I had a look at a huge windmill and was wondering how fast the blades are spinning. Obviously, the distance the blades make is different on the outside than on the inside. Is the speed of a rotating object always measured in rpm and not in mph?
In: 3
RPM is revolutions per minute. When talking about the rotational speed of an object you’re going to be counting its revolutions, the only question then is what relative time frame you’re interested in.
>Obviously, the distance the blades make is different on the outside than on the inside.
Since RPM measures angular momentum–how many many times the object rotates in a minute–the length of the blades is not really a factor. The axel that turns the blades will turn it at the same speed no matter how long the blades are.
RPM rotations per minute
rad/s radians per second (2π radians = 360°)
°/s degrees per second
All of these are rotational velocities. (ω)
You could also measure the tangential velocity (v) of the blades. That would be the speed the blades are moving at the tips in mph, kph, m/s, etc
ω = v/r where ω is in rad/time, r is the radius, so you can convert between rotational and tangential velocity
RPM is revolutions per minute. When talking about the rotational speed of an object you’re going to be counting its revolutions, the only question then is what relative time frame you’re interested in.
>Obviously, the distance the blades make is different on the outside than on the inside.
Since RPM measures angular momentum–how many many times the object rotates in a minute–the length of the blades is not really a factor. The axel that turns the blades will turn it at the same speed no matter how long the blades are.
The tangential speed of something moving at an angular speed of w at a given point that is a distance r away from the center is v = wr.
So for example, a windmill spinning at 10rpm = 20pi rad/min would have a tangential speed of 100pi feet per minute = 3.6mph at a distance of 5 feet from the center (v = 10rpm x 2pi rad / rev x 5 feet = 100pi feet per minute).
Revolutions per minute x Circumference
If the circumference is 10ft, and it spins at 60 rpm that’s 600ft/minute
Also, let’s be clear, in the real world (i.e. engineering and everywhere not in the US) you do not use mph.
In the case of rotating object mph or km/hr are meaningless.
Also:
>Obviously, the distance the blades make is different on the outside than on the inside
That’s why MPH is meaningless.
The only time I’ve ever heard speed in km/hr or mph being considered in rotating bodies is with turbofan engines (big plane engines) because if the outer edge of the blade exceeds the speed of sound your efficiency goes to shit.
As you pointed out the outside is traveling faster than the inside. So there is no one velocity (speed) answer like mph, here let’s use Meters per Second (m/s).
Looking at a large windmill (turbine) is an interesting case because the velocity of the blade, and specifically through or relative to the air is important, primarily because the force on the blade, being used to convert the wind to energy, will vary along the length of the blade.
So if you look at one of these enormous blades its shape changes along its length.
So the engineers that design the blades need to do complex modeling (in CAD) on the blade design.
Another issue is the tips, which are critical to managing the drag of the entire system, are traveling the fastest from a velocity perspective, in fact quite fast. They suffer from erosion and pitting, which impacts the required maintenance and inspections needed.
The tangential speed of something moving at an angular speed of w at a given point that is a distance r away from the center is v = wr.
So for example, a windmill spinning at 10rpm = 20pi rad/min would have a tangential speed of 100pi feet per minute = 3.6mph at a distance of 5 feet from the center (v = 10rpm x 2pi rad / rev x 5 feet = 100pi feet per minute).
RPM rotations per minute
rad/s radians per second (2π radians = 360°)
°/s degrees per second
All of these are rotational velocities. (ω)
You could also measure the tangential velocity (v) of the blades. That would be the speed the blades are moving at the tips in mph, kph, m/s, etc
ω = v/r where ω is in rad/time, r is the radius, so you can convert between rotational and tangential velocity
As you pointed out the outside is traveling faster than the inside. So there is no one velocity (speed) answer like mph, here let’s use Meters per Second (m/s).
Looking at a large windmill (turbine) is an interesting case because the velocity of the blade, and specifically through or relative to the air is important, primarily because the force on the blade, being used to convert the wind to energy, will vary along the length of the blade.
So if you look at one of these enormous blades its shape changes along its length.
So the engineers that design the blades need to do complex modeling (in CAD) on the blade design.
Another issue is the tips, which are critical to managing the drag of the entire system, are traveling the fastest from a velocity perspective, in fact quite fast. They suffer from erosion and pitting, which impacts the required maintenance and inspections needed.
Revolutions per minute x Circumference
If the circumference is 10ft, and it spins at 60 rpm that’s 600ft/minute
Also, let’s be clear, in the real world (i.e. engineering and everywhere not in the US) you do not use mph.
In the case of rotating object mph or km/hr are meaningless.
Also:
>Obviously, the distance the blades make is different on the outside than on the inside
That’s why MPH is meaningless.
The only time I’ve ever heard speed in km/hr or mph being considered in rotating bodies is with turbofan engines (big plane engines) because if the outer edge of the blade exceeds the speed of sound your efficiency goes to shit.
Latest Answers