LW - shoes with springs by bhauth

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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: shoes with springs, published by bhauth on December 31, 2023 on LessWrong.
There's something intuitively intriguing about the concept of shoes with spring elements, something that made many kids excited about getting "moon shoes", but they found the actual item rather disappointing. Using springs somehow with legged movement also makes some logical sense: walking and running involve cyclic energy changes, and the Achilles tendon stores some elastic energy. Is that perspective missing something?
big springs
In a sense, spring elements in shoes are standard: sneakers have elastic foam in the soles, and maximizing the sole bounciness does slightly improve running performance. Jumping stilts are the modern version of spring shoes. They actually work, which also means they're quite dangerous - if what the kids who wanted moon shoes imagined was accurate, their parents wouldn't have bought that for them.
The concept is obvious, but they only appeared recently; they weren't being made in 1900, and that's because high-performance materials are necessary for a net increase in performance. Those jumping stilts typically use fiberglass springs and modern aluminum alloys, and keeping weight low is still a problem. As that linked video notes, even with modern materials, the increase in jump height is only moderate.
This guy made a different type of spring boots for increasing running speed, and 16 million views implies that some people find the concept interesting, but it would be better to start from a proper theoretical analysis and then properly optimize materials and structure. This paper argues for a different geometry, where a spring is attached to the foot and hip instead of the foot and shin. It notes:
To reach the theoretical top speed of 20.9 m/s in Fig. 2, the spring should (i) store 930 J energy and (ii) weigh no more than 1.5 kg
and
state-of-the-art fixed stiffness running springs made from carbon fiber offer only about 150 J/kg
It might be possible to use gas springs to get that kind of performance, though matching the desired force curves is an issue. Another obvious issue is transferring vertical forces to the hip or torso without interfering with movement too much or adding too much weight. Of course, 20.9 m/s is very fast and not very realistic in practice, but some sort of setup with a thick waist belt and gas springs + carbon fiber springs could plausibly make people run significantly faster.
heels
A lot of women wear high heels, despite them causing higher rates of injury and foot pain than other shoes. That popularity has something to do with the effect on apparent body proportions and gait changes making women seem slightly more attractive. As for why certain walks would be more attractive, my understanding is, that's largely an association with pelvis width.
(I remember being told that pelvis width of human women had an evolutionary tradeoff between childbirth problems and walking/running efficiency, but apparently that was incorrect. (Learning about biomechanics of walking hasn't made me any better at walking, and wheeled vehicles on roads are obviously more efficient, but I guess if a Japanese billionaire ever needs me to build an 18m bipedal running robot, I'll be ready.
One of the main reasons that high heels are less comfortable is that there's a greater impact on hitting the ground. Padded insoles help with that somewhat, but the theme of this post is shoes with springs, so here's a high heel prototype with a spring heel. Apparently that design worked OK but was kind of heavy; using fiberglass instead of steel would reduce the weight. I haven't seen much interest in that sort of concept, but maybe it's actually a good idea.
We can also ask: why would high heels have more impact when hitting the ground? I think it's related to ankle position relative ...