New York Times on the "perils" of carbon fiber frames

[kbbpll]

youngs_modulus, thanks. Presuming the 220 joules in your calculation is correct, let's keep in mind that in the real world this represents a 100 kg rider/bike combined mass (with an indestructible fork) having an inelastic frontal collision whilst traveling at only 2.1 meters per second, or 7.5 km/hr. Or for a light rider/bike combo like me (73 kg), less than 2.5 m/s, or less than 9 km/hr.

Check my math, but we're saying 220 joules (kg-m^2/s^2) = 1/2 mv^2, or 440 = mv^2, substituting for m as 100kg, 4.4 = v^2, so v (velocity) = 2.1 m/s.

Again, I'm not sure this is a relevant test for real-world scenarios. I'm not going to impress my friends with that fact that my carbon bike is so much better than aluminum because it can survive a frontal crash all the way up to 9 km/hr.

Edit: I'll add that it's interesting to me that in the aluminum test, the weights still bounce significantly after failure. It still has some "elastic" properties. Whereas the carbon one is, as the original article says, "exploded".

[youngs_modulus]

Wonderful explanation! Thank you for your time.

I'm glad you liked it and I'm glad it helped!

Sorry about the lack of clarification. Since I posted under Tineas Pedis I thought everyone understood it was a response to his post. Simple misunderstanding.

You're right--a simple misunderstanding. And Tinea is right...you were totally following the forum convention in replying directly beneath his post.

I'm sorry if I was a little snotty in my first reply. I sincerely believed that your initial post was mathematically incoherent and I was trying to be gentle about that, perhaps with limited success. Your units might have been a bit off but you got the math exactly right. I'm not sure what more one could ask of a math teacher.

I once dealt with a guy on this forum (who has long since disappeared) who would try to bully others with meaningless mathematical/engineering jargon and by taking random integrals. His math really was incoherent. I was probably too quick to judge you in light of that experience.

(I suspect he was mentally ill and perhaps experiencing a manic episode. Whatever the truth, there was more going on than just switching some units).

I think it's impressive how much stronger the carbon frame is while being lighter too. Just so you know that carbon frame was ridden for over a year.

I agree...that is impressive. I have a carbon Santa Cruz Tallboy, and I have even more confidence in it now. The fact that the frame in the video was ridden for over a year implies that either it had no major surface damage or that the margin on a new carbon frame is even larger than what was depicted in the video. Either way, it was very impressive.

Off topic: Do you consider Wikipedia a reliable source in engineering math or in general? It's always an hot topic at my school. I'd like your opinion.

Ooh! Interesting question!

I think Wikipedia is a risky source in many cases. Things tend to be generally right, but the details are sometimes subtly wrong. This is a big problem because if you're looking something up on Wikipedia, you generally don't know enough about the subject to pick up on subtle errors or omissions.

However, IMHO Wikipedia excels as a place to get a general sense of a subject, and it almost always has links to authoritative sources. So I look things up on Wikipedia to find out where to look them up for real. When I was an engineering T.A., I'd always mark down student papers for Wikipedia citations; it's not a source on its own. That said, it can be immensely useful.

Is that similar to your experience with students and Wikipedia?

Cheers,

Jason

[bombertodd]

Our district has taken a firm stance against Wikipedia, yet we have had trainings (computer and math related) were the presenter has used Wikipedia. It turns into a hot topic because some of the teachers think Wikipedia can better serve students than other sources we currently use, but they can be written up for not following policy. It doesn't bother me too much because the math is pretty good but it much more confusing (the diction mainly) to students than places like Khan Academy or Purple Math. I'm always interested in hear other professional opinions regarding their domains.

[youngs_modulus]

youngs_modulus, thanks. Presuming the 220 joules in your calculation is correct, let's keep in mind that in the real world this represents a 100 kg rider/bike combined mass (with an indestructible fork) having an inelastic frontal collision whilst traveling at only 2.1 meters per second, or 7.5 km/hr. Or for a light rider/bike combo like me (73 kg), less than 2.5 m/s, or less than 9 km/hr.

Check my math, but we're saying 220 joules (kg-m^2/s^2) = 1/2 mv^2, or 440 = mv^2, substituting for m as 100kg, 4.4 = v^2, so v (velocity) = 2.1 m/s.

Again, I'm not sure this is a relevant test for real-world scenarios. I'm not going to impress my friends with that fact that my carbon bike is so much better than aluminum because it can survive a frontal crash all the way up to 9 km/hr.

Edit: I'll add that it's interesting to me that in the aluminum test, the weights still bounce significantly after failure. It still has some "elastic" properties. Whereas the carbon one is, as the original article says, "exploded".

I agree with your math, and you're right that the velocities are very low. But don't forget that impulse is really important here.

Force can be defined as the change in momentum with respect to time, or approximately F=M/t where F is force, M is change in momentum at t is time. So if the time of impact is very small, force becomes infinite. So in theory, even a very small amount of momentum, like a marble rolling at 1 m/s, would be enough to break a foot-thick steel plate. If M is small and t is infinitesimal, F becomes infinite and the steel plate fails under an infinite force.

But these collisions happen in short but finite amounts of time, and that reduces the applied force tremendously. The marble doesn't shatter the steel plate and your Nomad won't collapse in a frontal crash of 10 km/h.

So I would argue that these tests *are* useful in that they establish whether the carbon frame is at least as strong as the aluminum one. Besides, the first part of the video showed that the carbon frame can withstand a static load of more than 2000 pounds, which is pretty damned impressive to me.

[Ozrider]

I crashed my Madone 5.9 at about 45km/h 2 weeks ago in the rain. My LBS (Trek Concept Store) has stripped the bike down and given it a thorough examination for damage
Result is both shift levers badly scraped, rear derailleur hanger broken ( saved damage to frame) and rear derailleur broken.
Frame seems perfectly intact. Fork steerer shows no visible damage.
Amazingly there was no exploding carbon, no frame shattering into thousands of sharp shards of carbon or any other spectacular self destruction.
Looks like the bike will be repaired and ready for action before my injuries heal

[kbbpll]

youngs_modulus, certainly it is an interesting topic to me; I imagine because it requires resurrecting my previous life in physics classes. I don't get your force = delta momentum stuff, but what I do understand is that the negative acceleration during impact can be extreme, and thus the "force" (as defined in physics) is also extreme. I recall that elastic versus inelastic collisions and kinetic energy gets pretty complicated, and I still maintain that we're dealing with a transition between these two different outcomes. I also continue to assert that smashing a bike frame with a torquing force on the head tube and measuring the subsequent failure at the top & down tubes is not very representative of real-world scenarios. Certainly the tire/wheel/fork would be the first points of failure (and/or kinetic energy absorption) in the scenario tested, so it doesn't do me any good to say carbon is x times stronger than aluminum in this situation.

I would really like to see Santa Cruz repeat these tests with a steel frame. 110 lbs dropped from less than 1m seems like wimpy stuff to me... but I'd love to see it either way.

And again, I thought the original article was pretty unfair to carbon.

[djwalker]

Sorry to mention it but you guys are doing the calculation the hard way. The original equation was correct. The kinetic energy of the falling mass is the same as the change in gravitational potential energy when it falls. The change in potential energy is deltaE = m*g*deltaH where m = mass of weight, deltaH = change in height. So, if you are comparing two drops with different weights and heights the ratio of kinetic energies is E2/E1 = m2*deltaH2/(m1*deltaH1). To get the ratio of energies the units of the mass and height don't matter as long as they are the same in both cases. Thus, the ratio of the energies is E2/E1 = (110*900)/(85*450) = 2.59.

[youngs_modulus]

I'd argue that the original equation was incorrect, as it contained a term for rebound. Bombertodd ignored that term and got the right answer, a point I tried to acknowledge in my original calculation post. With the rebound term, that equation was really for the energy absorbed in a collision, which is not quite what we're after here.

You're not wrong, djwalker, but we get a bit more out of it than energy ratios would allow alone. Tinea Pedis' original question was about forces; he wanted to correlate the test to his real-world experience, and I suspect that's easer when we're talking about pounds of force rather than energy ratios. To be perfectly frank, Joules aren't that easy for most people to relate to their real-world experiences either, but Joules are the last thing we need (aside from time duration) to calculate the forces as requested.

By calculating the speed of impact, which was fairly slow, non-technical readers could see that time duration (impulse) really does matter quite a bit. So I think doing it "the hard way" was worthwhile. But this is something about which reasonable people can disagree.

This reminds me a bit of the truism that mathematicians look down on physicists, because physics is just applied math, while physicists look down on engineers, because engineering is just applied physics. That doesn't bother me, though; I loves me some applied physics.

Cheers,

Jason

[kbbpll]

Physicists also look down on chemists, because all of chemistry is just the physical manifestation of Schrodinger's equation.