mikbowyer said:
Actually after this semester I am done with physics and mechanics, so i'm about 8 weeks out. The second two years are more business and stuff.
The ref. to a degree and more years was done with the implication that you're not done yet. I don't know exactly what kind of program your in. I assumed the typical 4-5 year engineering track. Also, while a bike is simple, the analysis of the system and how it behaves is not quite as simple, and I thought it was possible that you hadn't covered the analysis of such systems yet. But now that you've pointed out the thousands of hours you've spent in the classroom, it's evident that you're completely adept at all types of analysis. FWIW, from the earlier post the Hamiltonian is just the sum of the kinetic and the potential energy in a system. The Hamiltonian is a powerful espression that is of great importance in Lagrangian mechanics, where instead of looking at forces as in Newtonian mechanics, systems are evaluated by how the Hamiltonian changes, i.e, by looking at the Hamiltonian and its derivatives, in terms of the system's degrees of freedom. Such an analysis is mathematically identical to Newtonian analysis. However, as I said before, you cannot just understand a system by looking at energies. As in Langrangian mechanics, you have to also look at how the energies change.
mikbowyer said:
And you are STILL saying things that are true, but have nothing to do with what I originally posted, and it is very obvious that you have NO interest in reading what I was replying to. The post I quoted said "Furthermore, the importance of frame weight and wheel weight are generally of equal importance unless we're talking about sprinting. The whole unit or system weight comprised of the rider, frame, components, wheels, tires and etc. is what's important in regards to your theory and your opinion."
and i said "well actually taking 10 grams out of your wheels is like taking 20 grams out of your frame"
No. Only in terms of total energy is what you claim true. However total energy is not the only constraint on the system. What the rider feels is the effect of a CHANGE in energy or how his POWER dissipates. And to see how those things are effected total energy is not the sole consideration: you have to define how the energy changes, so you can get work and power. Work and power are what the rider understands. An energy magnitude, say your 59.4 J of rotational kinetic energy, mean nothing to a rider. And in terms of the way the system functions, it's completely meaningless because what is more important is how you get to 59.4J or how it changes with changing dynamics in the system.
mikbowyer said:
and you keep establishing the points that
1: I have less credibility because of my engineering knowledge
-note how you have said that i have less, and not that you have any, which is a total e-lowballer way of arguing.
2: That 10 or 20 grams out of a bike don't mean crap anyway.
See the above comment before you get all huffy. And the fact is that 10 or 20 or 200g of weight change in a bike don't mean diddly in terms of performance.
mikbowyer said:
Congratulations you have just stated something completely new and not contradictory to what I said. When I was 9 I drank chocolate milk, but I am not posting about it since it doesn't have anything to do with the person I was quoting. What you are saying is as true as me drinking milk when I was 9, but it belongs as a reply about as much.
Nope. You didn't frame your solution correctly. In fact, you said zero re: changes in energy. You just gave energy magnitudes.
mikbowyer said:
I am in no way trying to say anything you have said was wrong, but please do me a favor and just read what I was replying to, it has nothing to do with the end magnitude of these changes, only them related to eachother.
I read what you said. In no way did you compare the work (dE/dt) or power (dW/dt).
What you pointed out, that a pound heavier wheel would be more detrimental than a pound heavier seat, is an oversimplification. The fact is that even the pound heavier wheel won't make a great difference. Granted, again, you have to initially put energy into the wheel, but, hey, you've got to put energy into the system anyway. Other inputs to the system are very small to those large inputs over very short intervals (sprints). Even in those cases, the effect of a heavier wheel isn't that great. Energy, both translational and rotational are linear with respect to mass. So any differences in energy are going to be less than an order of magnitude. If you do a detailed analysis you'll find that over a long climb, any time saved via lighter wheels is minimal and would probably only be beneficial to cyclists at the top of the sport. In fact, I'd say wheel weight even does didly for the pros as they get a much greater effect from riding along w/ the competition.
I am off on no tangent. I am saying that any benefit from lowering rotational mass is very minimal, minimal to the point of prolly not being noticeable. My guess is that someone would never notice a drop in rotational energy of 0.27%. For your rotational energy of 59.4J (and we'll assume, for now, that the relative change is still 0.27%. It's a close enough first order approximation), that equals a change of 0.16J. With that loss of rotational energy...if you could put it into a change in potential energy that you would allow you to elevate the system a few more millimeters.
Now you can definitely make the argument that over a long day of climbing that a change in wheel weight will let you have more power in reserve at the end of the day. But guess what? You'll use less power over the course of that day with a lighter seat and lighter handlebars.
The ol' adage that a "pound off the wheels is like 2 off the bike" is pure bupkus. And the reason it is bupkus is because the EFFECT of the loss of weight at the wheels is virtually negligible compared to a loss of overall system weight or loss of weight in non-rotating parts. It's mathematically and physically true that having twice the energy as another component does not mean that the energy changes are twice as large. It is mathematically evident, in the bicycle system, that the effect of changing rotational mass is very small.
For people not interested in the science, math, or whatever, I suggest they go to AnalyticCycling.com and plug some numbers in just to see how small changes in power and work are as a result of rotational mass changes.