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.
The track of a bicycle back tire [pdf]
11–20 of 83 posts
Re: The track of a bicycle back tire [pdf]
#12Earlier quoted context omitted.
At €70 a pop, my tyres get rotated front to back, as required. Back wears out much faster.
70€ for 15k kilometers or so is really cheap. It's incredible how cheap cycling is per kilometer. At least an order of magnitude cheaper than driving.
15K is an overestimate for most bike tires. It might be accurate for ultra hard commuter ones, but my experience is more like 2k miles for a rear (at 700x25c, single racing bike) and 5k for the front. At that point, the rear is a pretty square shape, with thin tread in the center, and starts to have some interesting handling issues.
Wider, more supple tires might do better than that, the 26x2.2 rear on my tandem is 2k miles in, and probably has another 50% of its life left. Tandems are kind of noted for eating tires due to the loads on them.
Re: The track of a bicycle back tire [pdf]
#13The 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…
While cyclists learn to turn intuitively, motorcyclists have internalized this knowledge. The avoidance maneuver is part of motorcycle license tests in many countries.
Re: The track of a bicycle back tire [pdf]
#14Earlier quoted context omitted.
At €70 a pop, my tyres get rotated front to back, as required. Back wears out much faster.
70€ for 15k kilometers or so is really cheap. It's incredible how cheap cycling is per kilometer. At least an order of magnitude cheaper than driving.
I've just done a back-of-the-envelope calculation about fuel costs, and the extra food you have to eat if you are cycling vs the fuel cost for the car for the same distance is in the same ballpark.
So if we also assume that during the lifetime of the vehicle the cost of fuel you'll burn will be in the same ballpark as the cost of the vehicle, then the total cost of riding the bike will only be around 50% of using a car.
Re: The track of a bicycle back tire [pdf]
#15The 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…
Wow! This explains the trouble I've had trying to ride with the end of my handlebar sliding along a smooth wall near the sidewalk. Thank you!
Re: The track of a bicycle back tire [pdf]
#16The 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…
Wow! This explains the trouble I've had trying to ride with the end of my handlebar sliding along a smooth wall near the sidewalk. Thank you!
I found this short video that very nicely describes what I tried to say with words: https://youtu.be/llRkf1fnNDM
Re: The track of a bicycle back tire [pdf]
#17Earlier quoted context omitted.
70€ for 15k kilometers or so is really cheap. It's incredible how cheap cycling is per kilometer. At least an order of magnitude cheaper than driving.
I've just done a back-of-the-envelope calculation about fuel costs, and the extra food you have to eat if you are cycling vs the fuel cost for the car for the same distance is in the same ballpark. So if we also assume that during the lifetime of the vehicle the cost of fuel you'll burn will be in the same ballpark as the cost of the vehicle, then the total cost of riding the bike will only be around 50% of using a c…
How are you calculating that?
Normally, one assume about 24% efficiency in human pedaling, so that 1kJ of energy going forward = 1 kcal consumed.
Now, fuel cost is anyways a small part of owning a car. My 1k bike + food has lasted me years, while that's less than a newer car loses in value each month.
Re: The track of a bicycle back tire [pdf]
#18FTA: Can we verify the folklore that on a long bike trip the back-tire wear is less than that of the front tire? 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. https://www.sheldonbrown.com/tire-rotation.html : “It is common for a front tire to outlast a rear tire by as much as three to one. Rear…
It depends on how you use the bike. When I was a kid I used to turn the front wheel left/right to go forward instead of using the pedals. This ofcourse wore out the front tire realy fast :-)
Re: The track of a bicycle back tire [pdf]
#19Earlier quoted context omitted.
70€ for 15k kilometers or so is really cheap. It's incredible how cheap cycling is per kilometer. At least an order of magnitude cheaper than driving.
15K is an overestimate for most bike tires. It might be accurate for ultra hard commuter ones, but my experience is more like 2k miles for a rear (at 700x25c, single racing bike) and 5k for the front. At that point, the rear is a pretty square shape, with thin tread in the center, and starts to have some interesting handling issues. Wider, more supple tires might do better than that, the 26x2.2 rear on my tandem is 2…
I was about to agree then I did my own maths.
I used to use GatorSkins - as they are perfect for London cycling. I used to commute 29 miles a day, 5 days a week, plus complete a 60ish mile ride on weekends - so times that by 47 weeks (5 weeks leave where I wasn't commuting) gives 9,635 miles. My gatorskins easily lasted a year, usually more - in fact I still have one of my London tires on my good bike, 7 years later (as the front tire) (I no longer cycle commute and only ride for leisure now.)
So I think those miles really are possible on a good tire. I used to use cheapo tires but ended up changing them 3 or 4 times a year and burning through inner-tubes.
Re: The track of a bicycle back tire [pdf]
#20Earlier quoted context omitted.
70€ for 15k kilometers or so is really cheap. It's incredible how cheap cycling is per kilometer. At least an order of magnitude cheaper than driving.
15K is an overestimate for most bike tires. It might be accurate for ultra hard commuter ones, but my experience is more like 2k miles for a rear (at 700x25c, single racing bike) and 5k for the front. At that point, the rear is a pretty square shape, with thin tread in the center, and starts to have some interesting handling issues. Wider, more supple tires might do better than that, the 26x2.2 rear on my tandem is 2…
2k miles is only 2 months for someone doing decent mileage, but even pros don't train on thin racing tyres.