"It's as simple as riding a bicycle" is a common expression.

But the science of staying upright on two wheels is anything but simple — and we know surprisingly little about the intricacies of how cycling actually works.

CBC Radio science columnist Torah Kachur has investigated some of the mysteries, and looked at the latest research on improving bicycle designs.

What mysteries still remain about bikes?

A better question might be, "What do we actually understand about the bike?"

In reality, we know precious little about how the bicycle actually works, beyond the basic mechanics of "pedal turns gear that turns wheel."

But it's the physics that are really fascinating, and somewhat mysterious — the forces that keep a bike going, the variables that make one bike better than the rest, why a riderless bike seems to be able to stay up and ride straight, and what the best design really is.

Although the basic mechanics of bicycles are well understood, the physics behind cycling remain somewhat mysterious. (Shane Fowler/CBC) Quantum physicist Michael Brooks summed it up nicely in a 2013 article in the New Statesman , when he wrote: "Forget mysterious dark matter and the inexplicable accelerating expansion of the universe; the bicycle represents a far more embarrassing hole in the accomplishments of physics."

Why are there so many questions about bike science?

You'd think with all the interest in high-end bikes, and just how many riders there are, there would be a lot of science in bike design. But that's something of a pervasive myth.

Sure, bicycle manufacturers put a lot of effort and energy into designing new carbon fiber frames, different sized wheels or tires with different thicknesses. But these are typically just educated guesses, as opposed to rigorously tested mathematical principles.

Bike design has really just been a "guess and test" model — we know it works because we can ride it, we just don't know why it works.

Take the riderless bike, for example. You can push a bike along a path and it almost self-steers. It can recover from wobbles to stay upright. That's ultimately the physics behind why bikes are easy to ride, and yet we know precious little about how that actually works.

A 2007 study on this for example concluded, "a simple explanation does not seem possible."

And even a video from the YouTube channel Minute Physics concludes, "science currently doesn't know what it is about the special combinations of variables that enables a bike to stay up on its own."

What do we know about bike physics?

First, we know the reason a bike will continue on its path isn't just because of the force of momentum pushing it there. We know that because if you lock a bicycle's handlebars so that they can't turn, then the bike falls over, regardless of how fast it's moving. So part of this riderless bike phenomenon has to do with its self-steering properties.

Second, a key property to the stability of the bike is its handlebar angle. If you look at a bike, you will see the fork — the part that splits and connects to your tire at the front — is angled.

That angle means the steering axis — the line that the bike is steering on — is ahead of where the tire actually touches the ground. The effect of this is simple — we've all leaned a bike against a wall, only to have the tire tilt and swing out to the side, resulting in the bike sliding down the wall.

This illustration from the Proceedings of the Royal Society shows the angled steering axis of a bicycle. (Proceedings of the Royal Society) That's because the steering axis and the contact point are at different places, so the front tire moves towards the steering axis. That helps the bike self-steer, and makes the bicycle stable when a rider is on it.

If the fork was at a 90 degree angle to the ground and sticking straight up to the handlebars, the bike would basically not be steerable.

What we still don't know is how these forces, as well at the gyroscopic effect of the tires turning, interact with one another. We don't know what the major driver of bike stability is, and how the interacting forces can be maximized to create a bike that is more stable and easier to steer.

How much has bike design improved?

The reality is that bike design really hasn't improved in decades, says Jim Papadopoulos. He's a bicycle enthusiast and mechanical engineer at Northeastern University, whose research on bike science was recently profiled in Nature.

Bicycle enthusiast and mechanical engineer Jim Papadopoulos says bike design hasn't drastically improved in decades. (Northeastern University) "When you turn to the physics of how fast the bike goes, a lot of things that have been put on modern bikes don't look like they do anything discernable," he said.

Bike designers have focused, for example, on crafting lighter bikes, with carbon fibre frames. And a bike that weighs, say, three pounds less might sound impressive, until you think that you are about to load that frame up with a rider who might weigh 150 pounds or more.

So those three pounds lost on the frame simply means you may have gained a two per cent efficiency, which for most of us would account for a few fractions of a minute shorter time for our usual rides. It might make a difference to the best bike racers in the world, but not much to the casual bike rider.

What changes could improve performance?

Most of the companies testing new designs use woefully inadequate and unscientific processes, like rider feedback and wind tunnels — where there is no rider on the bike and the wheels aren't moving and there's no friction on the surface.

But Papadopoulos said there are a few design factors that can affect bike performance.

"The aerodynamic position is certainly important. The clothing can be important for speed. The tires, the chain and the suspension if the road is not really smooth," he said.

"If you're feeling like it's bumpy and you're not very comfortable, then the handlebars can make a difference by being soft, or by being closer to you so your arms are bent a little more."

Those might not be very marketable factors for bike manufacturers, but they work.

That being said, the bike is a well-designed machine because the best machine is still the rider on top of it. The best shock absorber is the bent arms of the rider, and the best generator of a forward force is the power of the legs behind it.

So we can credit the bike for a lot of things — but the real machine is the athlete driving it forward.