since I can't completely envision what the math says. The pancake airplane got good results by placing the engines on the wing tips, thereby allowing it to shed (or use) the wing tip vortices, greatly increasing performance. In promoting the Hydrogen Peroxide rotor tip rockets, would not the steam generated cause the same effect? Realistic guess or just wishful dreaming? Always full of questions, as you probaly are aware by now. Thank you very much for illuminating one small corner of the world with the light of your knowledge, Al H.
Thanks for the scienceworld link, fascinating stuff that answers a lot of general question. sincerely, darrellwittke.

[Al_Hammer]

Darrell,

I have no idea. The authors indicate that results differ from expectations based on theory. In the case of the vortex reduction, the gains in performance aren't due to lift or drag per se, just a reduction in adverse angle of attack fluctuations as the blade tip runs into the preceding tip vortex. The tip vortices stay very close to the blade( although they can be blown down into the tail. )

[Chopper Reid]

Darrel. the blades Paul B uses here in Ozz are tapered and twisted, I have a set of these tapered and twisted blades and they are beautifully stable and give a great ride in very rough air however, they do not perform as well as alloy blades at Max weight in some conditions, although when the fuel load drops down say by 6 gallons, they start performing as they should.

This might be caused by the blades letting air out of the end of the blade somehow. I'm not a technical person so I cant help in that area, all I can do is tell how they actualy perform in the real world.

The unstable blades Paul B refers to where a early set produced some time ago.The current design are extremely stable.

While they certainly do provide excellent lift at low speeds compared to alloys, and allow the gyro to cruise a bit faster, I'm not sure that straight blades [of the same diameter] might produce more lift. Hope this helps you some !!

[REDHORSE556CES]

Tapered blades? As in??? From the Olney, Texas spring fly-in.

[Aussie_Paul]

Darrel. the blades Paul B uses here in Ozz are tapered and twisted, I have a set of these tapered and twisted blades and they are beautifully stable and give a great ride in very rough air however, they do not perform as well as alloy blades at Max weight in some conditions, although when the fuel load drops down say by 6 gallons, they start performing as they should.

This might be caused by the blades letting air out of the end of the blade somehow. I'm not a technical person so I cant help in that area, all I can do is tell how they actualy perform in the real world.

The unstable blades Paul B refers to where a early set produced some time ago.The current design are extremely stable.

While they certainly do provide excellent lift at low speeds compared to alloys, and allow the gyro to cruise a bit faster, I'm not sure that straight blades [of the same diameter] might produce more lift. Hope this helps you some !!
.........The first set that Rob and worked on and I tested on the lead sled Hubrid were negatively twisted from blade root to the blade the tip, slightly tapered, and slightly thinned from the blade root to the blade tip. The last 4' had a VR-7 airfoil that has no reflex. The improved performance of these was excellent BUT they were not as stable as Robs original 8H12 blades balanced at the 25% mark. They were neutral.

Because Hybrid was very close to CLT with 130 lb ballast, I had a great working platform to judge the stability from different blade design. Trimmed hand off at 50 kits, I would lift the nose and reduce the speed to 40 kits and let the stick go. The 8H12s would return to the original trimmed speed within a couple of passes of the nose through the horizon during approx 10 seconds. These blades almost stayed at 40 kits, just slowly coming up to 45 kits. Increasing the speed would end up doing the same.

The blades that most are using now are the same as those first blades BUT without the change in airfoil. I loved the blades with the VR7 airfoil. The trim spring pressure hardly changed over a large speed range, and they would fly so much slower. Musterers would love them.

I have a new student as I was conducting these exercises and he preferred to train with the 8H12s. They were much easier for a newbie to increase their skill levels more quickly.

I still have those VR7 blades and will try them again on the Firebird. I sent the VR7 blades back to Rob and he heated the training edge a little and added some reflex. This was a minor improvement. I added 8" long trim tabs on the trailing edge approx 2' from the tip. They stuck out approx 2" and had 5 degrees of reflex bent into them. This was a small improvement again. That is where we stopped and Rob made the current blades that a lot of people are flying and enjoying.

Brian, I was interested in your comments re the higher disc loading performance. Maybe they need to have another foot of Diameter to handle that scenario.

I look forward to working with blade manufacturers when I have the Firebird in the final form that will be sold. We can fine tune blades and torque tube offsets etc. to maximize performance on Firebird. I gave up on the testing due to not having a final product ready for sale. I did not see any sense in getting things perfect on Hybrid and then having to re fine tune to Firebird.

Anyway, just a little background of where we were heading with blades a couple of years ago.

Aussie Paul. :)

[Aussie_Paul]

Brian, what is the diameter of the Patroney blades, and what does your machine and yourself weigh? I take it you would have a 60 liter seat tank? Also what alloy blades are you comparing them against? Was the diameter and the chord the same? Thanks.

Aussie Paul. :)