I'm not surprised to hear about increasing accidents with increasing e-bike usage. Even for sensible people like us (OK, y'all anyway) there's enough torque in a perfectly legal bicycle mid-motor like the Bafang 8FUN BBS01 to do a wheelie from a standing start if you're careless with the throttle or the starting gear on a Rohloff-equipped bike. Slowing down and stopping is also fraught until the cyclist learns to let go of the throttle and to stop pedalling when he brakes for a standstill. In addition some motors have overruns, i.e they keep turning for several seconds after you let go of the throttle and stop pedalling, and the cyclist has to learn to allow for this, especially in traffic or when stopping. Front wheel motors, rear wheel motors and mid motors also behave differently and have to be adapted to by the cyclist. In addition, the size of and remaining charge in the battery is a factor because because the urge in the motor, whether controlled by throttle, electronic selectable program (stronger or weaker response), or pedelec built-in response (i.e. your cadence and the gear you're in), varies with the state of the battery, so that for the same power delivery with a half-full battery as with a full battery you must, for instance, mash the throttle a little harder, and when you slow down, the battery suddenly can deliver more coulombs because less is demanded of it, requiring a different braking pattern and distance. If the last sentence sounds baffling to you, take heart, it is damned counterintuitive; see
http://thorncyclesforum.co.uk/index.php?topic=12916.0 or search passim for "coulomb" without the curlicues. Note that even a throttleless, single-program, German-nanny-state-type pedelec with a relatively limp battery has its torque very substantially multiplied by gears 1 through 7 on the Rolloff.
The Bosch/Panasonic mid-motors used by many e-bike makers have torque-responsive software built in; Bafang claims the same, but what they have is a software simulation, not a direct measurement like the Bosch/Panasonic motors. But many of the reported rash of crashes must be on bikes with Bosch motors with the torque-management software, which to me points to a complex of further reasons for the crashes, including misdirected expectations of e-bikes.
One likely reason is speed that people are not used to. I read here and there about senior tourers who maintain 25kph or even 25mph, but my average speed with the motor is about 15kph/10mph, same as it was before I fitted the motor, because we talk as we ride; each ride is a social occasion. Dutch bicycle commuter traffic moves at about 15kph, and that is what most of the e-bike converts would be used to; they would have no or little experience of 25kph which almost every pedelec is limited to. 10kph faster may not sound like much on a Thorn tourer-board but it is 67% faster than they went before under leg-power -- for a lifetime. For the elderly, and especially the non-athletic elderly who are lifelong bicycle commuters in The Netherlands, 25kph is probably an adrenaline surge too far, very likely well outside their reflexes. Medical staff are often amazed at the speed of my reflexes, but reflexes that you learn as a young sportsman, especially if learned under stress, are never forgotten: they're like the ability to ride a bicycle; on the other hand, if not learned young, forget about learning good reflexes when you're already old.
