On Thursday, April 16, 2015 at 5:08:32 PM UTC-4, John Greenly wrote:
> On Thursday, April 16, 2015 at 2:10:58 PM UTC-4,
2potsin...@gmail.com wrote:
> > I am going to pop in from my usual lurk-mode, both to say again how much I enjoy and benefit from reading all your collective wisdom (and particularly Carl), and also add my small 2 cents to this topic. My rowing clubs are on a fairly long (13 miles) very sheltered public water supply reservoir, so we row hard and fast when we want to, but the water conditions (flow, wind and waves, other boat traffic) are rarely a problem. One practice last year, we were at our farthest usual distance from the boathouse when the coach's launch developed an engine problem. There was no one else nearby, so the coxswain took the launch tie-up rope in hand and we towed the launch 6 miles back to the dock. I cannot recall a better practice - we were able to put full effort into long steady rowing that was slow enough through all phases of the stroke that we were also able to work on fine-tuning some technical issues we were having. And the coach appreciated being a mere few feet astern of the shell and not having to shout over the din of the engine.
> >
> > Back to lurk-mode
> >
> > Dick White, in sunny Virginia where it is finally warm enough to row again.
>
> Dick,
>
> thanks for un-lurking! This is a very interesting example. I wonder- you added not just resistance but also mass (inertia) and that may have helped even out your speed and made the practice work out better.
> --John
Hey, yes, that's it! I should have realized this. To row slowly with the same pressure, so that all motions are slowed like a slow-mo video, the mass needs to change.
I should have realized this because a standard technique in physics to understand how some phenomenon scales with changes in parameters is dimensional analysis and the construction of dimensionless numbers to characterize the scaling, as for instance the many dimensionless numbers of fluid mechanics like Reynolds number, Mach number, Froude number, etc.
I want to keep the force, or pressure, constant and change the speed, so all quantities have to be transformed into units of force and made dimensionless by dividing by a reference value of force. That means acceleration must be multiplied by mass to put it into units of force.
Think about what happens as you slow down the video by a factor of two. The drive lasts twice as long, but the change in speed during that doubled time is only half as much as normal. That means the acceleration is reduced by a factor of 4. However, the driving force is unchanged, so we need to increase the mass by a factor of 4 to keep the product of mass and acceleration constant.
The drag force must also be held constant, and to have the same drag force at half the speed, we do need to add resistance to the hull (maybe a bungee?). Again, with the unchanged drag force and 4 times the mass, the accelerations during the recovery will be properly scaled down.
Strictly speaking, all parts of the system, the rower(s) and the boat, should have their masses quadrupled, but that obviously isn't practical, (among other things, certain sink-like-a-stone qualities would result). Anyway, the rower can slow down his internal motions as he wishes; the internal inertial forces will decrease greatly out of proportion, but maybe that's not too important to the feel of the practice. So, both extra mass and extra resistance must be added to the boat to allow an nearly unchanged rhythm at slower speed but full pressure, and I think that's what Dick White's experience tells us. And that's why just adding a bungee messes up the rhythm as has been stated.
And indeed, towing a suitable object, like a coach and his launch, might be a more practical way to do it than adding a lot of mass to the boat itself. But I know that wouldn't work in a single because of the lurch factor as I described. So a substantially heavier boat, like my wherry with some extra weight added, might do the trick.
Technical detail:
In the hypothetical slowed video, the dimension of length L is invariant: the boat (and everything else too, like how far it travels during the drive) doesn't get shorter or longer. So velocity V can be made dimensionless as [(mV^2)/L]/Fref, where m is mass and Fref is the reference force. So again, half speed means 4 times the mass to give the same dimensionless quantity. This scaling also makes the kinetic energy invariant, as it must be with invariant force and distance, that is, work done.
Is all this correct? I'm writing it on the fly, but I think so.
Cheers,
John