Common sense seems to say that it can’t be possible to generate the same or more power with just one wing than would be possible with two, three or more, why not thirty?

Interestingly, common sense and physics are not always in perfect alignment, and when that happens it is usually physics that prevails.

The answer to this question from a performance point of view lies in how wind behaves as it passes through the rotor disk. The first step in understanding this is to take away the question of the number of blades altogether and think of what is called an ‘actuator disk’. This theoretical device is a circular disk that lets the student of wind turbine performance offer a variable blockage ratio to the incoming wind and harvest without loss, the energy that is given up by the wind as it slows down. As wind passes through the disk and slows down, the stream has to diverge and spread out to maintain continuity of mass flow. There has to be some optimum ‘slow down’ factor so the wind still flows away downstream (you can’t stop the wind) but equally if you don’t slow the wind enough you lose energy recovery.

It was first established by Albert Betz that if you adjust your actuator disk so the downstream velocity is 1/3 of the upstream velocity, you have found this optimum. See Wikipedia for the explanation and derivation if you want to follow this.

Betz also showed that assuming no drag and ideal performance from the disk, the maximum recoverable energy in a wind stream is 16/27 (or 0.593) of the incoming kinetic energy in the wind. Once this framework is established, we can turn to designing the best possible real rotor to replace the actuator disk. As a designer, we can choose many blades, fewer blades, what are the effects?

The blockage created by a rotor depends on the number of blades, the width of the blades (chord), the rotation speed of the rotor, the lift and drag properties of the airfoil sections chosen in the flow conditions they see. If we go for a lot of blades, we find in order not to block the wind too much, we need narrow section blades (small chord), at a low rotation speed. This is typical of the water pumping turbines associated with the American West.

They are great machines and often tick along for decades after they have been abandoned, and as slow speed machines, they produce a lot of torque (turning force) which works well for operating a pushrod water pump. They do however create a lot of rotation in the wake, which is energy not being recovered, and their overall efficiency is very low. As designers have wanted more efficiency, and higher speeds to drive generators, they have moved to use fewer blades, of wider chord and turning faster.

Following this sequence, many designs have stopped at 3 blades with the tip speed ratio (the speed of the blade tip divided by the speed of the incoming wind) taken as high as is possible without becoming noisy. 3 blades also have the useful property of having the same rotational inertia about the turbine yaw axis (the one that aligns it with the wind direction) no matter what angular position the blades are in.

This last point is not true of two-blade (or 1 blade 1 counterweight machines). The rotational inertia about the yaw axis is different when the blade pair is horizontal compared to vertical which leads to issues when yawing
while running for both free and powered yaw machines.

We decided to investigate keep going not just past three blades, but also past two, to just one. What effects and benefits could we find by doing that, seeing we were starting the design from a clean sheet of paper?

First, we realized from Betz that we either had to go faster or wider with our single-wing than an equivalent two or three-blade design to get the right wind slowdown. Faster is attractive in terms of making the alternator lower torque and thus smaller but runs the risk of being noisy compared to the competing designs.
So wider at a similar speed with high-performance airfoils seemed to be the right path.

In theory again, for single-wing design compared to three blades, there is about a 6% loss in energy recovery for the same flow conditions. Doesn’t seem too onerous – a little bit longer seems a small price to pay for only having to make one compared to three – but wait – the flow conditions aren’t the same.

Our design is running at the same speed as a competing equivalent 3 blade design, but with a much wider and thicker (bigger chord) wing. There is a very important ‘dimensionless number’ called the Reynolds number (again see Wikipedia for the detail) which is an expression of the ratio of the inertial forces in a flow, divided by the viscous forces. It guides whether it is the mass effects of the fluid that are controlling the flow behavior or its ‘stickiness’.

In any flow situation as you increase the speed and scale of a flow, there is a transition between laminar flow (dominated by stickiness) and turbulent flow (dominated by mass). The transition is a place to avoid, as it is unpredictable, random and messy. For an airfoil the Reynolds Number (or Re) is defined as u.c/v, where u is the flow velocity, c is the chord of the airfoil and v is the dynamic viscosity of the fluid.

It turns out that small wind turbines are operating in a range where transition effects are important, and getting the Reynolds number up makes a big difference to how the airfoils perform. By going from 3 blades to one in our concept design (at the same tip speed ratio) we go from Reynolds numbers in the 200,000 range up to 600,000. This sounds a bit esoteric, but it makes an important difference to the lift to drag ratio of the airfoils, and also the smoothness of the stalling performance. This picks up that 6% again and a bit more, and puts us in a good position for the design, getting performance that is better than 3 blades with just one wider and thicker wing.

It still leaves some important questions for the concept, and more benefits to explore. First, of course, at least one counterweight is needed, and when you look into the dynamics, a teeter bearing (like a see-saw bearing) is needed so the unbalanced aero force doesn’t go into the shaft.

With one counterweight, we are in the zone where yaw problems will occur, so we thought about options to fix that and investigated 2 counterweights to give three rotating masses. Not only are the yawing problems removed by that, but the rotor assembly with the right detail design, is free to teeter to any angle in a 180-degree range, and we could see an advantage to allowing the wing to ‘park’ to horizontal in winds above the running range for a high survival wind speed.

We have also extensively investigated the aerodynamic performance of our realized blade design, which is very detailed and uses 3 airfoils through the root, mid-section and tip regions. The University of Otago, principally Dr Sarah Wakes, has provided invaluable expertise in guiding student projects which have used computational fluid mechanics (CFD) to investigate the running and stalling performance of the Thinair blade.

The papers that have come out of that research are good reading for anyone who is interested in knowing more about the aerodynamic performance of the Thinair design. The Modsim paper is a good starting point.