Understanding Wattage of a Blender

[geoduck]

If a blender has a power of 800 watts, what does that mean?

Doesn't the power output depend on the torque or speed of the motor, which depends on what you're blending?

A motor that is spinning freely should have no power output (assume superconducting wires), because there is no torque in a freely spinning motor and hence no current through the battery!

A stalled motor also delivers no power output, although a lot of power is burned at the internal source resistance.

Whenever a wattage is specified for a motor, doesn't there need to be a torque or speed specified for that wattage?

Also, what exactly are the design parameters for a blender? It seems you'd want low wire resistance R, so that the start-up torque (the maximum possible torque) is huge V²/R so that you can crush ice. But isn't that all there is? If you can't get R low, then you have to use gears. But what else is there to consider?

 

[AlephZero]

For consumer equipment like a blender, I don't think it means much more than "the maximum electrical power taken from the supply will never exceed 800W". As you say, how much of that is converted into useful mechanical work depends on many things.

It might also give you the general idea that an "800W blender" would be more powerful than say a "400W blender". Or at least, that's the message the advertisers might want you to get from it.

 

[dillonjerry]

The rating is for the "Maximum Draw" of the device. There is still internal resistance in the motor coil, even when there is no load. There is also a high load during the acceleration of the drive shaft, as there is a 'load' during that phase. Get yourself an ampmeter and measure the current draw if you really want to see the numbers.

 

[geoduck]

The rating is for the "Maximum Draw" of the device.

By maximum draw do you mean maximum current? As you say, the maximum current is at start-up, and is equal to the mains voltage divided by resistance in coil.

I calculated the maximum power delivered by the motor to occur when the current is half the start-up current. Does that sound about right?

V=IR+\epsilon

where V is mains voltage, and \epsilon is the voltage drop across the motor which is a function of only the rotation speed and geometry of coils.

P=I \epsilon=(V-\epsilon)\epsilon/R

Taking the derivative with respect to epsilon and setting it equal to zero, gives maximum power when epsilon is equal to V/2.

When epsilon is equal to V/2, from the first equation I=V/(2R) which is half the start-up current of V/R (since epsilon equals zero when the speed is zero, V=IR at start-up and hence I=V/R)

But for each motor, depending on its geometry, this maximum power (delivered when the current is half the start-up current) occurs at different speeds. For each speed you can associate a torque because torque only depends on the current I, and in:

V=IR+\epsilon

if you know the speed you know \epsilon, and hence I since mains voltage V and coil resistance R are known.

So do all blender makers advertise the highest power deliverable to the motor, even though the highest power might occur at a torque that is not relevant for blending (what you blend determines the torque that your motor will output - you don't determine the torque).

 

[dillonjerry]

I would say, that since you know nothing about how this value was derived from the manufacturer, the only way you are going to get useful data is from a meter. If you really want genuine numbers on this, you are going to have to wire it to a multimeter. I would say that the power rating determines the maximum torque deliverable before damage occurs to the motor. Just a guess . . .

 

[vk6kro]

The power rating just refers to the power used when the bowl is full and the blender is turned to full speed.

This would not include stall or other rare conditions.

It might be overthinking it a bit to be taking derivatives.

Although it does not include any allowance for efficiency, this power rating is a sort of guide to the buyer in the store who is faced with a confusing array of appliances.
In this case, more power might mean a better appliance, or just a more wasteful one.