So what? We have to deal with frictional and other heat losses because we cycle in the real world. Is there a point you're tying to make? Feel free to choose whatever terminology you feel most comfortable with, but the physics is still the same: climbing up a hill on a bike and descending are not path independent processes in a world in which energy losses always exist.howardjd said:
Well that point could have been made just by saying, "Make sure to do an out and back test." Note that starting where you finish does not guarantee anything. Doing a 5 mile, 3,000 ft climb that starts at point A that is followed by a 15 mile descent that ends at point A does not negate work done by gravity. Again, there is no path independence in the real world on a bicycle. I also don't see how this clarifies any test that's been done.howardjd said:
Speaking of friction, I've been wondering what the water inside an inner tube really does when the wheel starts to turn in the vertical plane. Do you think it moves as a column stuck inside the tube, or does it require some time to spin up, so that the acceleration of the water lags that of the tube? At a steady-state, would the water column rotate at the same speed as the wheel, or would there be a small amount of slip (and resulting power loss)?
If we simplify things a bit, we can say that the water in contact with the tube will tend to travel faster than water in the center of the tube volume because of skin friction betwixt the water and the tube. However, that skin friction is acted upon by gravity, surface tension in the water, and shear in the water (as the result of the water velocity increasing as you move from the center of the tube volume to a tube surface). All that results in turbulent flow. So the answer would be that there will be slip, and it will be chaotic. Of course it has to be remembered that turbulence is generated from energy put into the system by the rider (and the road surface).dhk2 said:
So you think that modeling the turbulence in the water is a straight forward calculation? Well, first you have to decide which turbulence model you want to use, then you need to the computing power (there is no simple hand calculation for determining losses from turbulence), then you need to crunch everything, and finally you'll need to repeat everything for every different water volume and inner tube. Turbulence modeling isn't trivial.howardjd said:
And I said something different....where? The point I made is that if you're going to do real world tests to come up with your theory, you need to take into account the fact that path independence is hard to find in the real world, and as a result, you'll have to factor that into your error budget. It's not at all a matter of semantics but rather a matter of considering everything that influences testing.howardjd said:
Frankly, I think you should first look to theory to find the appropriate equations and the relevant parameters. The theory will take you a long way. For instance, theory can show you in 3-space how a 3D wheel will respond to a given force. In four space, you can see how the wheel responds over time. You can then take those predicted responses and equations and see how they match up--via experimentation--with the real world. Unless physics gets turned on its head you'll find they should match up well assuming all independent variables have been accounted for. With respect to a wheel's angular momentum, MOI, and the rocking from side to side of a bike, you're going to have some parameters that are going to be real fuzzy and difficult to state explicitly, like how an individual's pedaling style influences the dynamics of interest, how a given rider's body influences said dynamics....... The human influence on the system will introduce all manner of uncertainty, hurdles, and headaches into your effort. IMHO, I'd break the problem down into manageable parts that can be tested with accuracy and precision and modeled in a straightforward way. Let's look at this in terms of a Hamiltonian: if you want to construct a Hamiltonian, the first thing you need to do is figure out the number of degrees of freedom of the system. You can try it head on and just attempt a single overarching Hamiltonian, but that might actually result in a serious cerebrovascular accident since there are, using a scientific term, shitloads of DOF. It's much easier to break things down into manageable segments: rear wheel dynamics; crank dynamics, front wheel dynamics...or however you need or want to break it down. There's a reason that particle physicists didn't start with writing an all encompassing Hamiltonian for the Standard Model of particle physics but instead assembled it out of parts. Have you see the thing?howardjd said:
