wrote:
It is far too long since I did Applied Maths at school but surely the
"track" at least partially supports the weight which is otherwise
completely supported by the cables in the case of a conventional lift.
Surely the work done is much less for this reason ? I'm sure sines or
some other algebraic magic are involved in the calculations but 60 years
have dulled my memory !!


Ignoring friction, the work consists of raising and lowering the cabin
between ground and platform level. So in a frictionless world, there would
be no difference whatever between an inclined and a vertical lift. But
because it's not a frictionless world, there is also work to be done
overcoming the friction because it also moves a horizontal distance on
tracks, so there is more work to be done in an inclined than a vertical
lift.

Your confusion is because you're getting the lower *force* in the cables in
an inclined lift mixed up with the greater *work* to be done in both
lifting the cabin and overcoming the friction of the rollers. The lower
force means that the motor needs less power and torque, but more energy is
nevertheless expended over the longer distance and time.