A unique mode of transport that would only work in an O'Niell cylinder would be a giant swing, suspended from an axle in the middle. Grab the swing, run as fast as you can, take your feet off the ground and you'll continue to move until air resistance slows you down.

The obvious draw-backs are that it only works for travel around the circumference (east and west), there may be problems passing trees and tall buildings, and there would be a lot of air-resistance on the kilometres long rope.

You could imagine a super-thin rope with a peddle-powered propeller contraption on the end, that would allow you to 'fly' without having to generate lift. This would be as fast and efficient as a bicycle on a super-smooth road. Add a rudder and you could steer around obstacles.

However I think it would work best when used as a barge or crane for transporting large heavy cargo. Much like one horse could pull a 50-ton barge along a canal, you could load tons of cargo onto a swing, push it to gradually accelerate it up to walking speed and then allow it to coast for miles.

Being sensible (alas!). The most obvious form of non-powered transportation inside an O'Neill cylinder would be the bicycle. It's non-polluting and healthy too. Why go past the obvious. A well-established and mature technology.

If we don't count food as fuel, how about plain old wings?

Climb far enough up one of the end walls, and the gravity gets low enough for people to fly on their own muscle power (potentially aided by thermal convection). Don't worry about the air getting too thin; with the gravity dropping off, there'll be breathable air all the way to the center of any reasonably sized O'Neill cylinder -- at the center, there's zero gravity!

So, you make yourself a pair of flappy wings, climb to the axis, lock the wings out, and launch. Build them so you can flap with the big muscles in your legs, of course. If you don't want to go all the way to the other axis point, just drop down a little and, when the gravity gets too high to maintain your altitude, actuate the latch that locks the wings in a gliding position and glide -- and potentially land anywhere on the interior surface.

If the inside gravity is kept a bit below Earth normal, and the air pressure is kept a bit higher, it's even possible take off from level ground with wings of this sort -- I've seen calculations suggesting that on the Moon, you could fly this way in about 1.5 atmospheres.

I think using some futuristic version of powerstriders would be pretty interesting. They already look pretty scifi as is, but you could imagine a fair amount of upgrades to make them more practical.

To start with, it would be cool if they could be retracted, maybe stored behind the wearer's calf, with the blade folded in some manner. Perhaps the blade is made of a material with asjustable rigidity to allow this.

Adding different "soles" to the stilts for different terrain could also be practical. Sharp studs like on soccer shoes could help adherence on damp soil, whereas ridged rubber could give better adherence on rocky terrain. Maybe they even come with a mountain climbing setting.

If they are retractable, maybe they are also adjustable, so that they can serve as just plain stilts for wading through swamps or other shallow bodies of water.

These are however quite energy consuming if I remember correctly, so they wouldn't be best suited for long distance travel.

For long distances, you could install a system of zip lines that would only require large poles to depart from and netting to land safely. It is possible to pull yourself along one, but I believe that it's quite strenuous on the arms.

Hang gliders and para gliders are two different heaver than air, non motorised crafts that can allow for fairly long distance travel without any prior installations. However, sustained flight requires thermals for lift, which I don't think you'd get in an O'Neill cylinder. You also need an adequate landing zone, for safety reasons.

You could have a pedaled aircraft (such as used to cross the English Channel). The more you pedal it up in the air, the less the 'gravity' will be, so you mainly have to expend energy when taking off.

A small pedal-powered airship could also be useful. You wouldn't need as much energy to get it up as a heavier-than-air aircraft, and it will quickly reach an altitude where the air is so thin that it stops rising. You would need to anchor it when it is parked, however.

Leverage the angular momentum of the O'Neill cylinder, itself. When one is standing on the surface of such a cylinder and drops his ice tea, it is not his own feet that get the bath, but the person next to him. In fact, the dropped beverage (aside from being a travesty in lost deliciousness) is attempting to move in a straight line while the person who dropped it is following a curve. That causes the path of the dropped beverage to appear curved from the perspective of those riding in the cylinder.

To make use of this, simply have a series of conveyor belts that simply wrp the cylinder at different levels. One level simply loops in place. A second spirals "clockwise" to allow transit to one end of the cylinder. The third level spirals the other direction to allow transit to the other end. If the conveyors move on frictionless rollers (while not being frictionless themselves), so much the better. This gets full movement capabilities at only the cost of keeping the cylinder rotating.

For a more complex approach, have two concentric cylinders rotating at different speeds (the inner having a greater angular momentum to simulate a similar gravity level as the outer, but possibly a different level for reasons that might be considered necessary in story). Radial movement would be as simple as transitioning to the other cylinder for a time. Lateral movement can be achieved by capturing the rotational differences and transferring the differential rotational energy into lateral conveyance of any type. There would be more energy involved in keeping the cylinders rotating at their prescribed speeds but transit would be "free".

Parabolic Tunnels

There has been some research into the idea of a tunnel in the shape of a parabola underground, where the momentum the vehicle gains dropping to the bottom of the tunnel is enough (or nearly so) to get it back up to the top on the other side of the parabola. You'd have to deal with friction, of course, so some sort of maglev would be required, though it could be simple static magnets if you can make them strong enough. Articles I've read quoted 1 hour from New York to London as a possibility with this method.

The major difficulty of course is digging a tunnel deep enough into the Earth's crust. And of course there's a limit to how far a single parabolic tunnel can travel before its bottom would sink below the crust. Point is, it gets you from A to B using almost nothing but gravity and momentum. (Elon Musk may already be looking into this, not sure if the Boring Company is doing parabolic designs or not...)

Horses were actually really quite good at what they did.

We abandoned horses as a method of transit mostly because they weren't as fast and their effective operational range (for a reasonable timescale) was therefor generally quite a bit lower.

Additionally, there are space/infrastructure concerns that scale poorly as a function of population density - They fit less gracefully into an urban environment, as they need room to run when they are not being used as transit.

The environment you describe is small enough to be crossed on horseback in a reasonable time, has plenty of open space, and sounds like it has low population density - horses would be an excellent fit. As an added bonus, you have no real need of spending manpower or resources on maintaining roadways, as the horse is an extremely effective all terrain vehicle.

I bet, at childhood you did a trick with a balloon: first inflate it, then release it :) So it hops over the room loosing the air pressure inside until deflated.

So why we can't create such a transportation method? You sit on a chair with, let say, small wings and attached balloon. Prerequisite: the balloon is inflated. Once opening a vent, you start moving (and this is your pilot skill to adjust the trajectory to desired one, he-he). Once the balloon is deflated, you're grounding down, closing the vent, inflating the balloon back (using old-school mechanic pump, let say, leg-driven one). Repeat the deflation hops until you're done from point A to point B. We can name it "sky golf" or something like that, what do you think?

If you are looking for something human powered, practical, suitably futuristic and still mostly unknown, look no further than the Shweeb:

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Using a network of multi-level rails and remote-controlled switches, trunk lines and branches can be built to achieve any density you require. The low weight of the rails and the pods lend themselves really well for commuting between vast skyscrapers and for the occasional steep slopes electrical motors can be built either into the pods or into the rails themselves. As a bonus, these motors can act as generators as well when the pods are going downhill.

Controlling the switches can be either done manually via remotes inside the pods or optionally the user can enter a pod at an end terminal, specify their destination and a routing algorithm sets the switches at the proper time just before the pod swooshes by.

For improved speed and efficiency multiple pods can travel close to each other in trains, reducing air resistance, and if outfitted with proper bumpers or towers, the stronger travelers can assist the weaker ones (or even move cargo pods). How's that for a post-scarcity, neo-communist utopy?

Hamster balls the size of humans!

They can also traverse water!

https://www.youtube.com/watch?v=tg7i30pXARQ

And be bouncy enough for the jumping trick!

And, if pressurized, could be used for the occasional EVA!

Every family needs one! Or several!

Since the cylinder has artificial gravity, there is one "human powered" transportation method that uses the variable gravity of the cylinder.

The person simply climbs to the spin axis, either at the end cap, or raised platforms spaced along the cylinder, and then while in the zero g zone, aims along the spin axis and pushes off as hard as possible. They wear a "wingsuit" so they can scull through the air while in the zero G zone, and also to provide the means of a controlled descent through the air as they drift into lower "altitudes" from the spin center and become subject to the spin gravity.

A skilled user could presumably travel several kilometers in the spin axis and then make a controlled glide to their destination on the ground.

For some reason, everyone seems to forget exactly what an O'Neill cylinder actually is. It's a spinning tube, that uses the fact that it must apply a force to you to accelerate you in a circle; this force is what simulates gravity.

The cylinder can only apply artificial gravity if you're in contact with it...

If you're not touching it, then you'll be floating in space as per any other space station; with this metal can spinning around you.

As such, jump (hard enough - springs may be required) in roughly the right direction, and float your way there. Sure you have to adjust the jump direction to account for the fact the ground is spinning.

Far less effort than a bike.

A climbing rope mechanism, if it's a cylinder then you tie both ends to and have a crank like mechanism that when rotated have a platform climb up the rope, seeing how a straight line is the shortest distance between two point you will reach the other end faster then walking around the cylinder & as a bonus you don't waste ground space that can be used for buildingfarmingetc.

Instead of using the power of humans, passively use the power of the O'Neill Cylinder itself.

At least, use an inevitable feature of the O'Neill Cylinder design: Wind.

Instead of horse drawn wagons, you'd have sailing wagons barrelling down your dusty dirt roads. Most of the daily traffic would go with the wind, anti-spinward, but it doesn't take much to learn how to tack like sailing ships do, allowing you to go in any direction you choose, including spinward.

You can even have sailing wagon races along your plains, and "X-Treme" land sailing competitions in any rocky terrain with bicycle- or tricycle-like vehicles.

SIMPLE ANSWER...... A BICYCLE.

VARIANT ANSWER...... A Recumbent Bicycle.

Note. Water on many alien worlds is as hard as iron because it is frozen and you said 'by land' and 'by water'.

(Not quite sure on the physics here.)

I think if you have a river that loops around the habitat, it will end up with a constant flow, because the water has inertia and will act against the movement of the station. You can then get in a boat to travel antispinward (I think?) without needing to row. (This is basically the conveyor belt answer, but water is easier to come by.)

The energy actually comes from increased drag on the station, but there's no energy needed at the point of use, and any nature reserve needs rivers anyway.

I think you have some basic misconceptions about what "fuel-free" should mean (food is fuel! etc.), but the question is an interesting one. If your goal is to allow transportation without needing large portable energy supplies that would be unsafe or impractical, human-powered transportation is an option, but will significantly impact nutritional needs for keeping everyone fed.

An alternate perspective that might be interesting is reducing or eliminating energy consumption per unit distance traveled. Fundamentally, you only need energy to accelerate/decelerate. The reason we need to spend energy per unit distance traveled is all a matter of friction and wind resistance. If you setup a system of vaccum tubes/tunnels with very-low-friction pods/vehicles inside, then essentially the only energy expenditure for travel via them is maintaining the system and some minimal amount of acceleration/deceleration proportional to the speed you want to travel at.