the optimal number of blades on a windmill is 3. Airplane props, helicopter blades, and ceiling fans can all have any number of blades. Why?
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How do you define optimal? That’s kind of key here as the needs and wants of wind turbine designers are not those of aircraft manufactures.
There are a number of criteria that going into an “optimal” blade configuration, in no special order –
1) Cost – more blades = more money
2) Vibrations – more blades = a more even spin without vibration
3) Drag – more blades = more drag = more fuel consumption
4) Power – more blades = more surface area for force exchange = more power
5) Size & Speed – The power produced/obtained from spinning blades is complexly related to the number of blades, the size of each blade, and the speed each blade spins.
As you can see, items 1-4 are pretty complex, but let’s boil them down to – we want as few blades as possible, right? But # 5 says that the number of blades, along with their speed and size, directly impacts the power. Putting all these rules together, you basically get an ELI5 of – the smaller and faster the blades are, the more blades you’ll need to use. The larger and slower, the fewer you can use and 3 is pretty much the fewest blades you’d use to create a well balanced, long term function machine.
Short Version – ceiling fans, airplane props, and helicopter blades are all short and spin really fast, so you want a bunch. Wind power turbines can be any size but are typically priced per-blade as opposed to per-blade-size. so they go fewer big blades because it’s cheap and effective.
You can have any number of blades on a wind turbine including 1, you do need a counterweight if you have 1 blade.
One problem is momentum on the tower when the wind changes direction, the rotor change direction too. With two blades the momentum is diffrent when the blades are horizontal or vertical but with three they will even out and be constant. I guess that any odd number will work the same way but am not sure.
More blades will be less efficient because of the drag increase. The most cost-efficient in regards just to power is a single blade but because of vibration and the forces when it changes direction three blade is a more cost-efficient overall system.
What you really like to improve efficiency is longer blades, wind turbines get taller and taller with larger and larger rotor diameters.
Airplanes and helicopters have practical limitations on how large you can have the rotor so adding more blades is the cheapest way to get out more power. You get more drag but can also output more power. The rotors on a helicopter and propellers on an airplane is not on top of a tall tower and the direction of their do not change relative to the vehicles so you do not have the same problem as a wind turbine with two blades.
Ceiling fans are stationary so two blades is a simple way to make them without a counterweight, you can add more blades to get more air moving with the same diameter. Another important factor is how they look even when they are stationary. It is not efficient you exactly care most about but looks size, and the amount of air they can move. Add to that sound is also very important.
The most efficient number of blades is one, a really long one. But that would be unbalanced so the most efficient practical number of blades is two. Two very long, slow turning high aspect ratio blades – that is ideal for efficiency.
Much of the time there is not room for tremendously long blades so you compromise and add more blades in order to get the thrust you need.
Three is very popular because it is the fewest number of blades that is balanced in two axis.
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Wind turbines is a more precise term for the ones that generate electricity. (Windmill is traditionally the ones that grind grain but enough people use it that it’s said to be acceptable.)
Wind turbines convert wind energy into rotational energy. Airplane props, helicopter blades, and ceiling fans are *driven* with shaft power.
Generally longer blades are more efficient for turbines: https://www.energy.gov/eere/articles/wind-turbines-bigger-better So fewer works better.
Propellers and helicopter rotors, you don’t want the tip to exceed the speed of sound, and to not strike other structures. They also need to be manageable to apply power to. Helicopters and larger propellers can, like wind turbine blades, change pitch: see https://en.wikipedia.org/wiki/Propeller_(aeronautics) under variable pitch. (Fixed-pitch propellers are for ones where the simplicity outweighs the efficiency benefits.)
Ceiling fans don’t have to design for maximum conversion of turning power to aerodynamics, so can go for quietness and aesthetics at higher priorities.
The eli5 answer it really it depends on many many factors and the number is selected based on what the design prioritizes and the power transfer required.
It’s a fluid dynamics exercise. For wind turbines (or water, etc) ideally the fluid hitting your blade stops. If it does you get all the momentum available, but if it did it interferes with new moving fluid arriving. That would slow down fluid speed on the blades and take away power. That all changes with fluid viscosity, density, and velocity. So we have to strike a balance for real applications.
We also consider what you prop needs to do, be light, efficient, maximize power transfer, be quiet, etc.
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Every blade tip allows air from the high pressure surface to move around to the low pressure side. This is a little simplified but it’s an OK way to think of it. The result is a tip vortex – a swirling flow that trails behind the blade. This is bad for lift generation and it causes drag. So, bad for helicopters, props, and wind turbines. The goal, then, is to minimize the number of blade tips subject to other considerations.
One of the early helicopters had one blade. It was built by a guy named Montgomery Knight. The aerospace engineering building at Georgia Tech is named for him. When I was graduate student there in about 1994, I worked in the Harper wind tunnel. We had to move everything out for a building renovation. Under the wind tunnel, we found that rotor blade and immediately all recognized from the pictures. It is now on display in the Knight Building entrance. Not what you asked, but a good story anyway.
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