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 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
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.
If an object has a uniform angular velocity, every point on it will have a linear velocity that depends on its distance from the centre of rotation. So yeah you can measure the speed in mph (or more reasonable units like m/s) of any point on, say, a windmill’s blade, but it’ll be a function of the radius up to that point. The angular velocity, as in, the speed at which its angle changes, that being what “rpm” denotes, is a much more comfortable measurement in this case because like I said it’s uniform. However, if I, say, swung a sword or a club in a roughly circular arc, the force of its impact is obviously determined directly by the linear velocity of the point of contact, in which case you’d want to measure and express that, but it’s still a function of its more-or-less uniform angular velocity and its length.
If an object has a uniform angular velocity, every point on it will have a linear velocity that depends on its distance from the centre of rotation. So yeah you can measure the speed in mph (or more reasonable units like m/s) of any point on, say, a windmill’s blade, but it’ll be a function of the radius up to that point. The angular velocity, as in, the speed at which its angle changes, that being what “rpm” denotes, is a much more comfortable measurement in this case because like I said it’s uniform. However, if I, say, swung a sword or a club in a roughly circular arc, the force of its impact is obviously determined directly by the linear velocity of the point of contact, in which case you’d want to measure and express that, but it’s still a function of its more-or-less uniform angular velocity and its length.
If an object has a uniform angular velocity, every point on it will have a linear velocity that depends on its distance from the centre of rotation. So yeah you can measure the speed in mph (or more reasonable units like m/s) of any point on, say, a windmill’s blade, but it’ll be a function of the radius up to that point. The angular velocity, as in, the speed at which its angle changes, that being what “rpm” denotes, is a much more comfortable measurement in this case because like I said it’s uniform. However, if I, say, swung a sword or a club in a roughly circular arc, the force of its impact is obviously determined directly by the linear velocity of the point of contact, in which case you’d want to measure and express that, but it’s still a function of its more-or-less uniform angular velocity and its length.
Maybe not entirely related, but almost all modern cars measure vehicle speed (and outputs that to the speedometer) at the wheels through ABS system. You do need to change the wheel size value in the ECU when changing to bigger or smaller wheels to make sure the measurments stays accurate
Maybe not entirely related, but almost all modern cars measure vehicle speed (and outputs that to the speedometer) at the wheels through ABS system. You do need to change the wheel size value in the ECU when changing to bigger or smaller wheels to make sure the measurments stays accurate
Maybe not entirely related, but almost all modern cars measure vehicle speed (and outputs that to the speedometer) at the wheels through ABS system. You do need to change the wheel size value in the ECU when changing to bigger or smaller wheels to make sure the measurments stays accurate
If you’re doing any serious math related to rotation, radians per second is the best. Absolutely anything else will require some conversion factor. That’s not to say they aren’t common. For instance, the number of poles in an induction motor is typically 120*f/s where frequency is in Hz and speed is in rpm. But that 120 factor is to make the formula work with rpm.
RPM is often used because it’s a more familiar number to work with. If I say something is spinning at 50.26 rad/s, that is going to be tough to work with mentally. But convert that to 480 RPM and you can already have an idea how fast that is. You know it’s slow compared to an engine, but maybe pretty quick if it’s a carnival ride. You can also use your multiplication tables to get to 8 rotations per second which is even more understandable to a human.
The one and only reason anyone should ever report a rotational speed in distance per time (like miles per hour) is a shock value. A news story might use it because it sounds crazy or deadly or impressive and they know it’ll get more clicks. But no engineer, mathematician, mechanic, or really any industry professional will ever use mph to represent rotational speed.
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