russ_watters said:
Can someone explain to me how this device, with no electronics, measures speed and time and then performs multiplication or integration?
I've no idea how it measures time.
Like the disc in the meter, some external agency makes it rotate. In the watt meter it is electricity. Here it is someone pushing it along the road.
The little counter attached is made of reducing gears which the wheel makes to rotate.
The speed of the rotating wheel ω(t) is integrated by counting the rotations. So the counter tells you ## \int_{t=0}^{now} ω(t) \, dt ##
You do need to read the counter at the start of your trip, to find ## \int_{t=0}^{start} ω(t) \, dt ##
Then ## \int_{t=start}^{now} ω(t) \, dt = \int_{t=0}^{now} ω(t) \, dt - \int_{t=0}^{start} ω(t) \, dt ## = distance travelled, which was what was wanted.
It doesn't tell you
the speed (well, any speed) but if you had a watch and recorded the time at the start and end, you could divide the distance by the difference in time to find your average (mean) speed.
If you wanted it to multiply, the only way I can think of off hand, would be to mark out a length representing one number, then walk the device along it the other number of times. Of course you want the latter number to be an integer, so you have to scale it as we had to on computers when we had only integer arithmetic available.
Edit 1: corrected error in w
5
Edit 2: I forgot to put constants in my integrals to allow for conversion from radians to turns (2π) and from turns to metres (circumference of wheel.)