I’m trying to calculate the force the wind will exert on a 6-meter-diameter wind turbine, to design a tower. I see that a wind speed of 80 kilometers per hour would exert a force of 279 kilograms per square meter (on a flat surface), but I have no idea as to how this relates to blades on a wind turbine. Can you tell me how to go about that calculation?
John Meyer • Midland, Ontario, Canada
You can use those surface pressure calculations to determine the wind loading on the tower itself, but the wind turbine blades are not at all like a static flat surface. The blades fly across the wind like the wings of a plane, generating a lift force that pushes back at the airflow and slows it down. Slowing the wind extracts its energy and drives the turbine. It’s possible to calculate the ideal amount of force to achieve this goal, but the reality is likely to be different, so it’s advisable to include a healthy safety factor.
When the wind gets stronger than necessary for full power, the turbine will have to protect itself by one of a number of possible strategies that also affect the thrust loading. For example, some turbines will stall their blades. This spoils their ability to capture energy, but it may not reduce the thrust very much. Others yaw sideways to the wind, dodging its force, but it takes time to yaw, and so a gust can create a high peak thrust.
If the turbine were still converting wind energy into electricity in 80 kph winds (50 mph; 22 m/s), it might produce up to 50 kW. The ideal thrust would be about 132 kg per square meter, approximately half of the figure you quote, adding up to 740 kg over the area of the rotor. It’s unlikely that the turbine would be designed to work like this. It’s more likely that it would start to furl or govern at about half of this wind speed, when the thrust would only be one-quarter as much. The actual working thrust could be around 180 kg, but for various reasons, the peak thrust would be quite a bit higher. Therefore, it would be wise to apply a safety factor of perhaps five times to that, which yields a nominal peak thrust closer to 1,000 kg of force for the purpose of tower design.
Designing a tower is really a job for an engineer. The calculations are based on the highest wind speed that the tower will experience. They include an element of wind thrust on the tower itself and also the thrust on the turbine. The critical load on the tower is usually the bending load at the highest supported point. For a guyed tower, this is the top guy level. For a freestanding tower, the bending load is at ground level. Bending moment is the force multiplied by the radius of action, so tall towers without guys need to be very strong. It’s wise to also factor in the gyroscopic moment that arises when the turbine yaws sharply around the tower top in turbulent conditions. The force calculations can also reveal the tension in the guys and the uplift forces on the anchors. In many cases, the designer will consider the natural frequencies of the tower in relation to the speed of the blades so as to avoid resonances.
Hugh Piggott, Scoraig Wind Electric • Scoraig, Scotland