I saw a video of a windmill a few minutes ago and they are quite fast.
But then i thought “Is the tip of the rotorblade as fast as the the point furthest in the middle?”
Let me explain the best i can:
So if you move 10km/h, after 1h you are 10km farther than before. Thats logical.
But with regards to the rotor blade, the point furthest in the middle moves less far than the one all the way outside.
Does that mean that the points move at different speeds even though they’re part of the same body?
Where is my mistake in thinking?
In: Engineering
Yes; the “outside” edge or tip of a fan is moving faster than the center.
Angular moment comes into play as the different points are moving at different angles
The outside of the blade moves faster than the center. If you find the circumference of the circle at the center and compare it to the circumference of the circle at the tip, the outer circumference is larger but they travel the distance in the same time. More distance/same time = faster speed
You’re absolutely right! The “linear speed” depends on the distance from the center. This is how rotation works – the speed depends directly on the radius of the circle you’re moving in.
On Earth, the planet as a whole is “stationary” but at the equator the ground (and the people on it) are moving at a whopping *thousand* miles an hour!
*Note: Linear movement is relative, so I’m calling the Earth stationary here because it is convenient, but of course relative to the sun or the center of the galaxy the Earth is moving pretty fast.
Speed is relative, so it depends what you’re comparing it to, but yes, compared to the surrounding air the tip will be moving faster than would a point closer to the center.
This principle also explains why songs on the outer tracks of old vinyl records can sound better than those printed near the middle (constant angular velocity). And also how gear systems work. ⚙️
The speed increases the further you travel from the center, but the angular velocity is constant. We know the outer edge travels further because of the greater speed, but since angular velocity is the same, they complete the same number of revolutions.
As a side tidbit, in rough terms, the surface of the earth is moving at about 1000 mph. And if we put a toy on a turntable, the toy would fly off. And the turntable speed is way less than 1000mph. So why don’t we fly off the earth? It’s because the angular velocity of the earth is calculated from 1 revolution per day, and the turntable is spinning at 33 revolutions per minute—much faster than the earth’s 1 rev per day
I think others have covered the different speeds aspect, but as a note, this is also why speed of spinning things is often noted as rotation per minute (rpm) or seconds.
Relevant: helicopter rotor blades are twisted to keep the angle of attack lower at the tips, accounting for the increased velocity.
Being “part of the same body” doesn’t matter. For an easy example, tie a ball on the end a string. Throw the ball while holding onto the other end of the string. Even though the end of the string attached to the ball moved, the end of the string you’re holding onto didn’t.
If you draw a line in the path that the middle and edge points take around the circle motion of the windmill, you get two circles, one big, one small. Obviously the big circle has a bigger circumference, the smaller circle has a smaller circumference. Let’s say for the sake of simplicity that the smaller circle (for the middle point) has a circumference of 10 feet, and the larger circle (for the point on the tip) has a circumference of 100 feet. If you run around the small circle at 10 feet per second, you would go all the way around in one second. However, if you run around the big circle at that same speed, you would get around the circle in 10 seconds. This can’t be true in real life because otherwise the tip of the blade would fall behind the middle, therefore the tip has to be going faster.
To think of it another way, if the windmill is spinning at 1 rotation per second, the tip of the blade has to travel a longer distance than the middle in the same amount of time. If you remember that speed = distance/time, then it makes sense that if the distance increases, then either the time or the speed has to change. If time changes, then the tip of the blade will lag behind, therefore speed must increase.
One thing I’d like to add is that this is all talking about linear speed. If you consider speed in this case as angular velocity, which is degrees(or revolutions, or radians)/second, then all values on the same blade should be the same.
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