Paper is a poor material for something meant to stand in rain. Its fibres are held together largely by hydrogen bonds, and water is very good at getting between them and taking those bonds apart. A sheet of untreated paper that gets soaked does not just become heavier; it loses most of its strength and sags under its own weight. So an umbrella made of paper and bamboo should fail in the first shower. It does not, because the paper in question has stopped being paper in the useful sense.
The difference is tung oil. Brush it over the sheet and it soaks into the capillary gaps between fibres, then cures. Curing here is not the water evaporating, as it would be with a stain or a thin glue size. Tung oil is a drying oil rich in conjugated double bonds; oxygen from the air attacks those bonds and links the molecules into a three-dimensional network. What was a liquid that could be brushed becomes a solid, continuous film that cannot be redissolved. The paper is still there as a reinforcement, but the surface that meets the rain is now a cross-linked polymer.
Why filling the pores matters more than beading
The usual explanation is that oil makes water bead up and roll off. That is only part of it, and the less important part. Dry paper is a bundle of capillaries; put a drop on it and the drop does not sit, it is pulled inside. Once the pores are filled with cured oil, there is nowhere for the water to be drawn into, so the sheet stays light and keeps its stiffness. A shiny surface that merely repels droplets but leaves the capillaries open would still wick water in at every pinhole and along every cut edge. The oil has to penetrate before it hardens, which is why it is brushed on thin coats rather than laid on as one thick skin.
There is a neat contrast with lacquer, which needs a damp room to harden. Both are traditional finishes that cure into a film, but lacquer's curing is driven by an enzyme that wants humidity, while tung oil wants oxygen and would rather the air be dry. A maker who treated the two the same way would end up with one finish that never sets and another that stays tacky. The workshop conditions are part of the recipe, not background detail.
Why the frame pushes instead of supports
The bamboo ribs are split along the grain, so they are springy and recover their shape after being bent. When the umbrella opens, a sliding hub pushes the ribs outward and the paper is stretched taut over them. From that moment the paper works in tension, which is the one thing a thin membrane does well. It is not being asked to carry a load from below like a roof; it is being held tight so that rain runs along its curved surface and off the rim. A slack sheet would flap, crease and eventually tear at the crease. Tension is the structure.
This is also why the canopy is domed and why the crown gets extra layers. Curvature gives the water a downhill path in every direction, so it leaves before it can pool, and the extra patches at the top seal the one place where all the ribs converge and the paper has to be pierced. A flat canopy of the same materials would collect a puddle in the middle, and a puddle is a slow, steady supply of water to exactly the weakest spot.
Compare that with a folding umbrella, which is a spring with fabric on it. The modern object solves the same problem with metal ribs, a central runner and a catch, and its failure modes are mechanical — a bent rib, a stuck runner. The oil-paper version puts the chemistry into the skin and keeps the mechanics simple. Neither is more clever; they simply chose different places to spend their complexity.
You can see what the oil is doing without waiting for rain. Hold an untreated sheet of thin paper and a cured oil-paper offcut up to a bright lamp. One is a haze of fibres and air, the other reads almost like a translucent membrane. Put a drop of water on each. The first darkens and sags within seconds; the second sits there until it evaporates. No wax, no plastic film, no coating applied in a factory — just a liquid that was allowed to become a solid in the right place.