Using the right math to determine power from a load cell

Hi all,

I have a triangular bracket shaped load cell which is used to see how strong a person's knee is. The bracket has been calibrated for its output signal in mV for an input in Nm in torque.

Thanks a lot!



I am interested in determining the power consumed by the user. Say the user extends their knee for a duration of 3 seconds, the Arduino will record data during all that time, and get a whole bunch of torque values for the 3 seconds duration. Refer to attachment 1.

Now, if I want to convert this data into power, say wattage, how should I proceed mathematically? should I derive the torque data? I need something like these graph conversions (see attachment 2) (this is probably not an accurate reasoning, but just to let you know my final objective is to determine power, if its feasible)

Mr. Google says "Torque is the rotational equivalence of linear force. The relation between torque and power is directly proportional to each other. ... The power of a rotating object can be mathematically written as the scalar product of torque and angular velocity.".
So you are missing the speed of the leg movement.

But Google also says
0.1 W equals 0.1 newton meter/second

So, shouldn't it work if I derived My Nm by second graph?

Its not your math thats wrong its your concept. Power is the rate at which work is done.

0.1 W equals 0.1 newton meter/second

is for linear motion.

You are measuring angular rotation so you need

power = torque * angular VELOCITY

Look at it this way. You are on a bicycle going up a 30m hill.

The work (=energy) you do (Joules = mgh) is the same whatever your speed. (m=mass, g=gravity, h=height)

The POWER in watts is W=J/sec = mgh/t t=time taken

Your experiment can measure the energy expended in raising the leg, but for measuring power you need something like an exercise bike.

From your graph I guess you are perhaps measuring how long a person can hold their knee extended against a restoring force (eg gravity? - or that provided by the load cell?)

The unit you would be measuring is IMPULSE = force * time.

But Google also says
0.1 W equals 0.1 newton meter/second

So, shouldn't it work if I derived My Nm by second graph?

linear power = force x velocity, W = N x m/s
angular power = torque x angular velocity = Nm x rad/s

You are confusing the linear motion equation with the angular one - that "rad/s" is vital

In fact the properly correct units for torque would be Nm/rad or J/rad so
Nm/rad x rad/s = Nm/s = W

You have to measure angular velocity to do what you want - ie add an encoder to
the device.

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