Incredible bike wheels that aren’t round

Bob Forgrave

Simple questions and their logical follow-ups often start a cascade of learning in an interesting direction.

So let’s do that today with bicycle wheels:

1. Why are bicycle wheels round?
2. Do bicycle wheels need to be round? 
3. Can they physically be made in other shapes and still work? Do they work well?
4. Under what conditions might a non-round wheel work better than a round wheel?

The commonly used answer to the first question is that all wheels are round because they ride better; a shape with a constant distance from center to outside—also known as a circle–is the only way to keep the axle a constant distance from the ground, for a smooth ride. 

But in reality, even with the standard definition, we’re already going off-road, because a shape with constant diameter is also . .  a sphere.

Is it possible to make a functional bike with spherical wheels? Absolutely. Here’s one with basketballs as wheels:

But, even this bike still has round wheels—perhaps the roundest wheels of any bike ever made!

In addition to this 3D perspective, we can also add a fourth dimension.  Do all parts of a bike wheel need to be round at the same time?

Surprisingly, that’s a No:

And yet… we’re still talking about round wheels, in one form or another. Which brings us back to Question #2…

Do bike wheels need to be round?

After all, artists and graphic designers have fantasized about different wheel shapes for bicycles for years…

From a design standpoint, triangular wheels have an interesting ability to parallel the frame tubes. The fact that the wheels can’t turn is irrelevant. This is about design.

Similarly, from a design standpoint, there’s nothing like the traction footprint of a square wheel—that never turns.

So given that these “wheels” don’t actually function as wheels, is it possible to make them actually work? Is there a better version?

We’re not exactly looking for this level of breakthrough, just the ability to make square and triangular wheels work at all!

This is when we bring in the fun-loving engineers. Hold onto your bike seat…

Three unusually shaped bike wheel designs that actually work.

Engineers have an amazing ability to make the impossible possible. Consider the triangular wheel and this image.

At first glance, this design models the triangular design above, with wheel lines that parallel the frame lines. But this one is ridable, even though the triangles don’t spin, thanks to a moving belt guided by 6 smaller wheels.

So if the triangles don’t spin, are they still wheels? Does this bike have 2 wheels, 4 wheels, or even 6 wheels?

It’s beginning to become clear how a square wheel would work:

It might look the same as the square design on the outside, but there’s a whole lot more going on inside. This one actually works. (Image courtesy of The Q and Sergeii Gordieiev)

This design, by engineer Sergii Gordieiev, combines the simplicity of a designer’s square-wheel bike fantasy with the reality of a bike that is possible to ride. It contains elements of the triangular-wheel bike above, but carefully concealed inside a frame that looks just like a tire. Brilliant!

And here’s how he built it, with the magic inside:

But even these amazing, functional wheels don’t turn. Can we still call them wheels? And can a wheel that actually turns be square?

Mythbusters even did a segment on this exact topic, seeing if square wheels work if you go fast enough. Do they help with climbing dirt hills? For an unusual thought experiment that we’re exploring, we sure have a lot of company…

Big surprise…actually turning square wheels are not comfortable to ride–so far. Despite the spinning, we’re not counting this as a design that actually works. Besides, it’s not a bicycle wheel.

But consider this design for a near-triangular bike wheel.

In this case, as demonstrated in this article at TheQ, the roughness of a near-triangular wheel is countered almost perfectly by mechanically separating the bouncing of the axles from the ride at the seat, using front and rear shocks–a method first seen at Burning Man in 2012.

In a physics sense, this bike relies not on a constant radius from the axle to the ground, but from a constant diameter; as the radius decreases below the axle, it increases above the axle, keeping the bike seat in perfect stasis. This also provides a foreshadowing about what physical situations would favor a non-round wheel over a round wheel.

But first, a slight diversion…

Under what conditions might a non-round wheel work better than a round wheel?

Maybe if smooth riding is boring?

On April 1, 2023, custom wheels manufacturer Nobl introduced their Novl oval wheel geometry. The April Fool’s prank went over so well that they continued it after April Fools Day…

But for the rest of us who actually prefer a smooth ride, the answers lie in the physics observation about a constant diameter, not a constant radius from the axle.

If we focus on a constant diameter with variable radius, anything is possible—even highly functioning square gears!

And let’s not limit ourselves to squares.

So what does this mean for unusually shaped bicycle wheels?

It means that a variable radius is OK… as long as the ground is variable in a precisely matching way.

With the right matching road, you can have a…

Functional triangular wheel that rotates smoothly…

Functional square wheel that rotates smoothly…

…or a functional pentagonal wheel that rotates smoothly. (Images courtesy of Herman Serras)

Note that as the number of sides gets greater, the matching parabolic arc to ensure a linear axle movement and smooth riding gets shallower. With infinite sides (i.e., a circle), the matching shape of the road would have infinitely flat parabolic arcs (i.e., a straight line). 

So mathematically, while a circle is far from the only possible rotating wheel shape, it is the most optimized for most bike travel.

After all, when are you ever going to come across a surface optimized for a square wheel (called an inverted catenary surface)?

Ok, maybe in the physics department of your local college, if you’re lucky. Yep, it’s a thing across multiple colleges. 

Riding on square wheels at Macalester college (Image courtesy of The Mathematical Tourist)

For the rest of us, we’re stuck with regular roads.

Not much luck with square wheels on flat roads.

But now that we’ve explored all the alternatives, round wheels are definitely the way to go.

Happy riding (except possibly on washboard-worn gravel roads, which resemble catenary surfaces),

Bob Forgrave

Bob Forgrave is president of Flatbike, an
ecommerce company offering full-size folding bikes
and kits to make any bike take up half the space.