Yes, we are all used to recumbent riders telling us how much more aerodynamically efficient they are than us "wedgie" riders. Funny how I have passed by a recumbent perhaps 5 times in my decades of riding. Any chance that the rider position so compromises the ability to produce power that it can't compensate for the improved aerodynamics? Not that you would ever get a recumbent rider to admit, so it must be that recumbent riders are all just slow.
Most are. Also, like with uprights, not all recumbents are created equal. Trikes take a huge speed hit.
Because of this discussion, I checked with three engineers I know - different ages different disciplines (civil, metallurgical, chemical engineers) and NONE use the distinction between exponentials and power function. ALL had to have the distinction "re-explained" to them. ALL would say that a cubic function is an exponential, where the exponent is three. Not a statistically significant sampling, but I would be very surprised it if was any different across a much bigger group of engineers.
A variable is not the same as a constant. x cubed is not a function of 3 it is a function of x. And _not_ an exponential function of x. The exponential function of x is e^x, but all functions like a^x are related to this (as I am sure everyone knows) by a^x = e^(x ln(a))), i.e. the exponential function of a multiple of x.
Not many engineers use exponent calculations, unless your going to the moon!
Excuse me? Please explain this statement. A quick look at the "major" engineering formulas, regardless of the engineering discipline, shows them full of exponents. My favorite from chemical engineering has one of the terms raised to the 0.14 power.
How is it possible in this day and age that someone like Zinn could get this so wrong? I expect this kind of nonsense from Bicycling magazine, but not Velo News and not Lennard Zinn.
Well, he's at it again. On VeloNews.com he tried to talk aero and rolling resistance. If "Aerodynamic drag increases exponentially with speed." wasn't bad enough, we get, "internal energy losses within the rubber itself result from hysteresis — the lag between the application of a force on a material and its deflection in response." I stopped at that point. His time has passed. He should leave such things to people who know.
OK, what term was that and when was the last time u used it?
flow in pipes - used all the time. For laminar flow: dimensionless correlation of h(i)*D/k = 1.86* (cube root of Reynolds Number) * (cube root of Prandtl number) * (viscosity/viscosity of water to the 0.14 power) * (cube root of diameter/length). Similar equation for turbulent flow.
Most engineers I know would use a chart, similar to this one and forgo all that math. It's been done a million times before, unless your going to the moon!
A variable is not the same as a constant. x cubed is not a function of 3 it is a function of x. And _not_ an exponential function of x. The exponential function of x is e^x, but all functions like a^x are related to this (as I am sure everyone knows) by a^x = e^(x ln(a))), i.e. the exponential function of a multiple of x.
Yes. Exponential growth means that the rate of change is proportional to the quantity itself. Anything else isn't exponential.
dy/dt prop to y
Integrate it and you get the quantity depends on a number to the power of t. If t isn't in the power it isn't exponential.
The essential thing is the rate of change is proportional to the quantity.
afaik, it can be mathematically proven that exponential growth will always outstrip any power law.
I've never heard anyone who works in science refer to a squared or cubed power law quantity as exponential. It's ridiculous and wrong that Zinn uses this term to describe aero power losses.
He gets pretty confused about hysteresis as well.
(edited for clarity)
Last edited by carlosflanders; 03-28-2020 at 09:43 PM.
Most engineers I know would use a chart, similar to this one and forgo all that math. It's been done a million times before, unless your going to the moon!
I suspect you don't know many chemical engineers. Where is viscosity on that chart? Where is fluid density? There are many useful pre-calculated charts available, but when you're doing fluid dynamics, you have to actually do the math. That's why many chemical engineers take a course in advanced numerical methods. Charts don't solve those problems.
May I ask what chemical engineers are doing when they are using fluid dynamics?
Calculating specifically what and to what ends?
Hold on. First you tell us how they do it, and now you ask what it is they do. How can you know the how, if you don't know the what.
Originally Posted by duriel
Most engineers I know would use a chart, similar to this one and forgo all that math. It's been done a million times before, unless your going to the moon!
May I ask what chemical engineers are doing when they are using fluid dynamics? Calculating specifically what and to what ends?
Is this some kind of troll? What argument are you trying to "win"? A simple example would be polymer flow in an extruder. Not simple in terms of computational fluid dynamics, but simple in the case of varying temperature (and so varying viscosity and density). Another example would be a kinetic mixer with two different fluids of differing viscosities and densities. Another example would be a stirred tank reactor. Actually there are a LOT of examples.
Why don't you just tell us that you don't really know what chemical engineers do?
Send it to [email protected] and just tell them to get it to Lennard. Yeah, it's kinda weird they don't have a staff contact link on their web site. I've written him a couple times and received prompt responses, but that was years ago. In fact, I actually spoke to him on the phone at length in response to an e-mail I sent him.
Do it.
Hah, Kerry! I see you wrote to VeloNews and Lennard answered! Good for you!