Design Calcs for Power Assisted Wheelchair

Update to correct my deliberate mistake...Answer is still about the same, but I am now designing to a 1 in 3 (18 deg) gradient.

A very quick go at some preliminary design calculations for the power assisted cross country wheelchair.
The idea is that the motor should be capable of preventing it slipping backwards on a 18 deg incline (fairly arbitrary, but needed to make a design assumption).

• Based on an assumed mass of 50kg, would give a weight of 490 N.
• This resolves to a force down the 18deg slope of 152 N.
• Which is equivalent of a torque on an 18" (0.46m) od wheel of 85x0.46 = 35 Nm.

Alas this is more than twice the torque delivered by the bicycle hub motor (15 Nm).  Now the motor is likely to have internal gears, but it could be tricky to make some new ones to reduce its speed and increase its torque... [Update - oh no it doesn't - it is shown as gearless].
So it looks like if I am going to use hub motors, I will have to use two of them.  This would probably  be sensible, as it will be better to drive the rear wheels, but also expensive...

I have ordered an electric wheelchair conversion kit off ebay - will see how that goes.  Torque and speed should be ok, but it looks heavy and clunky, so I expect to upgrade it...