Hollow Wheels in F1?

[Ciro Pabón]

I'm pretty sure they are not bringing down the strength. On the contrary, this could be the reason: BMW would obtain a lighter wheel if they use "caisson beams" for spokes. The farther is the material from the bending axis, the better.

Actually, I fail to see why they do not use two discs, parallel to the wheel covers, so to speak, with internal flanges to adsorb torsional and lateral forces. That would be the ideal "static" structure.

I don't know how much good design goes into racing wheels, but some I've seen appear as terrible designs from the structure point of view.

I'm not sure if I'm taking this OOT, but if you don't "get me" at first sight, then maybe you could try to do this exercise I use when I teach how a bridge works. This is for 9-10 years old kids, so forgive me if you find it simple.

Let me assure you that if, and after, you follow this exercise, all the equations that your brains know become feelings that your hands "understand"... and that's what makes a good scientist or engineer: good, "knowledgeable hands". So, pick up a piece of paper and try it!

[Carlos]

Simple is always better. Every class of 9>10 year olds has a precocious little one that will ask for more than a folded paper lesson. Here's a little Java applet for that one, (hopefully 5 or 6 little students), that does T, L, U beams. Just whip out your laptop for the inquisitive tiny people.

http://www.strucsoft.com/applets/BeamSt ... amStrength

[ginsu]

I don't get it, are you guys arguing that a U-beam section is stiffer than an I-beam section?

From everything I know from all my engineering classes, if you want a lightweight and stiff beam in Bending in one direction, you want an I-beam section with the long axis aligned with the bending axis. The I-beam section maximizes the area moment, and thus makes the stiffest structure. If the I-beam is the stiffest structure, then you can use less material and thus it would also become the lightest structure.

Remember, BMW had those wheels specifically made for them. O.Z. makes regular I-beam sectioned wheels for all the other customers. The fact is that BMW went out of their way to have O.Z. design something different. Usually a customer would not tell a supplier how to make their products unless that customer wants a specific requirement to be met.

My whole point is that BMW had O.Z. make different wheels because they have a customer requirement that prioritizes air volume hence a different structure for the spokes.

[Ciro Pabón]

No, we're arguing that solid beams have less strength than the same amount of material arranged in a hollow beam. So, the argument about "less-resistance compensated by larger-air-chamber" seem improbable.

And yes, a caisson is more rigid against lateral flexure than an I beam. The I beam is superior only against shear forces, and that's good for a bridge, but not for a spoke. That's one of the reasons of the tendency toward caisson beam designs for large bridges. The argument is even stronger in the case of several I beams vs one large caisson, as is the case in many bridges, but I think the general argument holds for this thread.

[ginsu]

Another, better BMW wheel pic from Australia Free Practice. Obviously BMW are the only team running wheels like these. Heck, they don't even have a sponsor logo. I really would like to know the scoop. Scarbs? Anyone?

And yes, a caisson is more rigid against lateral flexure than an I beam. The I beam is superior only against shear forces, and that's good for a bridge, but not for a spoke.

You might want to review some Fundamentals of Engineering. And the flexure equation:



by far, an I-beam cross-section has the largest area moment for a beam of given cross section, thus reducing the stresses due to bending by the greatest amount.


Also, this is the shear stress equation:



In no way does it take into account the shape of the cross-section of the beam, thus any beam that has the same area regardless of shape will have the same average shear stress.


Also, the term caisson does not specifically refer to a beam cross section. Please be more specific with your terminology.

In geotechnical engineering, a caisson is a retaining, watertight structure used, for example, to work on the foundations of a bridge pier, for the construction of a concrete dam, or for the repair of ships.

No, we're arguing that solid beams have less strength than the same amount of material arranged in a hollow beam.

This, also, is absolutely not true, at least for the bending case.

Circular Cross-Section


Hollow Circular Cross-Section


It should be obvious from the equations that a hollow cross-section of the same diameter will have a smaller area moment, and thus the beam will be under greater stress which will require the use of more material to equal the strength of a solid beam.

[Reca]

It should be obvious from the equations that a hollow cross-section of the same diameter will have a smaller area moment, and thus the beam will be under greater stress which will require the use of more material to equal the strength of a solid beam.

Obviously a solid beam will be stiffer than a hollow beam of same diameter, for nothing else than the latter is the result of the solid one with lot of mass removed, clearly it’s going to be “weaker”; which is why there’s no point in that comparison, adding more mass to a section, in a bad place, isn’t exactly the way to make an efficient structure, it will be stiffer but also much heavier.

What you should compare, that is what Ciro meant, are two beams, one solid and one hollow, of same mass, which means that the solid one has a smaller diameter. In that case the amount of material is the same, so the same is the weight, but since in the hollow beam it’s arranged more distant from the centre it results in a larger area moment for the section. And the larger the outer diameter, the better (up to the point the wall is so thin that you have instability and/or manufacturing issues).
Obviously all these intuitive things are also evident from the formulae for the area moment you posted, just write the relationship for d to have same area as the tube with diameters Do and Di, and you’ll see it.

[ginsu]

Just wanted to update this because it has been soooo long and I think the technological advantage is still there but OZ might not be as secretive since they've been manufacturing them for like 3 years now.

Not long after I started this thread I received a personal message from an OZ engineer with pictures showing that indeed they were manufacturing a hollow wheel. Nobody believed me and I swore to him that I would not post his pictures so I kept this quiet for a little over a year (I am the only one who knew outside of BMW/Sauber and the OZ engineers-I was just waiting for once a tire would shred itself and everybody would know OZ's secret wheel, but somehow it never happened)

Finally, Scarbs messaged me about a year and a half after I created this thread and he told me he finally got a picture of the OZ wheels with the tires removed, so at that point it became public knowledge. I am assuming that Scarbs updated his column with this information.

Well, I guess I just want to end this thread with a bit a proof and that is a public posting of the OZ wheel with Scarbs confirmation of its design.

http://scarbsf1.files.wordpress.com/201 ... 030483.jpg

Oh yeah. The reason for a hollow wheel is obvious! Increased Air Volume -> Lower Spring Rate on the Tire for the same given tire pressure -> Better Traction.

I still think this wheel is the tits of the field. I'm surprised other engineers are not running them, but maybe they don't know about them.

[ringo]

You guys aren't considering rotational stress.
It's a very interesting topic.

[747heavy]

not sure, if it is the "tits" of F1 wheels, but hollow wheels/spokes are used in other applications too, since a while.



the spokes not allways increase the airvolume of the tire, allowed it would make sense to do so.





like in this example


Enkei racing wheel/rim as used in the JGTC



the word >> Cored Cavity Technology << is used in this context.

[Richard]

An I beam is best for bending applied in plane, assuming thick flanges and thin web. That only applies over a short span because I beams are poor when it comes to lateral torsional buckling over long spans(ie they flip sideways). However, the span/depth on a wheel is tiny so we can ignore buckling.

Actually a truss is more efficient than an I beam but that's just complicating things.

However, the spoke is not in simple single plane bending. The spoke is having to transfer the rotational acceleration/declaration from rim to hub. It is also transferring the lateral forces from rim to hub. There is also an element of compression to transfer the weight of the vehicle.

That's a lot of forces in a lot of directions, so a hollow section will provide maximum strength in all directions for a fixed amount of material. Or least material for a constant stiffness. An I beam would be a lot less effective because it is only strong in one plane.

The above points are all well and good, but bending is rather irrelevant. I'd say the short span/depth ratio on an F1 wheel would lead to the spokes acting with a strut/tie action not a bending action, a bit like a stub or corbel. The principle of a hollow sections being a more effective use of material still apply.

I'd conclude that the hollow section is used primarily for least weight/material, the benefits (or not) of the air volume are secondary.

....

I have a question too - is the open hollow section a simpler manufacturing process? That might relegate the air volume issues to tertiary consideration

------------------------------------

edit to add - Scarbs says "Sauber continue to use OZ Racing wheels with hollow spokes" no mention of air volumes or spring rates. http://scarbsf1.wordpress.com/2011/01/3 ... -analysis/

[DaveW]

Oh yeah. The reason for a hollow wheel is obvious! Increased Air Volume -> Lower Spring Rate on the Tire for the same given tire pressure -> Better Traction.

The idea is seductive, but I think tyre stiffness (spring rate) is proportional to pressure amongst many other parameters, but not including air volume, at least not to first order. Apologies....

Modified heat transfer characteristics might, I suppose, help to make pressure more stable.

[riff_raff]

The drawback with hollow spokes is that they cannot be forged, they must be cast. The best wheel construction for strength and fatigue is forged and 100% machined.

The cored spoke Enkei wheel is a cast body that then has the rim sections spun formed and finish machined. Not as good as forged, but better than conventional casting. Having good mechanical properties in the rim area is important, since this is the part of the wheel that most often takes impacts. A forged or spun rim section is less likely to fracture than a cast rim section under impact. A bent rim can still hold tire pressure, while a cracked rim will not.

Although I don't think it's a process used to make race wheels, some high performance production light alloy wheels are made by "squeeze casting". It's a neat process.

http://iweb.tms.org/Communities/FTAttac ... asting.pdf

riff_raff

[JaymzVsTheWorld]

Sauber has OZ hollow wheels.

[Caito]

Ok, so a hollow wheel would provide a larger volume.

Why would you want more air volume? I believe you have greater cooling with more air volume.


As to a lesser spring rate, why would you want a smaller spring rate? Why would you want the tires to work even more than the suspension?


bye!

Caito.-

[riff_raff]

Caito,

While hollow spokes would provide a greater gas volume within the tire's internal space, I don't believe it would affect the tire's spring rate much. The tire's spring rate is mostly a function of the pressurized tire sidewall structural stiffness. Since the tire's internal gas volume does not change appreciably during operation (ie. the internal volume mostly displaces under load), the internal pressure also does not change. And the reduced "compression ratio" effect provided by an increased gas volume would not be significant.

On the contrary, having thin spokes is of benefit with an F1 wheel. F1 brakes are carbon, operate at very high temperatures, and need lots of air cooling. Additionally, F1 wheels are small diameter with limited flow area through the wheel center. Having thin section, solid forged spokes is better for brake cooling than having thick section, cast hollow spokes.

And finally, having hollow spokes with internal tire pressure is less reliable. If a hollow spoke wheel sustains damage to a spoke, the tire will lose pressure. A solid spoke wheel will not.

riff_raff