I can't seem to find a straight (approximate) answer to this question.
What is the maximum weight of a pedal vehicle (cargo bike, rickshaw etc) an average person can drive at a decent speed, say 15-20 km/h?
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According to Bikes At Work:
Our experience has been that most people can comfortably pull 300 lbs (137 kg) with a typical mountain bike and cargo trailer or cargo trike. How quickly a person can move load of that weight will depend on his or her physical condition. Someone in reasonable physical condition can generally pull a 300 lb load at 10 mph (16 km/hr) on level ground if there's no wind. A person exerting the same effort could pull a load of 600 lb. (275 kg) at a speed of about 8 mph (11-13 km/hr), and a 1000 lb load at about 6 mph.
At the page linked above there is a calculator:
to estimate how much weight a typical healthy individual could transport on a warm day in still air using a bike and trailer or cargo trike. Things like wind speed, equipment condition, and personal health can have an enormous impact on results, so use this only for rough approximations.
Bikes At Work is talking about a bike pulling a cargo trailer but the information can be extended to other pedaled vehicles.
Once you get a weight moving on the flat you can move a lot of weight - given the right gearing given a reasonable level of fitness. Hills are a whole other world.
You question is difficult to answer directly because bike and rider mass isn't a major factor that determines velocity for a given rider power output.
A rider exerts force on the pedals which translates into a force that moves the bike forward. At a constant speed the forward motion is opposed by aerodynamic drag, all the friction in drivetrain components and the rolling resistance of the tires. Aerodynamic drag and rolling resistance only depend in part on mass (heavier bike is bigger, bigger tires have more resistance).
The limiting factors would actually be the acceleration a rider could achieve or the maximum slope they could ride up at a given speed. In these cases rider output power and total mass directly determine the answer.
First we need to agree on the power we are willing to contribute. A trained cyclist may produce 400 W that is already not easy. Then the load is limited by the hill gradient we want to be able to overcome at the reasonable speed (4 km/h I think).
As power = speed * force, 400 W means we can have 400 N at 1 m/s (3.6 km/h, reasonable). If the gradient is say 5 degrees (a serious but manageable gradient for a train), 400 N / sin(5 degrees) = 4590 N = 459 kg. This includes also the weight of the bicycle and the cyclist, not just the payload.
Another limit is the acceleration. We probably want to reach that 1 m/s in 1 second or about, otherwise it is difficult to stay standing. This means moving with 1 m/s^2 acceleration. As the force is acceleration by mass, our 400 N can provide the wanted acceleration for 400 kg that is about just right. Of course, something like a third wheel would allow longer time for acceleration.
Hence it looks like about 300 kg could be transported. For such a load, the friction may not significantly increase with the mass, a big part of the friction comes from the air. While 400 W are not easy to produce for longer, we would only need that much uphill and for starting, so overall may be doable. This payload is also consistent with capacity of the cycle rickshaw bike that is usually built for the two passengers at most.
For a less trained person seeking a comfortable ride, I would reduce the power requirement to 200 W or about. This means that about 200 kg of the total mass, or 100 kg of the payload should be possible.