The track of a bicycle back tire [pdf]
tlakoba.w3.uvm.eduThe 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.
I have taught several kids to ride bikes. My instructions were very simple: ride, and if the bike starts tipping to one side, turn the handlebars that way.
With humans, that's about all you need to say. You very quickly feel how the lean changes based on the steering input, so righting yourself becomes obvious. And when you inevitably overdo it and end up leaning the opposite way, you turn the bars that new direction. WOBBLE WOBble wobble straight.
Do the same steering physics apply to riding a bicycle on rollers? That's so much more difficult I wouldn't be surprised if the fundamental steering behavior is changed somehow.
Iirc what makes rollers so tough is that the contact patch is much shorter on the roller than on the road, so the wheel turns more easily. Your reactions need to be that much quicker.
I had a winter of long roller rides (3.5 hours was the longest) and by the time I hit the road again I could ride on the white line with no effort. I think the dynamics are the same, just higher stakes on the rollers!
This is one of the challenges of riding on such a thin (narrow) line (like a plank - or even just the painted line on the side of the road) is so difficult.
The thing is that in order keep a srtraight line on a very narrow path, you need much finer motor control of your arms, a good 'feel' for your bike, some good components, and the ability to remember to be able to look farther in front of the bike, but keep your awareness of where you are steering based on your inputs to the bike, but not looking down.
If you want to be impressed by one of the best in the world at steering difficult scary /r/sweatypalms courses:
https://www.youtube.com/channel/UC9kOkY1nYc0uADWRiRH64Rw
Watch the "do a wheeelie" vid on his YT home -- doing a wheelie on a train-rail, and jumping to the other train-rail without losing your wheelie or momentum - but all his vids are mind blowing.
So same thing as spinning on black ice in a car.
Same instructions, different reason. In a skid, your tires have lost traction and are no longer pointing in the direction they're moving. You steer into the skid to return to the usual "static friction" regime instead of the "dynamic friction" state of the skid. Only once your tires are gripping the road again do you have much ability to control your direction.
The way this is described in a control systems framework is that the dynamics are non-minimum phase. A cool high-level video from Mathworks[1] explains in more mathematical detail. Being an experienced rider but having not looked into bicycle models in detail, I think it would make intuitive sense if the dynamics were only NMP for some operating points, particularly very low roll rates at very low roll angles. Or equivalently, the system behaves differently when it's in a banked turn (moderate roll with low roll rates) because gravity is starting to couple into the steering more. There is an angle where the steering switches modes depending on the geometry of the bike, and I think this is why road bikes "feel" "twitcher".
[1]: https://www.youtube.com/watch?v=jGEkmDRsq_M
Edit - also OP, very cool thesis work!
Road bikes are twitchier because they have less trail. Even 25 year old MTBs are twitchy compared to modern equivalents succumbed to the fashion for negative stem lengths and slack head tubes trying to imitate DH bikes.
Good point and makes sense - probably the reduced trail dominates most of the feel. I wish I had time to dive into a model to see if there really is any non-minimum-phase behavior.
Also, I skimmed the following to help my understanding; others may find it useful too: https://www.cyclingtips.com/2018/11/the-geometry-of-bike-han...
While cyclists learn to turn intuitively, motorcyclists have internalized this knowledge. The avoidance maneuver is part of motorcycle license tests in many countries.
This is also why it's impossible to balance a bike without at least a tiny amount of speed. (Even a trackstand that looks completely still uses tiny amounts of forward and backward wiggle to allow the bike to move sideways under the rider.)
The handlebars aren't really used to steer the bike, the way most people think of steering. What they do is shift the bicycle further away from under the rider, which then, due to the bicycles naturally self-stabilising, steer to upright itself.
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!
Also about half the time when you hear about a cyclist dying because they "lost control of the bike" in traffic this is what happened. Car passes slow and too close to give you room to countersteer and you fall into and then under it.
I found this short video that very nicely describes what I tried to say with words: https://youtu.be/llRkf1fnNDM
There are people who can ride bikes on rails. I would not be able to do that. It seems impossible, but I guess they are able to minimize the amplitude of deviation from straight to such a low value they can correct tiny deviations with shifting their weight and manoeuvering the front wheel.
Well, that explains why I did an endo riding my bike down the ramp of a Ryder box truck when my tire hit the edge of the ramp—fortunately I was wearing my wool beanie. It was Burning Man, 1998. Seemed like a good idea at the time
FTA: 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 tires have more weight on them, and also have to deal with drive forces.”
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 :-)
How does that work? I don't see any way that just turning the bars would imprint forward momentum.
By "pumping" it's quite easy: https://www.youtube.com/watch?v=5tVlAlZ9wfM
You can to some extent do it without that much motion as well. Basically, you're "falling" to one side and getting momentum, and then you "save" the fall by twisting back getting the bike under you, and that instead puts the momentum forward.
I would like to add that you are not just "turning the handlebars" - you need to apply a lot of force to get the forward action to take place.
Pumping is fun skill, easy to get the hang of with a little dedicated practice, and a prerequisite for BMX racing or any advanced MTB riding. Its also extremely inefficient for forward motion. You don't see any TDF guys using pump motion unless they're saving a crash.
It was 40 years ago, what I remember it works but not very good. As they say lower down, you need more movement to actually get any sort of speed forward. It was just something I liked doing while waiting for someone to show up.
Yeah - that just seemed completely wrong based on my experience. I've commuted by bike for years, and my back tyre is always the first to go.
Same. Also same on my road bike, which I bike in a very different manner (not as much stop&go, short turns etc). And I even do most of my breaking using the lever connected to the front tire.
From my experience, front tires only wear of age, not use. Backtires experience (frictional) shear forces, pushing along the earth. This erodes the surface.
Cornering and braking does wear the front tire, and it is more notable when mountain biking where cornering tends to be more forceful and the tire knobs concentrate forces on more noticeable parts of the tire.
And from those glorious big fishtailing skids we do as kids...
never stopped being fun this is why fixed gears are still a thriving niche
I picked up riding again after .. 40 years and a car braked in front of me and I did a perfect skid stop without even thinking. we are really amazing things.
This has been my experience as well. The back tire gets worn down and the front tire lasts until the rubber starts cracking from age.
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.
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.
2k miles is only 2 months for someone doing decent mileage, but even pros don't train on thin racing tyres.
The 2k figure was from a Michelin lithion 2, which was a decent for the price cheap (15 eur) 700x25 tire. It’s not an event tire. Mainly chosen for its relatively price and predictable performance (1 compound).
The tandem and wider tires are not the cheap ones though, they’re Rene Hearse, roughly 90eur or so. I’d say they’re worth it, but they are about the same price as my last car tires.
My Schwalbe Marathon Plus last around 20k. That's about five years for me.
And if you can do your own maintenance, and buy used frames and parts, you can probably say 2 OoM difference. You'd spend more on the calories that fuel your commute than on the bike and accessories.
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.
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.
https://biketips.com/calories-burned-biking/ says I burn ~600kcal to ride 20km.
600kcal is ~200g of bread + 20g of butter. Bread costs about 5€/kg, butter costs 2€ / 250g so 600kcal is roughly 1,25€.
My car uses about 6l gasoline per 100km, current price is ~1,60€ per liter, so 20km need 1,90€ of gasoline.
So if I just eat cheap food riding a bike is cheaper.
If I eat at McDonalds, then 600kcal is a hamburger with medium fries, which costs ~4,50€. Then taking the car is cheaper.
This is quite surprising!
The costs of sitting idly every time you travel, compared to doing some low-impact cardio over the same distance, for trips shorter than about 3 miles, definitely adds up over the years.
The results looks absurd because the math is ignoring a lot of real-world considerations.
There's really no question. Cost of bike maintenance vs car maintenance. Societal cost of road wear due to a huge car vs a tiny bike. Burden on healthcare system, regulation and enforcement for dangerous driving habits. We all pay so much for cars, even when not driving one, when usually a bicycle is perfectly sufficient.
maintenance and road wear are clear winners for bikes being cheaper.
Healthcare burden, I'm not so sure. Even with the massive difference in usage, street car tracks in Seattle cause a lot more healthcare burden to bikers (and pedestrians) than car drivers. There's certainly a benefit from exercise, but bicycling also has more exposure to injury during use, and not all of them are superficial injuries. Add in things like poor form inducing nerve injuries and it looks even worse.
Thousands are dying directly from car usage ("accidents"). A lot more indirectly from being sedentary, and lots of shortened life spans due to the pollution.
So it's not even comparable. It's probably multiple orders of magnitude better on a societal level to be biking. Even better if we got rid of the cars causing the cyclists to be killed.
There were apparently 454 non-traffic bicycle deaths in 2020[1], compared to 38,824 traffic deaths reported by NHTSA in 2020 [2]. I don't feel like bicycles are doing 1% of the trips in the US, even though they're more than 1% of the deaths. I feel like non-traffic death eliminates car vs bike deaths, but captures the basic idea that bicycles are more immediately risky.
All sorts of terrain issues that are minor for a car are dangerous for a bicycle, especially at higher speeds. Where I live, it's very hilly, so it's hard to go anywhere on a bike without hitting speeds of at least 25 mph at some point on the journey. Mechanical issues, unexpected objects in the road, or errors in piloting at that speed will result in an injury for sure.
[1] https://injuryfacts.nsc.org/home-and-community/safety-topics...
[2] https://www.nhtsa.gov/press-releases/2020-traffic-crash-data...
Found some data on person trips by transportation mode [1] and person miles by transportation mode [2]. Based on that, about 75% of miles are done with car/truck/suv/van, and 0.2% with bicycles; but trips are more balanced, 80% by car/truck/suv/van and 1% by bike.
So I think the fatality rate per trip is probably about the same for bike vs car/etc; but the rate per mile for bikes is significantly higher. It'd be interesting to look at comparable rates from say the Netherlands or another country where bicycling is better positioned.
[1] https://nhts.ornl.gov/person-trips [2] https://nhts.ornl.gov/person-miles
You are also 17× more likely to pay the ultimate price if you travel the exact same amount on a bicycle (according to UK stats).
Edit: Source: https://assets.publishing.service.gov.uk/government/uploads/...
Are you making a point? What is it?
The comment I replied to makes the point that bikes are better "no question" from the cost perspective since car maintenance is obviously more expensive.
It is a more complex equation than that..
Probably the hardest variable to quantify is the risk of injury/death.
While I agree it could be better if everyone used bikes, but in the current reality if I choose to ride my bycicle, I'm going to share the road with 2000Kg metal boxes which are sometimes driven by distracted drivers, and I'm not willing to take that risk.
So even if I combine all the costs associated with both options, and bikes are cheaper objectively, it will still be more expensive for me.
But you can't compare the negative impact of one thing to the positive impact of the other vehicle. The bikers get hurt by the cars so that is negative on the car account, not negative on the bicycle account.
I think bicycle calorie burn calculators are basically just nonsense. 600 calories is a ton to burn for a relatively short leisurely ride. Maybe 5x too much.
I have an older garmin that has told me I have burned 9000 calories in a weekend, and uh, I didn’t. No evidence for that, but I simply don’t believe it. Bicycle tourists would have to have wild food intake to sustain that for weeks.
I agree 600kcal is on the high side, but I don't think it's as far off as you think. Most estimates I've seen are between 300-500kcal per hour, depending on effort.
It depends a lot on the bike and on the route. On a road bike going down a straight, flat road wearing lycra 20km/h is zero effort. On a city bike loaded with groceries going through urban environment with a bunch of traffic lights 20km/h average is quite an effort.
What if the added calorie need comes from rapeseed oil or something really cheap? :D
But I think there's some factors at play here. One is that if I didn't commute to work, I would have to work out some other way to get my daily movement in. So it's not necessarily that I eat more just to bike. I just use that energy to move myself to work instead of on a treadmill going no where.
Another interesting factor is what about electrical bikes? The amount of kWh needed to move a small person vs multiple tonnes of car should make it a huge win.
If we do this kind of calculus, it’s probably worth including the expected health costs of not exercising. Especially if your normal meal is a hamburger at McDonalds :-)
Even when just sitting around your body requires energy.
I'm pretty sure the 600kcal are what my body burns on top of the base metabolic rate, not the total amount burned in an hour.
2000kcal of noodles costs like one Euro and fuels you for like five hours of cycling, 100km open road maybe. An average car burns 7l or 12€ of gas. But if you're concerned about calories, just buy an ebike.
You should still need to exercise if you drive.
You're not actually saving anything in the long term, though.
Let's say you start with brand new tires on both wheels. Let's further suppose that you completely wear out your rear tire in 1 year and your front tire in 4 years. If on the first anniversary you rotate and place the new tire in front, you'll need to repeat the procedure after 9 months, and then every 9 months after that. On the 4th anniversary you'll have bought 5 tires: on the 12th, 21st, 30th, 39th, and 48th months. If you simply replace each tire as it wears out without any rotation, on the 4th year you'll have bought 5 tires, 1 to replace the front tire once and 4 to replace the rear tire 4 times.
True. What you do have is a more consistent / good front tire, which is important for handling curves in wet weather. So still worth doing, instead of riding with a front tire on its last 20% of life.
IME as long as the tire is not flat there's no difference in handling between a new and a worn front tire, at least on asphalt.
Road tires wear unevenly on the sides due to crowned streets. You should also flip rotating direction, assuming unidirectional tires.
Rear tires do must of your braking. If you hit the front break too hard/fast, you flip over the front tire, hit the rear brake hard/fast and you burn rubber/lose traction.
As a bicyclist, I use my front brake vastly more than the rear.
I don't even have a rear brake.
Weight is transferred to the front on heavy braking, and if you have proper technique, you will not go over the bars. The front tire does all of the actual stopping.
The rear brake is very important for initial braking, in order to transfer weight to the front, which allows harder braking without locking up the front tire.
When you initially hit the brakes, your braking potential is split around 50:50. At absolute maximum potential braking force, your rear tire is near lifting, so it's around 100:0.
That said, if you only have one brake, it's better to have it on the front than the rear.
Interesting. I have to replace the shoes on my rear brakes about 10 times more often than my front brakes.
But then, if I'm not going very fast, I only use my rear brake. That might explain it.
I have to replace the shoes on my rear brakes about 10 times more often than my front brakes.
That just means that you brake with your rear the most. I'm talking about maximizing braking potential.
I've been riding motorcycles for decades and it's drilled into you to practice panic stops regularly, which habituates the transition from 50:50 braking to 90+% front brake. I don't think many cyclists do this exercise, but they'd probably benefit from it.
Do you ‘ride the brake’ to control your speed a lot?
Agree that front brake is more important.
However, I like to have both (and suggest you do too!) because:
1. Brakes can fail
2. In slippery and inconsistent conditions, locking up the rear is preferable to the front
If you don't have a rear brake, perhaps listen to people who have front and rear brakes, and thousands of kilometres of riding.
I have literally seen people flip over their handle bars by solely using their front brake going downhill.
I have done thousands of KMs of riding.
Cool, I've done thousands in a month. Do thousands every year.
But if your bike doesn't have two brakes as you have stated, it doesn't matter how many KMs you ride, because you are not getting that experience to inform you.
I’ll back him up - I do thousands of kilometres a month and log component changes when they happen!
My rear brake pads last about 5000km before they need a change, my front brake pads last about 3500km.
It would appear by observation of the consumables that the front brakes do the most work. This is in-line with my expectations from the experience riding the bike and established knowledge about how weight transfer works in vehicle braking - there is a reason cars always have bigger discs on the front and some cheap hatches still have drums on the rear.
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.
Where else would the department of theoretical physics engage itself in modeling bicycle tires than in the Netherlands?
Somebody had to advance Feynman's work on spinning plates.
How on earth science.uva.nl was inspired to pair up plates, add some thickness and a drive chain will likely remain a mystery for the ages.
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.”
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.”
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.