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. (Yes, that's not a practical thing to do even if it's become possible, but neither is this.)))

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 to the impact point. Normally, the heel strikes the ground slightly below and behind the ankle; with a high heel, the ankle is higher, and it's also difficult to rotate the heel so it's behind the ankle while stepping forwards. Should people who wear high heels do the sort of foot stretches that ballerinas do so they can rotate their feet downward more? Would that help? I'm not sure.

If the problem is the impact point relative to the ankle position, then it might also help to have a curved extension backwards from the bottom of the heel, so that the impact point would be on that extension and then the shoe would roll forwards. I'm not sure about the aesthetics or effectiveness of that, but sometimes fashion involves gratuitous novelty, so maybe someone should try it. And perhaps that rearward heel extension could be...slightly springy?

Another problem with high heels is the foot sliding forwards, causing the toes to get crushed. Perhaps that problem could also be mitigated by...adding springs? Suppose an ankle cuff was connected to the main body of the shoe with a fiberglass spring that pushes the shoe forwards; when weight is on the foot, it would shift down slightly, but when the foot gets lifted the spring would push it forwards again. Of course, all that sliding forwards and back makes some friction, which isn't ideal. That happens already because the squashed toes push the shoe back when weight is removed, but it would probably happen even more with a spring.

The usual solution to friction between feet and shoes is wearing socks so that sliding happens between the sock and shoe instead. This is quite effective and socks have become fairly popular. (In fact, I'm wearing socks right now.) In extreme cases, like soldiers or hikers carrying heavy backpacks, it can be a good idea to wear 2 layers of thinner socks; I actually think armies should probably issue double-layer socks as standard.

However, socks with sandals are uncool, and high heels are often sandals or at least sandal-like. Why is that, anyway? My theory is, socks with sandals stay uncool because they're practical and uncool, which means that only people who care more about practicality than fashion wear them, and those people are considered uncool, so socks with sandals stay unfashionable by association. An obvious possible solution is for an outfit to be fashionable or impractical enough to avoid association with uncool german dads. High enough heels are impractical enough to potentially make socks and sandals OK. Combined with a girly outfit, it would be countersignalling: "nobody could confuse me with the uncool sort of person who wears socks with sandals, so I can".