This thread is so completely full of technically incorrect statements, it is probably irrecoverable at this point. Some are mistaking stiffness for strength, discussing increasing stiffness without considering strength implications, ...all sorts of crap, ... err,... I mean,... misconceptions, that's it, misconceptions and inaccuracies are floating around in this thread. The thing is, the crap is interspersed with technically correct info.

with or without pictures, the value of that post would remain the same

Why not answer the question without misconception, rather than just complaining about the crappy answers?

Well, reading through everything so far and filtering out the obvious misunderstanding of the question and misconceptions about the physics (yeah, I started out studying mechanical engineering though I changed majors) I would have to say that I'm still not entirely convinced that a bicycle is stiffer purely due to a compact frame (notice I changed frame to bicycle as that's really what I meant in the first place - nobody rides a bare frame). I find Caterham's arguments in favor of the compact frame being stiffer the most convincing. Particularly the changes to the rear triangle.

On the other hand, I suspect (though obviously I have to hard proof) that the majority of flex comes from the areas around the head tube and bottom bracket. Chain stays are very narrow and are often ovalized such that they would better resist flex in the vertical plain. Seat stays are just as narrow if not more so and are so close together at the top that I doubt they offer any significant resistance to lateral forces whether the frame is traditional or compact. And while an oversized bottom bracket and stiffer (whether from thicker tubing, larger diameter, whatever) seat tube and down tube will offer increased stiffness, I don't see how angling the top tube down such that it intersects the seat tube at a lower point would increase stiffness. If anyone read Jan Heine's recent tests comparing frame stiffness (all traditional horizontal top tube frames) he theorized that a stiffer seat tube was more likely to cause rubbing under heavy loads because the bottom bracket shell itself deflects. I've had similar experiences with my bikes - my old Bottecchia Special with thick hi-tensile steel tubing would rub like hell and I'm sure I could actually see the flexing when sprinting out of the saddle. My Gran Turismo never rubs and I don't notice any flex even though it's made of thinner Columbus SL tubing.

Honestly though, if I were a young person buying a bike today and had no prejudices either way, I think the compact frame offers sufficient advantages to make it a viable choice, maybe even a better choice regardless of whether it's actually stiffer as a direct result of the design. As it stands however, I'm an old coot who thinks traditional horizontal top tubes just look so much better (along with lugs and wheels with lots of spokes, and polished aluminum doo-dads and chrome, lots of chrome) that I would choose a traditional frame anyway. But I do like to keep up with the latest technolgy and understand why it may (or may not) be better, hence this post.

BTW - Jan's tests also indicated that a stiffer frame was not necessarily better at power transfer but you'll have to read his article and make up your own mind.

High Tensile steel frames are bound to be very flexy, quite heavy, or both, regardless of toptube angle.

As pertains to road bikes, in my size, I find sloping toptubes unattractive and unable to provide a ride better than the finest horiz. top tube frames. I'd be reluctant to purchase even an OS tubed road frame. I've tried Cannondales and no way I'm riding a century on one. I don't find compact road bike frame design to offer enough advantage to the end user to compensate riding such an ugly frame. My old Univega Super Sport and current Pinarello are just about perfect frames and both are horiz top tube.

I'd imagine for larger frames there might be more of an advantage. If a builder uses thicker tubing on larger sizes, he could likely go one size larger using the lighter tubing for sloping toptube design than with horiz toptube design and still get the desired stiffness.

On the other hand, there's NO WAY I'd want to go back to horizontal top tubed CX or MTB frames, for reasons other than perceived stiffness, and my mongoose has a fair amount of seatpost showing yet is amazingly stiff in the pedals.

Of course, you are correct with the possible exception that it seems to me to be important to dispel the myths and to correct the previously posted inaccuracies. When I added all that up, the scope of the response required was just too great.

the problem here is that a bicycle is a "simple machine" which in reality makes it one of the most complex devices to fully understand and implement.
every component part has multiple , interdependant and critical functions, making quantifiable,measureable scrutiny of the benefits of singular properties & effects a nearly impossible task.
vehicle dynamics are affected dramatically with modulating intensity of cornering forces; changing road surface & terrain & aerodynamic interactions; the rider's mobility & fitment affecting weight distribution & transfer and efficiency; a broadly varied,yet very low power application levels and disparate operator skills,physiques,fitness levels & motivations, compounded by their ability & quickness to adapt as well as their sensitivity to the machine and its behaviors.
one just cannot make any sort of all encompassing proclamation of benefits for any specific design or property without assessing that element's affect on the whole in terms of efficiency, handling, cornering, rideability, predictable behavior, reliability, comfort and, as demonstrated all too clearly in this thread, one's aesthetic values, expectations and biases.

That's not true - only the tensile strength of steel increases significantly with alloying. All steel is essentially the same when it comes to flexibility. Thus, all other factors being equal, a hi-tensile frame of the same design but using thicker tubing than one built with a thin walled tube will be stiffer (and yes, heavier). If for some reason you built two otherwise identical frames, one with hi-tensile steel and the other with chromoly for example, and used the same tube thicknesses for both, they would weigh the same and you would not notice any difference. Of course that rarely happens in real life as there is no reason to do it outside of a few loaded touring bikes perhaps. But even those are typically butted.

And in fact are.

Actually, they make some crossbow prods in aluminum alloy.

tcs

You forgot the third leg of the stool: strength. A high tensile steel frame could be made that would be as stiff and light as one made from superalloy. Obviously the rider would have to be very light, very smooth, ride on smooth surfaces and not be a strong pedaler to safely stay within this frame's service envelope, and since material cost is only one part of the total cost of fabricating a frame (especially a very light one) building a flyweight high tensile frame would hardly be worth the trouble.

tcs

Well, if you got some 1020 tubing made with the same wall thicknesses as an SLX set, that frame would not serve you for as long as the SLX frame.

I'd be afraid to ride it with any vigor.

And that's precisely why they spend so much time developing new alloys of steel and aluminum and many other metals. So you can have strong tubing that doesn't weigh as much as the old tubing.

And if you arrange them in smaller triangles, the resulting frame will be stronger than one made with larger triangles.

Keep in mind that "stronger" is a relative term. Any bike you ride is going to be strong enough to not fall apart on you while you ride it unless it has been in a crash. Ride what you like.

An armored truck will be stronger than my Honda but I'm not driving an armored truck to work everyday. Just ain't gonna happen.



But the question "Why are compact frames stiffer?" was answered long ago with the simple "smaller triangles are stronger than larger triangles".

Quite true! I was thinking of going the other direction.

No, the stiffness of any steel tube really only depends on its diameter. But a high-tensile steel tube will not be as strong as a chrome-moly or manganese-moly tube of the same diameter, so it is likely to have thicker walls to compensate, and therefore will be heavier.

You do realize that this statement is inherently incorrect, don't you?

If the question is about stiffness, you cannot answer it by discussing strength. You must respond in the context of stiffness - rigidity, resistance to deflection, high natural frequency. Strength really has nothing to do with it (stiffness).

Any bike that you can buy has already been designed by someone out there who had to do the design studies, make the trade-offs, elect the materials, build a protoytpe and test it, refine the design, ... Then they had to make further compromises as they moved into mass production. They've already done the stiffness and strength work for you.

Have you ever watched an aluminum wing on a large jet. If they don't flex it must be an optical illusion. Don't you think it is more about design than material?

Precisely so.

However, aluminum is notch sensitive. There's no doubt at that. Still, even notch sensitivity can be dealt with during the design process.

Okay, Mike, we'll do it your way: small triangles are stiffer than larger triangles.

Close, but not quite. For a given torque (axial) a tube of a certain length will twist a certain amount. If you put the same torque on a longer tube, the twist will be greater. This assumes the twist is measured by how much the two ends are moved out of line with each other.

It's not really work, though you could say energy is stored in the tube when it's twisted, if it's metal. If it's carbon, a significant amount is dissipated as heat. Still tends to resist twisting.

So in a compact, the top tube is part of the system that resists twist due to pedaling forces and due to hand forces as the rider pulls on the handlebar. Those two couples impart a twist that tends to pull the head and seat tubes out of plane, by twisting the downtube and the top tube. Downtube and seat tube stiffness are important. The top tube is shortened in a compact because it approches perpendicular interface with the seat tube. That would represent the shortest top tube. As an additional stiffness benefit, the seat stays get shorter. A compact will be stiffer than a conventional frame, even if they share the same materials and construction, assuming they have stiff seatposts.

Excuse me? You can exercise your Constitutionally-given right to blabber as if you know some science all you want, and join the masses of Americans who know NO science but speak as if they do, but there's no reason to take gratuitous shots at people who ACTUALLY know something about science, and without whom you'd be shivering in the fricking dark, having trouble surviving the winter!

Unless by "overeducated" you mean "unseasoned" or "inexperienced."

No. The inherent stiffness (strain to stress ratio) of high tensile steels is the same as that of CrMo and MnMo. A set of frames brazed up out of those three materials with the available variations in wall thickness, will show load, shock, and torsionally-driven flexing commensurate with the differences in tube wall thickness and outer diameter. This assumes the joints are of equal rigidity in all frames.

What's different among the steels is strength. Better allows, such as Reynolds 853 or Tange Infinity, are stronger, not stiffer. This allows making tubes with thinner walls. Thinner walls make tubes more flexible, so to restore suitable frame stability (not TOO much flexing), the outer diameter is increased.

Interesting discussion thus far. One thing I started thinking about as I was making some adjustments to my wife's mixte is why the designers decided to run the twin diagonal tubes back to the rear dropout rather than attaching them to the seat tube or just using a single sloping downtube. According to what many are saying here, a frame should be stiffer by positioning the top tube lower on the seat tube. But in the mixte design (at least the Peugeot that I'm looking at) the twin diagonals go from the head tube to the rear drop outs and aren't connected in any way to the seat tube. So those designers apparently felt that it is not necessary to brace the seat tube at all as it's only attached at the bottom bracket and the thin seat stays. Now granted mixte frames aren't likely to be put through the same level of stress as a racing frame but still, it does make one wonder about the argument that the top tube is there to somehow reduce flexing of the seat tube. Apparently its primary function is to support the loads on the head tube.

You mistake my perspective on this. I can make a large triangle that is stiffer than your small triangle. Stiffness doesn't necessarily have anything to do with size. In one way, larger is stiffer.

Who says stiffness is the be all and end all of bicycle design, anyway?

Kommi, go back to the mixte thread started by Veloria earlier this summer, we went through all of that. My reference for believing the top tube is involved is basically my knowledge and physical insight as an engineer, but it's shared by a physicist/frame builder/author, Tony Oliver, and explained very well in his book, "Touring Bicycles; a practical guide." I provided a complete reference to the book in that thread. Sorry to pass you around, but I have made this case a number of times on BF.

The fact that Peugeot and others did not choose the solid top tube design does not mean it is not beneficial, or better with respect to torsional stiffness than the (let's call it) floating twin lateral design. I still don't fully understand the purpose of the conventional mixte frame design.

Maybe it doesn't have a strong enough effect for the expected mixte riders. Maybe ... it is just style, a nod to the space frame concept - aircraft, Bucky Fuller, the Birdcage Maserati, Raymond Leowy, I don't know. But engineering-wise a large (say 25 mm or more) top tube in line with the rear axle and the top of the head tube or all the way up to hirizontal will make a frame that better resists twisting around its longitudinal axis, as might be created by pedaling and handlebar reaction forces.

We also need to consider what kind of stiffness we are talking about. longitudinal torsion? Vertical deflection due to road shock and rider load? or one of the many other ways a frame or its elements could twist or flex?