Boots of Speed - How fast can they go?

Question

Alice is in a rush! Luckily, she recently divined the location of a pair of boots of speed ®. How far can she get in 10 hours?

Well, upon closer inspection, a slightly disappointed Alice will tell you they're more like "the long-limbed exoskeleton of speed", but here are the basics:

Must have:

• Must preserve the cartilages, bones, skin and general body integrity of the wearer.
• No, it's not a full body suit, so wind (and bugs, yuck) will be a factor.
• Must move significantly faster than a human (duh).
• Must not take off into the clouds with every step (unless that provides the fastest means of transport)

Nice to have:

• Zero or close to zero extra fatigue compared to walking
• Able to handle rougher terrain than a perfectly flat paved road
• Not blow up the place when you get going and avoid throwing shards of pavement concrete into the faces of grandmas doing their grocery shopping as you pass by.

Optional to have:

• A system that does not desperately need a handwavium or other non-portable powersource

Answer 1

We got some options. Let's start with low-tech and work our way up. Also, as a baseline, we're taking Usain Bolt's records, who did the 100 m dash in 9.58s, which is about 23 mph. Obviously, most people do not come even close to this speed. Marathon runners have covered 1 marathon (26 mi and 385 yards) in 2 hours, 45 minutes, and 46-ish seconds. That's 9-ish miles per hour.

Kangaroo Locomotion

Your boots/exoskeleton of speed can be made of a some springy material which allows them to hop like a kangaroo. The nice thing about hopping is that your previous hop can contribute to the energy needed for the next hop. This makes it potentially more energy efficient compared to other forms of locomotion. A "comfortable" speed for a red kangaroo appears to be around 15 mph, with a maximum of 44 mph.

Cleats or Snowshoes

Your boots of speed could just provide better traction over rough terrain. As Lindybiege hilariously relates here, hobnails and cleats improve your grip, which in turn can improve your speed. Not exactly an exoskeleton, but you can take more direct routes and therefore move more quickly than normal.

What About Stilts?

As seen on the records, stilts do not actually help people move faster, despite the increase in stride length you can get from them. Worse still, stilts are powered by the people using them. (For instance, the 7'13" world record for running a mile? Not impressive.) No, stilts will not help you move faster unless they're powered by something.

Powered Exoskeleton

There are some design issues with powered exoskeletons. It seems most of them are designed for either heavy lifting, or to help the disabled. Most products out there are not designed for speed. If you would, you would find they are:

1. Light
2. Very Energy Efficient

I would go with a solid state battery, which stores electrical energy really well compared to many other batteries, and could be potentially recharged by solar arrays. Some simple linear actuators or hydraulics could help get some speed in those legs, but both of those are relatively slow.

Answer 2

I think she needs some heavily tech modified version of Bamboo Boogie Boots.

With a warning label this big, you know they gotta be fun!

Adjustable Height

The boots provide adjustable extensions. To make walking easier, the extensions should retract with each step, this reduces the moment of inertia required to take a step. Think adjustable length powerbocks. The adjustable length allows Alice to choose a comfortable walking/running pace that keeps her level while walking over uneven terrain. Users of regular passive powerbocks have been clocked running at 20mph.

Powered

But Alice's boots are not spring powered passive affairs, they're nano-tech-fusion-fuel-cell powered. They literally eat ground with every step. The boots assist with the pushing, allowing for significantly larger steps.

Cruising

Comfortably striding at 30mph will allow Alice to travel 300 miles in 10 hours. Maybe a little faster than 30mph if she has some goggles, squints really well, or likes the taste of bugs.

Answer 3

Fast Travel By Human Slinky

So I think the killer factor you're going to run into here is air resistance. Since it increases by the square of your speed, going faster didn't seem viable - it will take more and more effort on Alice's part. At first I didn't have any ideas on how to bypass it, but then I thought of divers - someone stretched out, limbs together, designed to minimize water resistance. I think we can use the same concept for your "boots" here.

So starting with the diver position as the basis, the problem becomes the landing. Rotating in air is possible but hurts air resistance. But what about having the arms and hands also be capable of handling the landing/springing?

So then our technique becomes:

1. Spring off from the ground in a diver's position to minimize air resistance.
2. At the last moment, open hands and land. Then spring off with your arms, in a reverse diver's position with your feet pointed.
3. Land on your feet, re-orient. Go back to 1.

The end result is that Alice will travel like a super-efficient slinky, going from feet to hands and back again, minimizing air resistance the whole way. As a bonus, minimizing air resistance also minimizes Alice's bug intersection count.

Details:

1. Suit Construction - we need the suit to act like a spring on both ends. Possibly some sort of advanced metamaterial? Effectively it will act as a form of Regenerative Braking, absorbing the kinetic energy of each landing and turning that into power for the next jump.
2. Travelling this way will be technically difficult (as in, it requires a high level of skill). Based on previous questions I think Alice might be capable of doing it with no assistance, but the average user would probably be in trouble. So I would suggest some sort of vampiric computer assist system - this would be a HUD, a computer with a dumb AI, and micro-motors at each joint. It would take some of the energy of each jump to power, requiring increased effort, but would help the user coordinate each jump and go where they should be going.
3. Priming - Alice will need to "prime" the suit before use by jumping straight up and down. Each jump up will add energy, which will be absorbed and used to help power the next jump. This will build up until the energy lost at each point equals the amount Alice is adding.
4. Environmental and Alice damage - the most efficient angle to jump would be 45 degrees. However, consider that with this mode of movement, the amount of force impacted to the ground - and the amount of G-force Alice needs to handle at each landing and jump - is proportional to the vertical component of her movement. The horizontal component is mostly carried through from jump to jump. So the shallower the suit can move, the less damage the environment and Alice will take. I suspect an angle in the 25 to 35 degree range will work best in terms of functionality vs speed, but Alice might need to experiment. Increasing the height of the suit also reduces the G-forces Alice will experience by giving the suit more time to decelerate and accelerate.
5. Hills - it will be difficult to go directly up hills this way, although going down might be fun. I would recommend switchbacking up and down rather than going direct.

An interesting side effect is that this method uses more of Alice's body - in addition to her legs, she utilizes her arms for half of her movement. This should help with endurance. I will try to dig up some math to support this later, but my WAG is this method of travel would yield speeds in the 30-50 MPH range with approximately the same effort as a light jog, depending on the user's ability and the exact properties of the suit materials. So she could go 300-500 miles in your time frame.

She could go faster for short bursts if she's willing to put in more effort and accept additional environmental/body damage, probably up to 100-150 MPH.