The plain of Soggi experiences a constant rainfall. Can a rain powered vehicle be built according to the following conditions?
The plain of Soggi experiences a constant rainfall of 10 cm per day
Flooding doesn't occur because the plain is floored with a porous volcanic rock that naturally drains into the Big Wet Lake.
The inhabitants have smoothed the rock in places to make roads and other flat areas
Wood is plentiful but non-vegetable materials (including metals) are expensive and have to be imported.
In this pre-industrial society, stationary rain-powered water-wheels are in common use to power mills and other basic machinery predominantly built from wood.
The vehicle is to be made from a wood very similar to oak. Minor metal components can be used but minimally to avoid expense.
The vehicle must fit into a 3 metre cube to satisfy local laws. There are no draft animals in this world.
This must be a go-anywhere vehicle that does not require any special infrastructure beyond the existing flat-and-level roads - no digging canals or building railway tracks or regularly spaced "charging stations"
Someone has the bright idea to power a moving cart by harnessing rain-power. This will consist of a water-wheel that drives the wheels by a system of leather belts.
The inventor decides that the minimum useful speed is walking-pace (say 1.5 m/s) and that the vehicle must be able to carry at least him (he weighs 60 kg) but preferably a much heavier load.
The vehicle will travel over levelled volcanic rock and has a similar configuration and technology to this one from the 1800s.
Reality check: Are there any obvious flaws in this plan that makes it highly unlikely to work
Some people are suggesting alternative inventions which I find fascinating to read. However they aren't true answers because I'm asking solely about the vehicle and conditions specified above.
In-story justification: This guy wants to set up a door-to-door collection and delivery service. He needs to use existing roads and driveways. He can't start digging canals or building large engineering projects. See condition (8) above which wasn't added by me but with which I agree.