OK, I’m going to come out and say it: All tires should be flat! Air and a thin wall of rubber have no business holding up the weight of a car. Take the air out and you have a flat tire, take the rubber away and the wheel would sit on the ground. But somehow, putting them together gives you something that can hold a lot of weight. How does a tire do that?
I learned the answer to this question many years ago from David Van Emberg, Executive Vice President of Original Equipment Sales at Michelin, and what he told me was not what I expected but made perfect sense once he explained it.
The Bicycle Model
Let’s start off with a simple example: a bicycle wheel with its three main components — the rim, the hub, and some number of spokes connecting them. For the moment, we will ignore the fact that a bicycle wheel also includes a tire. We will get back to that later.
The spokes connect the hub to the rim and keep it centered inside the rim by being tightened in a specific order by the wheel manufacturer. This puts each spoke in tension and allows the drive torque from the rear sprocket and the brake torque to transfer from the hub to the rim. The spokes also carry the weight of the bike and rider.
But now imagine a wheel where the number of spokes has been reduced to just four:
Would such a wheel work? In theory, yes. The hub is being constrained in all directions and if we now attach it to a bicycle, the wheel should still hold up the weight of the bike and rider.
But what if we make it even simpler by removing the spoke at the top:
What would happen now? If we attach this wheel to a bicycle, would it still hold up the same weight? Remember, the spokes of a bicycle wheel are made of very thin metal and are always in tension. In fact, you could replace them with strong wires and the wheel would still work the same. These spokes don’t do well in compression. Try to compress one and it will buckle very easily.
Putting weight on our three spoke wheel, we would expect it to quickly look like this:
But now, instead of removing the top spoke, what if we removed the bottom spoke?
If we now put weight on this wheel, the top spoke will be in tension and since spokes are very good at carrying load in tension, the hub would stay right where it is.
Of course this is all well and good as long as the wheel stays still. As soon as it starts to roll, the gap at the bottom will soon end up at the top and we will have the same situation we had before where the spoke that started out at the top is now the bottom spoke and will buckle. But this is one of the reasons why we have so many spokes. No matter how the wheel rolls, there will always be at least one spoke at or near the top to carry the weight.
The spokes have another very important job to do though. And that is to make sure the rim stays round. While a bicycle rim is made of steel or some other strong metal, it is fairly thin and narrow and isn’t infinitely strong or stiff. The weight of a rider will force the bottom part of the rim to try to flatten out against the road, just like the bottom part of a tire is flat against the road.
But in order for the rim to be flat against the road, it would need to get shorter in that area.
Compare the length of the red line representing the undeformed rim and the yellow line representing the flattened rim and you’ll see that the yellow line is slightly shorter. Since the rim is made of metal, it really doesn’t want to get shorter, so for the bottom to flatten out, the rim will need to bulge out somewhere else to maintain its length.
What happens in reality is that the rim doesn’t bulge out in any particular area, but instead increases in diameter everywhere except where it sits against the road. This means all the other spokes need to get just a little longer and since these spokes are very strong in tension, they don’t want to get longer and they limit how much the rim can bulge out. Limiting how much the rim can bulge out means it also limits how much extra length it can absorb and therefore how much flattening can happen at the bottom.
In this way, the tension in the spokes and the strength of the spokes make sure the rim stays round even when it is carrying weight.
Let’s Get Back To Car Tires
So how does this relate to a car tire? While I learned a lot from David Van Emberg, I wanted to know more, so I spoke (pun intended) with Jason Bokar, Original Equipment and Technical Sales Manager at Michelin. Prior to his current position, Jason led the Design School at Michelin where tire technology is taught. Needless to say, the guy knows a thing or two about tires and how they work. He provided me with an unpublished book called “Tire Mechanics: Membrane Theory” written by Timothy Payne, PhD at Michelin describing how tires work.
Jason uses this book in classes he teaches outside of Michelin as well and it is full of heavy theory about tires. There is a lot of very serious math in this book which I won’t try to describe here but you don’t actually need all those numbers to understand how this all works.
Tire Construction
Let’s start by looking at how a typical tire is constructed:
Image via: diagramtire (abbsrytire.com)
A tire is made up of a few key parts. These parts are common in all tires, regardless of who makes them or how they are made. There is the tread area on the outside, which is made of rubber, with a number of steel and synthetic belts and plies right underneath. There is another part which is hidden, and most people don’t even know it’s there but is critical to the way the tire works and that is the bead.
The bead is a thick braided steel wire that sits very close to the wheel and is very strong. The bead wire is why you need a tire installation machine to install tires on rims. It’s not easy to just do it with a set of tire spoons like you would with a bicycle tire.
The last major part of a tire is the sidewall, which connects the tread and belts to the bead. The sidewall contains a series of radial plies, sometimes called “cords”, which wrap around one bead wire and run all the way over to the other bead wire. These cords are very strong, and they give the sidewall a lot of strength in tension.
Comparing this construction to our bicycle wheel example, we see that the tread and belts underneath them are analogous to the rim while the bead wire, which sits tightly around the wheel, is analogous to the hub. The sidewall must therefore act like the spokes, right? But does it?
The sidewall of a tire is not very good at carrying load in compression. This is obvious by the fact that when we let the air out of a tire, it goes flat. The sidewall just buckles under the weight of the car, just like a bicycle spoke would if we try to push on it. But if we pull on it, the cords inside will prevent the sidewall from stretching, just like the spokes of our bicycle wheel.
But what about the rim? Our bicycle rim was pretty strong just by itself, but the tread area of a car tire is quite flexible. In fact, take the air out of a car tire and you can deform the tread and steel belts with your hands. Clearly this part of a car tire isn’t very stiff. The one aspect where our bicycle rim and a car’s tread area of a tire ARE similar is in the fact that both want to stay the same length.
The metal of a bicycle rim doesn’t want to stretch or compress and neither do the steel belts of a tire. This means that if any part of a tire sits flat against the road, there must be another part of it that is bulging out just like in our bicycle example. Let’s look at the case of a flat tire. Obviously, a flat tire has a large area at the bottom that is flat against the road so a lot of the tread must have gotten pushed upward and outward to account for the difference in length between the tire when it was round and the tire now that a large part of it is flat. With all the air gone, this isn’t really a problem since the sidewall is flexible enough that it allows the tread area to bulge out to compensate for the fact that part of the tread is flat.
But that doesn’t do us much good if we want to drive our car, does it? How do we get our tire to act more like a bicycle wheel so it can carry the weight of the car?
To Explain This, Let’s Start With A Flat Tire, And Add Air
This is where the real difference comes in. A bicycle wheel doesn’t need compressed air to support weight, but a tire does. Now, I know many of you will be shouting at your screen that a bicycle wheel also has a tire that needs compressed air, and you are absolutely right. But bear with me for a little longer and I’ll explain.
As you can see in this image, with no air pressure, the weight of the car has pushed the wheel down, buckling the sidewall, and making the bottom of the tire go into a flat shape against the road surface. What is not clear in this image is that this flattening has caused the entire tire to grow in diameter slightly in order to absorb the extra length of the part of the tread that is now flat. Here’s what I mean — notice how the flat tire has a larger diameter in this little sketch:
This image shows the concept in an exaggerated way, but you get the point. The yellow line and the red line are both the same length, but because the red line has been flattened at the bottom, the extra length had to go somewhere so the entire circle has grown slightly. The difference in radius between the yellow and red circles is called the “counter deflection” because the tire is deflecting in the opposite direction from the deflection happening at the bottom.
I’ve drawn it in a simplistic way above, but this diagram from Payne’s book shows it in more detail:
Image via: Michelin North America, Inc.
This diagram also shows that there is a transition area where the undeformed tire (at the top) transitions to the flat of the contact area. The tire doesn’t instantly go from round to flat.
But there is something else happening inside the tire sidewall that is not visible from outside. The cords that are running from the tread area to the bead wire normally run in a purely radial direction, shown here as yellow arrows representing an undeformed tire:
But as we set the tire down on the ground and the bottom part of the circle gets flattened out, the tread gets pushed upwards and these cords have to follow along. This means they get skewed and are no longer radial:
The green and red arrows denote the cords after the tire has been deflected and you can see how they are skewed relative to their original position denoted by the yellow arrows. This phenomenon is known as “de-radialization” since the majority of the tire cords are now no longer in a purely radial position. You can also see how the de-radialization is worst near the point where the tread transitions from round to flat and slowly gets less as you go up the tire until you get to the top where the cords are still exactly radial.
Now, let’s start adding air into our tire and see what happens. As the pressure builds up, the air starts pushing outward on all parts of the tire. It tries to force the tread back into the round shape it normally has, but more importantly, it pushes outward on the sidewall, putting the cords into more and more tension. As the tension in the cords grows, they don’t want to be skewed anymore. Imagine pulling on a string at an angle:
The string wants to straighten out. The same thing happens with the cords. They want to straighten out and go back to their original radial position. But they can only do this by pulling the tread back down, reversing the process that previously allowed the flattened part of the tire to push the extra tread upwards. This forces the flat part at the bottom of the tire to get smaller and smaller.
Here you can see how the inflated tire has much less skew in the cords and a much smaller flat portion on the ground as a result. The tension in the cords simply doesn’t allow the tread to get pushed up and outward like it was in the deflated tire. You may also notice that the difference in radius between the yellow and red circles is much less. The counter deflection has been greatly reduced by the addition of air pressure.
What’s happening is that the air pressure is forcing the tread of the tire to form a hoop, and the cords in the sidewall to straighten out. And just like the hub in a bicycle wheel is held up by tension in the upper spokes, a car wheel is held up by tension in the sidewall at the top of the tire. The wheel is literally “hanging” inside the hoop formed by the tread. The sidewall at the bottom has no ability to support the weight of the wheel, and air pressure doesn’t change that. All the air is doing is creating that hoop and putting tension into the cords.
Keep in mind though, as the tire rotates, each cord is changing from a purely radial position to a de-radialized position. Back and forth, back and forth, with every rotation of the tire. The cords are squirming around inside the sidewall as they are forced to change position, and this causes heat to build up. Keeping the right amount of air pressure in your tires keeps this to a minimum and extend the life of your tires. Heat is the enemy of tires, so you can see why keeping this squirming around to a minimum is so important.
Load Capacity
But there is another function of the tension in the cords. The tension in the cords that results from the air pressure is directly related to the amount of load the tire can carry. Since the weight of the car is held up by tension in the cords at the top of the tire, the cords must be strong enough to handle that load. That’s not a very difficult thing to do since the cords are actually very strong. But as the tire rotates, a particular cord will move from being on the bottom of the tire, to being on the side, to being on the top, to being on the other side, to being on the bottom again. Over and over. Only when the cord is at the top of the tire is it under tension. Everywhere else, it is loose. And on the bottom, it is being squashed. This constant change from tension, to relaxed, to squashed, will eventually cause the cord to break, just like a piece of metal does when you bend it back and forth enough times. It’s called fatigue. Air pressure solves this problem by putting the cords into tension right from the start.
Imagine if we stretch a wire between two walls so that there is 100 lbs. of tension in the wire.
If we now want to increase the tension in the wire, we could pull on it close to where it attaches to one of the walls, but we would first have to overcome the 100 lbs. tension that is already in the wire.
If we pulled on it with a force less than 100 lbs. the wire would still remain in tension.
The same thing happens in the cords of the tire. The air pressure puts them under a certain amount of tension, and as long as the weight of the car does not exceed that tension, then the total tension in the cords will not change even as each one rotates from the bottom of the tire to the sides and to the top. This keeps the cords from fatiguing since the tension never changes. It also shows another reason why it is so important to keep your tires inflated properly. Low air pressure means the tension in the cords is less, and now the weight of the car could cause the tension to fluctuate and result in failure due to fatigue.
Tire Stiffness
As we increased the air pressure inside the tire, the amount of deflection at the bottom became less and less. Clearly, a flat, or underinflated tire, has a lot more deflection at the bottom than a properly inflated one. Since the weight of the vehicle doesn’t change as we add air, in order for the tire deflection to reduce, the stiffness of the tire must be increasing.
If we follow along in Payne’s book and go through all the math that describes how a tire works, we will eventually get to the equation for tire stiffness which is:
Kz = 0.685 x √P x √W x √Kλ
Where Kz is the tire stiffness, P is the air pressure, W is the tire width, and Kλ is the counter deflection stiffness. This may look daunting, but don’t worry about all these other parameters, just look at P. As you can see, as we increase air pressure, P, the tire stiffness, Kz, also increases. This makes sense, since, as we saw earlier, adding air to a tire reduces the deflection and since the vehicle didn’t get heavier, in order for the deflection to go down, the tire stiffness must have increased.
Air Pressure is Key
So, after all the math and fancy theory, your tires, at their core, aren’t sitting on a cushion of air, they really work just like a bicycle wheel, with the car’s rim acting like the bicycle wheel hub, the tire sidewall acting like the bicycle spokes and the tire tread acting like the bicycle wheel rim.
I know there is a lot to unpack here and the math behind it is absolutely crazy. But if there is one lesson to learned from all this, it is the importance of keeping the right air pressure in your tires. It is critical to making the sidewall behave like bicycle spokes, and that is the key to how a tire supports the weight of your car.
Your tires, and your wallet, will thank you.
Top graphic base image: Vredestein Tires
Ah thats why it doesn’t matter if you set tire pressure with the vehicle in the air or on the ground. Always wondered that.
“I was told there would be no math…”
Fun fact: the front of a S1 Lotus Elise is so light that if you get a puncture the tyre doesn’t go flat, the sidewall will still support the weight of the car. I read it somewhere and tried it out on mine.
On my dad’s farm, we had a manure spreader and it had tires from a large military vehicle on it. The non-directional treads. After about 25 years, one of the rims rusted out and we took it to put the tire on a new rim. The guy said it was one of the most difficult tires he had ever mounted. Those things had so many plies that they were nearly impossible to stretch over the rim. I honestly think they would support the 3 tons of manure with about 5 psi in them.
How did older non-radial tires work? I’m guessing pretty much the same, just not as well, plus, explaining this without radial tires would end up using the “thought experiment” of imagining individual radials in the sidewall instead of just continuously flexible rubber. Anyone have any insights into how old, bias ply tires differ from radial tires in the context of this article?
They work the same way except that instead of the cords being radial, they were placed in a cross-hatch pattern. The concept is still the same but instead of the cords de-radializing, the cross-hatch pattern would get skewed. The air pressure would put tension into the cords and they would seek out the balance they had when the tire was built, which would force the skew out again.
And here I thought it was the concrete I put in my tires that kept them from going flat…
https://www.youtube.com/watch?v=eusgXEa22oE&ab_channel=Garage54
This hurt my brain
I know right!? I remember having a shower thought that tires are just balloons that we drive around on. I was trying to figure out how t.f. they work. Huibert did a good job explaining it.
Based on the Goodman diagram, I thought adding initial tension would increase the fatigue phenomenon.
Am I missing something?
Adding enough initial tension means that you eliminate load reversal completely, it’s just in varying tension rather than tension/compression cycles.
I googled the goodman equation and one of the components is the fatigue limit for reversed loading, if you aren’t reversing the load maybe it doesn’t apply.
Thank you! I’m a little rusty on fatigue issues. The only mechanics I’ve done recently were only rigidity oriented (how to prevent an aircraft fuselage from moving more than 0.1mm) !
Exactly!
The article says “The air pressure puts them under a certain amount of tension, and as long as the weight of the car does not exceed that tension, then the total tension in the cords will not change even as each one rotates from the bottom of the tire to the sides and to the top. This keeps the cords from fatiguing since the tension never changes.”
I understand that the load reversal has been eliminated, but there’s still a cyclical variation in tension, no? In that diagram showing tension on the wire, the section on the left would have 100lbs plus the force applied, while the section on the right would have 100lbs minus the force applied. The two numbers could still be positive, but should not be the same, correct?
Or am I misunderstanding something?
Nicely explained. Thank you.
I will now forever look at cars as being suspended by their hubs from above rather than sitting on something below. It is not something I had thought about before, but as an ME it makes perfect sense, and is plainly obvious once considered.
Some more detailed implications, as I see it:
– the math would get more complex with bias ply tires as opposed to radials
– the bead and hub are actually suspended not by the tension in the upper cords, but by the difference in tension between the upper cords and the lower
– the suspension concept also explains why the bead must be so very tight. Breaking down the analysis a step further, the hub rests on the lower half of the bead, which pulls through hoop stress on the upper part of the bead. The hoop stress results in an inwardly-directed radial stress component, the portion of which is on the upper half of the bead must oppose the suspensory tension of the upper sidewall cords. So, if there were not enough hoop stress put into the bead from its pretensioning in mounting, the bead would be pulled away from the rim by the tension of the upper cords, and leak air since the tire is tubeless. Unless you had rimlock tires mounted.
Interestingly, heavy trucks do not have very much bead tension, or very much pretensioning during installation. They are much higher pressure tires though, so that helps to hold the bead to the rim.
You’ve got the right idea here. If you look at the cross section of the tire I showed, you will se that the bead wire is quite large. That’s why you need a tire installation machine to install them on the rim. That wire is seriously stiff! And yes, tension in this wire is what carries the load of the car from the bottom of the bead wire up to the top where it is connected to the cords in the tire.
The bead wire isn’t really in much initial tension though. It stays in contact with the rim because the air pressure pushes it against the lip of the rim plus, the wire is very stiff and strong. If it were in a lot of pre-tension from mounting, it would be almost impossible to break it loose during dis-mounting.
Ok, that makes sense, that the bead couldn’t be too much pretensioned otherwise installation and removal would be impossible.
So then, I imagine the bead area needs to be a sufficiently inward-turned lip towards the centerline of the wheel in order to provide enough air pressure to produce the inwardly-directed force that I was supposing came from bead wire pretension.
So, don’t put bicycle tires on your car?
Now you tell me!
Unless it’s a BWW i3
On a certain level, this is intuitive. If one puts weight on a balloon the part of the balloon with the weight on it will collapse, and the other parts of the balloon will expand, so tires need structure to prevent that expansion in the areas not supporting weight. However, it is good to see the math and science, especially as a person who pretends to be a race car driver.
I found this wheely informative
Not tiresome at all!
Hardly any bias.
Too bad it’s written for lugheads and knobs.
And this thread is terrible.
* tread
A punny thread like this is where the rubber meets the road here at Autopian, but this joke will probably fall flat.
Nah I think you nailed it. There’s a lot of hot air in this tread though.
I camber for the puns and have no reason to be offset.
I’ve always just thought of it as something being attached to the side of a balloon that’s rolling. I think that’s a nice, simple analogy.
Good article, but I have to take issue with this. The reason you can’t have that 3-spoke configuration is that you don’t have a tensioned structure anymore. That doesn’t mean that in a tensioned, spoked wheel that the top spoke carries the load.
If you measure the spoke tension around a loaded wheel, most of the spokes will not (or barely) measurably change compared to the unloaded condition, including the top spoke, but the bottom spokes will lose substantial tension, which makes sense since it’s in the flatten zone of the rim that you drew. This loss in tension is like a wooden wagon wheel bottom spoke increasing in compression—both are the active location and direction of the resultant force countering the load. So arguably in a tensioned, spoked wheel the bottom spokes “carries” the weight while the top spoke is just one of the many other spokes keeping the wheel tensioned.
As @CSRoad mentioned, Jobst Brandt’s book “The Bicycle Wheel” explains this quite well. He has FEAs for the bicycle wheel under radial loads (as well as braking, etc.) that shows that the load affected zone in the bicycle rim actually has slight bulges just in front of and behind the bottom zone too.
Brandt was a Porsche engineer in the 1960s working mainly on suspensions like you. He’s the best-known engineer among cyclists because of his bicycle wheel book, but also consulted on various bicycle parts including tires, cyclo-computers, saddles, etc., leading big rides in the SF Bay area, promoting riding in Europe, and for being the engineering voice for a couple decades on the newsgroup rec.bicycle.tech. Here’s an archive of his thoughts/hot takes on VWs, Porsches, and Corvairs:
Porsches and VW beetles (Jobst Brandt; Mark Drela; P. L. Albrecht) (yarchive.net)
Thanks, the rec.bicycle.tech archive link was a blast from the past.
Actually his newsgroup persona could be a little overbearing, but I exchanged emails with him and he actually could tolerate questions from idiots. (-; A nice guy, he seemed to like most things mechanical from trains to bicycles and we even discussed the valvetrain on my drag car at one point. His passing was a loss to a lot of people.
Thank you for posting this. I had not heard of Jobst but I will certainly look him up now.
A good article again, thanks.
Bicycle wheels, not so simple, they are a two edged sword of tension, especially heavily dished wheels, which are a b*tch to center and keep the spoke tension at the rim reasonable.
I recommend “The Bicycle Wheel” by the late Jobst Brant, a good read.
It spun my head as I was a person who was convinced the hub hung on the spokes.
Jobst also found humor in airless bicycle tires, which historically have resurfaced every few years it seems.
I think you’d enjoy it.
Jobst Brandt is essential for understanding bicycle wheels.
As an engineer (albeit of the electrical/electronics variety), I do love me a good Huibert article – and I especially enjoyed this one. Thanks for the well written and extremely insightful article, Mr. Mees!
Excellent article! I’ve never really thought about how a tire works, so having it explained is very cool.
I never would have thought of tires and air pressure in these terms, but you laid it out brilliantly. Its wonderful getting to learn more about how some of “simple things” don’t actually work how you’d think.
Wow this is too complicated for me!
*peruses Craigslist for gently used hovercraft*
Hmm. What about run flats?
“Run Flats” have reinforced sidewalls with higher flexural modulus that allow them to support the load without air pressure. They also give a harsher ride, and many change them out for a more compliant ride. I suspect his goal here was to give an informative conceptual overview without glazing over too many eyes of the casually curious.
I was under the understanding that many run flat tires had a big foam donut inside that acts as a solid tire if the air pressure isn’t supporting it. Is that not true, or is it not always true?
The ones I’m familiar with do not have foam inside, and are only recommended for up to 50 mi. at up to 50mph. to get you to a service shop to replace.
Ive seen both, but most run-flats have a stiffer sidewall that is capable of carrying load once the air is let out. They do have a much harsher ride since part of the job of a tire is to absorb energy coming up from the road and a flexible sidewall is much better at that task than a stiff sidewall.
many change them out for a more compliant ride
It’s me. I’ll take better tires for the 99.999% of the time I don’t have a flat, and a repair kit in the trunk for nails and whatnot. For anything more, it’s AAA.
Ditto. 2/3 of my current fleet don’t have spares, but a patch kit and a pump. In all my years of driving all the hoopties and hotrods I’ve owned, I’ve had a flat precisely once. There are more 9s behind that decimal than you let on.
I’ve had all the ones you didn’t have. Right now, my car’s had 3 in 12 years, two I changed, one by road assist. Over the years probably half dozen others. Spares got me home when today’s cars would have left me in a hotel room.
Once every 4 years isn’t all that often… For average American driver miles, that’s about once in 50K. How much does the spare weigh vs. the patch kit and pump? What are the fuel savings? How much trunk space are you giving up? I’m not saying swapping out a spare isn’t easier than a patch, but if you add the time to just do the patch on the side of the road (mostly just waiting for the pump to fill the tire), you’re over and done with right then and there. With the spare, you still have to get the tire patched, swap them out a second time, there’s more cost associated with that, and so on. The patch kit and pump really just makes more sense if you zoom out from the 30 minute window of the event itself and look at the bigger picture. You’re already late, and have a bullet proof excuse. Why not save yourself more time and money later, and you get more space and better fuel economy for the 99.(many, many 9s)% of the time you’re not actively dealing with the flat on the side of the road.
Btw, you’re plugging and not patching the tire. There’s a meaningful difference.
Your logic overlooks damage that can’t be repaired roadside, this still occurs. Some deal with road conditions or risk factors differing from yours that possibly increase both frequency and degree of tire and wheel damage. Plug and pump won’t help with more than a clean poke in the central tread zone. Different degrees of insurance for different circumstances, yours isn’t the only valid approach.
Semantics aside, sure. More damage could occur. Granted. For the sub 0.00000000001% of the time you get a flat, what fraction of that occurs in a non-PLUGGABLE manner? For those ultra super mega rare occasions, most insurance policies have you covered. If not, you’re out a tow. I never said it was the only way. If I worked construction or lived somewhere with a lot of construction, I’d probably err on the side of a spare. I don’t know what sort of conditions you’d need to be concerned with splitting side walls on a regular basis though… I live in the mountains above Denver, and frequent unpaved roads (often the only roads up here). Only thing I can think of short of failing to miss major debris in the road that might cause such a thing is a sharp rock, and that has never occurred to me or anyone I know that wasn’t doing some serious off roading.
Huibert articles are the best articles!
So what changes between tires with a low profile vs high profile sidewall? The angle of the deflection is smaller despite the distance moved staying the same due to the smaller bead diameter it’s “hanging” from vs the outside diameter?
Edit – I’m asking from the perspective of why do tires with big sidewalls feel softer than low profile ones mathematically.
Lemme guess: one, the additional height of sidewall allows a bit more lateral deflection in operation; two, the additional volume of air enables tire tread and sidewall to temporarily deform over road defects more easily. Note that additional sidewall is well known to protect rims from impact, too.
Lateral deflection is such a satisfying phrase. It seems like it should be a science fiction jumble of syllables, but nope.
I love these articles where I almost pass thinking I already know much of it (in this case from bicycle mechanics and observation and thinking when I was a tire jockey), but learn something new and other things become a little more clear.
What might be an interesting note, my antique bicycle has wood rims and the spoke tension is much less. Part of it is probably that the wood can’t support too much tension, but I wonder if it’s also down to the difference in fatigue resistance. The ones I ride are modern clincher wood wheels with 2mm spokes, but the original tubular rims have spokes like piano wire. I don’t know if that’s down to convention of the time or engineered to the lower tension the rim would require. It was a high end bike for <1912 and the engineering in the frame and bottom bracket is impressive*, so I figure it’s the latter, but a lot of things also seemed to be done as much by intuition as calculation back then.
*Iver Johnson were also a gun maker, so the tubing was bored-out billet steel that was then rolled to desired wall thickness, which is just nuts to think of anyone doing today (nobody would as we have better methods, but just thinking of the relative cost perspective is interesting). As welding was in its infancy, the tubes are soldered per standard industry practice, but the lugs are internal, so all the tubing joints together kind of like a mockup with no external fillets. I can’t quite remember the BB now from when I rebuilt it about 10 years ago (damn, I should probably tackle that again), but it was their own design, very well made, apparently forged (IIRC), with the crank in 2-pieces, meeting in the center with a kind of radial fork joint and the ability to fine tune the bearings was well thought out and machined. Taking it apart without knowing how it was built was a bit of an adventure as it wasn’t intuitive for someone familiar with relatively modern stuff and I had to make a tool for it, but I didn’t break anything.
Modern spokes are 2mm because much smaller than that and the threaded ends fail at the stress raising root of the thread. Take that feature away and you can take the same load through a thinner wire.
That makes sense—like butted spokes (which I was surprised to find on a ’61 Columbia Firebolt). If they weren’t buried in a box somewhere, I’d take a look at the original wheels—they were tensioned differently, but I can’t remember what the deal was. They might have been tensioned at the hub.
Also, I just noticed I typed “soldered” when I meant “brazed”, though I suppose they’re the same idea.
Great explanation and it really highlights the importance of keeping proper air pressure in the tires! I had never thought this deeply about it but so glad you did and could pass it on!
You’re welcome!
Fun fact: Plane fuselages are stronger and stiffer in flight when they are pressurized for very similar reasons.
And yes, the fuselage also inflates and gets larger in diameter with the pressurization.
Hence one reason that gives me anxiety to fly. The constant expansion and contraction of pressurization and depressurization will eventually stress harden the aluminum which doesn’t really give much warning before breaking. I know they engineer all that in when designing the plane but it still sits in the back of my mind 36k feet up in the air.
This is why airplanes have such a strict inspection schedule. They strip the entire interior out of the plane and inspect the structure for cracks. Look up the British Comet for an example of what used to happened before this was fully understood.
Oh, I know they get inspected frequently and throughly. But I also know how people are, and things get overlooked or ignored. If I’m not mistaken, wasn’t there a flight out of Hawaii many years back that once it pressurized, a large chunk pealed off sucking a flight attendant out with it. And if I remember correctly, people commented on how they saw cracks in the fuselage as they were boarding. Flying may be the safest form of travel but the thought that all maintenance is being done by people not much different than the mechanics I’ve worked with most of my life, scares me.
Where do I get the “I heart Huibert” t-shirts again?
Thanks for the hub-spoke-rim = bead-cord-tread analogy, that really clicks for me. Spoked wheels and pneumatic tires really are pretty magical. This is clearly why bicycles are so awesome: because they typically combine both!