Strange blades...anyone seen this before?

[makenzie71]

The blade tips are actually angled against the wind.  Is this a normal design?

[Adriaan Kragten]

You can get a negative blade angle beta at the tip if the rotor has a high design tip speed ratio. The angle phi in between the relative wind and the rotor plane is always positive but only some degrees at the tip for a high design tip speed ratio. If the rotor is designed for an angle of attack alfa which is larger than phi, you get a negative blade angle (see report KD 35 figure 3.2). But the negative blade angle of your rotor can also be the result of manufacturing inaccuracy of the blades or the hub. 

[makenzie71]

If there's some rationale behing it i can accept that.  I thought “they made it wrong” t9 begin with but the hub surface is flat and all the blades are identical...so if they made it wrong they made them all wrong (which i'm sure is also possible).

[MattM]

The greater the air pressure the  angle increases in the angle of attack.  Unloaded it may be a negative AoA, but twists to a positive AoA as wind speeds increase the pressure on the blades.

[Adriaan Kragten]

The greater the air pressure the  angle increases in the angle of attack.  Unloaded it may be a negative AoA, but twists to a positive AoA as wind speeds increase the pressure on the blades.

If the blade is twisted, twisting is caused by the aerodynamic moment. For most airfoils, the aerodynamic moment is given around the quart-chord point (but for a cambered plate, it is given around the airfoil nose). The moment around this point has a direction which increases the blade angle beta. But in this case the blade must have a blade shaft which has an axis lying at the quart chord point. The given blade has no blade shaft and it seems that a cambered airfoil is used. In this case the blade twists around the neutral line for twisting. This neutral line lies half way the chord for a cambered airfoil. If the aerodynamic moment is transferred from the neutral line to a line half way the chord, the direction of the aerodynamic moment changes, mainly because the lift force gives a right hand moment around this axis. So this means that the blade angle will become even more negative. So this don't explains the negative blade angle at the blade tip.

The procedure how the aerodynamic moment can be transferred from the airfoil nose to another point is explained in public report KD 501 for a cambered airfoil for five different positions of the axis.

[MattM]

Adriaan Kragten, I highly respect your input.  Some times your explanations don't seem to tell the whole story.

Every wing under a load is going to deform in some manner.  We see it at the greatest amounts with the fastest aircraft and the most flexible materials.  A slow flying Cessna has a different wing shape sitting on the ground that changes as it lifts off the ground, but it is not super dramatic of change.  The F-16 wing actually has a resting negative pitch not unlike that of makenzie71's blade at the wing tip.  But once there is sufficient wing loading it twists to the positive pitch.  In unloaded cases the shape makes it easier to handles the control of the aircraft as one approaches a stall.  Until there is adequate forward speed and weight under the wing there is not enough wing loading to twist the wing.  The B-52's long wing has a similar characteristic.  So hard maneuvers and heavy loads will induce twist at the wing tip, but under light loading it will not.  Engineers specifically chose materials that have these characteristics.  So an eyeball test is not going to be sufficient to know what shape is at any given aerodynamic velocity.  Wings are not static shapes under a load and I suspect this is the case with this design, too.  In both cases they use loads on the outer wing to suppress this twisting because in a dynamic situation when it comes to loading there can be a corresponding "flexure-torsion binary flutter".  Wind turbines often have much higher tip speeds than a Cessna that approach the velocities of jets.  With no input regarding materials it is impossible to be sure what the blade shape is at any given tip speed.

[Adriaan Kragten]

What I have explained in my previous post is that the wing may twist because of the load. However, this load causes a moment with a direction such that that blade angle becomes smaller in stead of larger if the blade is twisting around the neutral line for twisting. So if the blade angle is negative at the tip for the unloaded situation, it becomes even more negative for the loaded situation. This is also called stall flutter. The lift gives the main load on the blade but if the moment coefficient is transferred from the quart-chord point to the neutral line for twisting, the lift causes the main change of the moment coefficient. So it is not true that I have neglected the effect of the load. The effect of the load is incorporated in the new moment coefficient.

A massive blade which is made from a single material will always have a neutral line for twisting which is lying far behind the quart-chord point. Only if the blade is built up from different materials or if it has hollow sections, the neutral line for twisting can be moved in the direction of the airfoil nose. Only if the neutral line is lying in front of the quart-chord point, the effect becomes opposite and then the load makes that the blade angle becomes larger because of the load.

The formulas for the displacement of the axis of rotation from the quart-chord point to another point lying further away from the airfoil nose are given for the Gottingen 623 airfoil in chapter 4 of public report KD 463. In figure 14 of this report you can see that the moment coefficient for the quart-chord point (Cm0.25) is almost constant and has a negative value of about -0.07 for angles of alfa in between -6° and 14°. The moment coefficient is defined right hand and so the moment for a negative coefficient is working left hand and so it has a tendency to decrease the angle of attack alpha (see figure 13) and so to increase the blade angle beta. But the Cm0.4-alfa curve is positive for angles of alfa in between -1° and 16° and it has a peak value of 0.131 at alpha = 10°. So if the neutral line for torsion is lying at a distance of 0.4 * c from the airfoil nose, the angle of attack will become larger and so the blade angle will become smaller if this airfoil is used.

[MattM]

One thing that bugs me about that picture is it looks like the blades are mounted wrong.  The curvature IMO suggests that they should be flipped over.

[makenzie71]

Nope they're the on correctly.  These blades only fit one way and they're contoured correctly at the hub.

[makenzie71]

They're not a straight(ish) airfoil like my other setups.  These have a rather large "scoop" closer to the hub and a very small profile toward the tip.

[MattM]

The scoop as you call it tends to be on both sides.

Are they keyed to only mount that direction?

[makenzie71]

The one side is convex, the other is concave.  They're keyed in a way...tops are flat and there's divots on the other side that sit over little domes on the hub.

[MattM]

Sounds like it is keyed.  So unless the rotor plates are reversed it must be correct.  Are the blades sandwiched between two plates?  If so, could they have been inserted in the wrong order?

[makenzie71]

Nope single plate.  I promise they're on there correctly

[MattM]

Thanks for entertaining the questions.

[SparWeb]

Matt
Socrates would be proud of you. 

[Adriaan Kragten]

The one side is convex, the other is concave.  They're keyed in a way...tops are flat and there's divots on the other side that sit over little domes on the hub.

So the airfoil is a cambered airfoil. Cambered airfoils can have a rather low Cd/Cl value but only if the camber is low and if the sheet thickness is thin with respect to the chord. Aerodynamic characteristics are available in report KD 398 for 7.14 %, 10 % and 12.5 % camber. The minimum Cd/Cl ratio for 7.14 % camber is about 0.03 and only this low camber is useful for a high local speed ratio. However, the sheet thickness should not be more than only 2 % of the chord. If this is done for blades made out of synthetic material, the torsion stiffness becomes very low and so the blade will be very sensible to flutter. If the blade is made out of steel, the torsion stiffness can be made high enough to prevent flutter and to realize a high maximum Cp (see wind tunnel measurements as given in KD 616). The torsion stiffness increases strongly if the sheet thickness is made larger than 2 % of the chord but this increases the Cd/Cl ratio.

If I look at the photo of the airfoil at the blade tip, I see that the sheet thickness is very large with respect to the chord. So the airfoil will have a lot of drag. There is a way to increase the sheet thickness without strong increase of the Cd/Cl ratio and that is to round the airfoil nose and to sharpen the airfoil tail. This results in an airfoil like the Gottingen 804 (also called the Eppler airfoil) which has a maximum sheet thickness of 6 % of the chord. Information about this airfoil is given on pages 3-83, 3-84, 3-85 and 3-87 (3-87 for the airfoil geometry) of report R-443-D, "Catalogue of Aerodynamic Characteristic of Airfoils in the Reynolds number range 10^4 - 10^6" which can be found on the Internet by typing this tittle in Google. But this procedure has clearly not been followed for the airfoil of this rotor.