OK,
An interesting little bit of calc and excel sheet working for a Friday morning.
So starting at an OD of 100mm, this roll takes 13 revolutions to roll up the curtain at 7mm thick. The end OD is 185mm.
Whilst velocity increases as it goes up, this is more than matched by reduction in weight being lifted per revolution.
So for one minute, you need an RPM of your roll of 13. That's a lot of gear reduction going on there for a motor doing say 3000 or 1500 rpm
For potential energy alone you need 680W (~1hp).
With starting friction and the friction of the gears, support rollers etc, a factor of 3 or 4 maybe needed. Once it starts moving it all gets easier and faster if you keep a constant RPM.
At the start you're doing about 7cm/sec rising to 12.5 cm/sec at the end. Slowing it down before the end would be a good idea as you will have a fair bit of inertia by then.
So at least a 2kW (3HP) motor I would say, but maybe more if you can get it. 3kw / 5hp should eat it.
A drawing, photo or sketch would be good to see.
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