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I saw a video of a treadmill stopping when the power was cut, and it slowed down pretty quickly - maybe within about 2 seconds. I can imagine that if I were jogging in "autopilot mode" at 20km/h and it slowed down that quickly, it could send me into a nasty crash with the console in front.
So my question is, do they ever design treadmills to slow down gradually (say over the course of 5 to 10 seconds) in the event of a sudden power loss?
I can't answer this from a manufacturer's standpoint, but from a physics standpoint.
Just to compare it to something familiar, this is entirely the same as if your car is running along a flat road, and you turn the engine off, you'll still keep rolling. Why? Momentum!
First of all, if you disconnect the power while the treadmill is running, there would have to be an internal battery/UPS there to allow for a soft stop. It's entirely possible that certan manufacturers have implemented this, but I'd argue that it wouldn't be entirely necessary.
Have you ever tried standing on a treadmill that is switched OFF, and leaned forward and kicked back? Have you noticed how you can start the rotation without the treadmill being switched on?
This is because there isn't a whole lot of friction in the engine. You're making the engine rotate, because it isn't locked.
Now, because there isn't a whole lot of friction there, this ensures that if the treadmill is running at full speed, and its power is disconnected, even if the motor is immediately switched off, the momentum of the existing rotation will drag the engine along until it comes to a complete stop.
The more friction there is, the more sudden the stop will be. But as we've seen, there isn't THAT much friction, because we were able to make it rotate with no power.
Again, go back to the rolling car analogy. If you're going at 100km/h, and you turn the engine off, it's not going to stop on a dime. It's going to keep rolling and rolling and let friction to the job.
