I've never been very clear on the correct design for a Whitcomb winglet. Is a straight flat plate fin in line with the airflow any good, or do they have to be cambered and twisted?

Do you know of a (NASA maybe) web site where I could get more info?

From : Don Stackhouse

There's probably something, but I don't have any URL's for one. I'll check with some of my friends at NASA, they might have something.

Part of the problem with winglet design guides is that each airplane is different. The configuration of the flow at the tips, and the best way to harness it, will be different for each application. For models, often the best approach is to first get a good qualitative understanding of exactly what it is that winglets do, and then do a lot of flight testing to fine-tune your design. I think I can help a little in this particular area.

A finite span wing in upright flight has more pressure on the bottom of the wing than on top. Lift is always measured perpendicular to the local airflow direction, and drag is always parallel to it. Once you know these two bits of information, it's not hard to understand how winglets work.

The higher pressure air under the wing wants to spill around the wingtip to try to fill in the low pressure area on top. This flow results in a tip vortex trailing aft from the wingtip, like a horizontal tornado. You can see these vortices at the wingtips of a jet fighter during a high lift maneuver in sufficiently humid air, or at the tips of an airliner's flaps during a landing approach in wet weather. The energy extracted continuously from the aircraft to make the air swirl like that is what we call induced drag.

As you probably recall from our previous discussions of induced drag, it's at its worst when we're trying to make lots of lift with relatively little airflow. This means that slow flight (low speed, low mass flow, high lift coefficient) is one of the worst cases. This also means that the intensity of the tip vortices will be highest at these kinds of flight conditions.

Now we need to talk about "helix angle". If you understand the pitch of a prop, you're already familiar with it. Helix angle is one way to measure how far something rotates compared to how far it travels forward in the same time. The blade angle of a propeller blade is nearly the same (minus its efficiency effects and local angle of attack) as its helix angle. A wingtip vortex has a helix angle as well. This angle will be nearly parallel to the airplane's direction of flight when induced drag is low, but twist up into increasingly greater angles relative to the flight direction as we slow down or pull more "G".

If we have a significant amount of induced drag, and a correspondingly stronger tip vortex, then the flow at the wingtip will not be parallel to it, but rather at an inward angle on top and an outward angle on the bottom. This is where the winglets come in.

If we park a lifting surface in the middle of this angled air flow, it will develop lift perpendicular to the angled air flow. The resulting lift will be angled forward, and the forward component of that lift will be producing thrust. The lifting surface (i.e.: "winglet") will also be producing drag of its own, including both parasite and induced drag.

If the drag the winglet produces is less than the forward component of its lift, then there will be a net thrust applied from the winglet to the aircraft. This thrust actually represents some of the energy in the tip vortex, harvested from the vortex by the winglet and given back to the aircraft. That's it. That's all there is to it. It's so simple!

OK, now the catch. How do we maximize that thrust? This is where it gets complicated. If you increase the angle of attack of the winglet by increasing the "toe-in" angle, then it makes more lift force (which should theoretically increase the forward component of that lift), but it also makes more drag force. Depending on the specific situation, this could increase, decrease, or not change the net thrust of the winglet. It's going to depend on a lot of factors, including the flight condition.

This last item is particularly critical. Because the amount of induced drag, and the helix angle of the vortex decrease as you increase airspeed, the energy available for "harvesting" by the winglet decreases as you fly faster. Meanwhile, the parasite drag of the winglet is increasing. Eventually you get to a point where the total drag of the winglet is equal to the forward component of its lift, and at that point the winglet produces zero thrust. This is called the "crossover velocity". At airspeeds higher than the crossover velocity, the winglet adds to the aircraft's total drag, and you would be better off without it. BTW, because high speed performance is critical on an R/C HLG for penetration and launch, winglets generally are detrimental to overall performance. This is why you don't see them on my HLG designs.

Obviously the L/D of the winglet itself is a major factor in this. Keeping a decent L/D on a small span, small chord, low Reynolds number surface is a very difficult job. You need to approach it the same way you would approach the design of a wing, with good airfoils, proper twist and planform, etc.. Of course winglet twist is related to the helix angle characteristics of the wingtip vortex being harvested, and the helix angle of the vortex varies with the radius from the center of the vortex. You should also consider the stall characteristics of the winglet. Local stall (such as tip stall) on the winglet itself isn't a big factor, but overall stalling of one winglet and not the other can lead to some unpleasant handling characteristics!

The incidence angle of the winglet relative to the airframe is probably one of the most critical factors, and to make matters worse, the optimum angle is different for each different flight condition! Because of this, winglets generally work best on airplanes that spend most of their time at a single, fairly high angle of attack. It just so happens that park flyers and indoor R/C models often just happen to fit this description.

Determining the correct angle of washout and incidence for the winglet clearly involves a host of factors. In general, it's best if the angle of attack of the winglet (which depends on incidence, twist, and wingtip vortex helix angle distribution) is at the angle corresponding to the winglet's best L/D when operating at the most important flight condition. For models, we usually don't have reliable information on this, and if we're trying to get good performance at more than a single operating condition, we're going to have to make compromises anyway. Often the easiest way to determine winglet twist and incidence for a model is good old-fashioned trial and error.

One method for testing winglets is to trim the model for straight flight, then land, adjust the winglets, and see of the model wants to turn toward or away from the adjusted winglet. This method works OK if the winglets are longitudinally on the C/G, since the turning effects in this case are caused mainly by differences in thrust between the two winglets. However, if the winglets are located anywhere else (like in your case) then the winglet's turning effects could be due to their ability to act like rudders, in addition to any differences in thrust. It will be impossible to tell which one is more efficient. In this case, it's probably better to change both winglets, then try to measure some performance parameter, such as speed, or rate of climb, or minimum power required to sustain flight, or maximum time per charge without using thermals or other natural lift sources.

In many cases, the difference will be so slight that you won't be able to measure them with the equipment available to most modelers. Welcome to reality! It will probably be only in cases of models with a really serious induced drag problem that you will be able to measure any significant benefits. OTOH, a 20 inch span, 9 ounce model just might be one of those cases!

One problem I have regarding the winglets is that I am worried they will increase the wing's dihedral effect. I am afraid this will reduce the aileron's effectiveness. The usual fix - adding lots of differential aileron movement - will not be ideal as it would be like mixing in up elevator with the aileron.

It is true that winglets can increase dihedral effect (although usually only a small amount). It is NOT true that ailerons and dihedral effect are incompatible!

Dihedral effects and ailerons are incompatible only if you have an adverse yaw problem. Adverse yaw problems are the result of poor aileron efficiency; conversely, if your ailerons are well designed, you will not get much adverse yaw, and you can have as much dihedral as you want with no significant problems. Our old Monarch 'CX' R/C HLG, the last of the wood-wing Monarchs, is a case in point. It had full span flaperons (similar in size to what we use today in our Wizard series), but the exact same polyhedral setup as the Monarch 'C' 2-channel poly HLG. Roll rate on ailerons alone, using zero differential and zero rudder, was about the same as the poly ship using rudder alone. By combining aileron plus an excess of rudder (i.e.: about the same amount of rudder throw as we used on the poly 2-channel version) we got extremely high roll rates.

You are correct about differential on a tailless model, it does result in an unintended pitch command. Some of the flying wing slope fliers use differential and claim that it improves roll control. My own experience with my old 2-meter Klingberg flying wing would tend to support this. However, it also comes with the inevitable "up" pitch command mixed in, so you either need extra speed and nose-down pitch attitude at the beginning to compensate, or else you will have to add down elevator during the maneuver (which of course exactly removes all of the differential!).

Of course all of this is a moot point if you use rudder for roll control, or if you do a good job of designing very efficient ailerons!

One problem I have regarding the winglets is that I am worried they will increase the wing's dihedral effect. I am afraid this will reduce the aileron's effectiveness. The usual fix - adding lots of differential aileron movement - will not be ideal as it would be like mixing in up elevator with the aileron.

Don Stackhouse
DJ Aerotech