The math and physics and engineering behind bicycles is so cool. Such a "simple" device, but so many interesting things to dive into. I wrote my thesis on spoke patterns for the wheels [0]. Another cool thing is how the steering of a bicycle works. You don't really turn the way you want to, you actually turn the other way first to initiate so the bike moves from under you, and you then lean the other way to actually turn. This is why, if you're for instance biking close to a curb and want to get away from it, you really can't and it feels like the curb is "sucking" you closer and closer. Since it "feels" wrong to first turn towards it, but without doing that you actually can't get away from it.<p>[0]: <a href="https://news.ycombinator.com/item?id=10410813" rel="nofollow">https://news.ycombinator.com/item?id=10410813</a>
FTA: <i>Can we verify the folklore that on a long bike trip the back-tire wear is less than that of the front tire?</i><p>I’ve never heard that folklore. I thought ‘everybody’ knew back-tires wear out a lot faster because the load on them is higher and because they’re the one being powered. <a href="https://www.sheldonbrown.com/tire-rotation.html" rel="nofollow">https://www.sheldonbrown.com/tire-rotation.html</a>:<p><i>“It is common for a front tire to outlast a rear tire by as much as three to one. Rear tires have more weight on them, and also have to deal with drive forces.”</i>
I've probably been a computer scientist too long, but this feels like a problem that requires complicated maths or a very simple computer simulation. In this case they end up with equations that can (for the most part) only be solved numerically, so simulation seems just as effective. But then they deduce that in general the amplitude of the path of the rear tyre is always less than that of the front. And while we can demonstrate this with simulation, we can't prove it.
As much as this may seem like merely an interesting dive into the subject of wear and tear, the broader world of bicycle geometry and design is fascinating. I used to race downhill and the tire path of the bike's design combined with how that path changes as the rig goes through its suspension travel is integral to feeling stable/planted. When you see some of the patents regarding modern bike design, especially in the world of suspension linkage, its mind boggling how much depth is put into these machines. All so I can go fast down a hill, fall on my ass, and get covered in mud.
TLDR: “We have shown that if the path of the front tire of a bicycle is specified, it is possible to derive the corresponding path of the back tire.”<p>Possible I am wrong, but there is a critical assumption, that being: “With additional inspection, knowing that the tangent vectors from the back-tire point with fixed distance to the front-tire track, we can find which way the bicycle went.”<p>As result, if the front and back tires do not maintain a fixed distance, prior research does not apply. Examples of factors that might produce minor variations include: suspension, untrue wheels, etc.