Palm-sized engineering. Why compact umbrellas with 5 or more sections are stiff.

With the miniaturization of modern bags, compact umbrellas with five or more sections that fit into a size similar to a smartphone have become a necessity in daily life. Recently, even smaller models with six or seven sections have appeared. However, in exchange for this convenience, many users face the problem of the weight at the final moment of opening the umbrella.
In fact, that resistance is a purely physical phenomenon that occurs precisely because the multi-stage structure allows for ultimate portability. This time, we will unravel the true nature of that "hardness" from an engineering perspective.
Geometry creates barriers to power conversion efficiency
The action of opening an umbrella is the process of converting the "vertical force" that pushes up the center rod into "horizontal force" that spreads the fabric through the bone joints (link mechanism).
Compact umbrellas with five or more sections have a very complex rib structure in order to fit into limited storage space. Just before fully opening, the closer the angle of the ribs is to horizontal, the less efficiently the upward force is converted into "opening force." This is the same principle as why push-ups are most difficult just before you fully extend your elbows. Due to their structure, the angle at which force is least easily transmitted is the moment when it is most needed. This is the primary reason why the "final push" becomes difficult.
Correlation between increasing number of joints and "fabric tension"
Multi-section umbrellas have multiple split shafts and ribs, which means they have far more joints (moving parts) than a regular umbrella.
Towards the end of the umbrella opening action, the tension that holds the fabric taut reaches its maximum. When this strong tension is applied to the entire complex structure, it exerts intense pressure on dozens of joints. This pressure increases friction at each point, creating a major barrier to the final few centimetres of movement. Furthermore, if the fabric is coated with a multi-layer coating that achieves 100% light blocking, the firmness and stiffness of the fabric itself also affect this feel.
Protecting the ultimate value of portability
The final hurdle is the moment when the spring of the "repel" locking part is overcome. The inefficient angle, the tension of the fabric reaching its peak, and the friction that increases in proportion to the number of joints. Only after overcoming all of these resistances will you hear the satisfying "click" sound of the locking part.
This feeling is a design choice made to achieve the amazing shortness, a price, so to speak, paid for functionality. We continue to pursue the boundary between functional beauty and ease of use by taking this physical characteristic into account and employing low-friction materials and repeatedly fine-tuning parts. The force that goes into the final push of a " compact umbrella " with five or more sections could be said to be part of the intelligent process of mastering a tool that has been made as portable as possible.