Mathematician Solves Rowing Boat "Wiggle" Problem ...
Kit
http://www.technologyreview.com/blog/arxiv/24437/?a=f
I don't think this is as revolutionary as the article makes out. I
believe Italian rigs have been known to be better balanced for a while
(or at least AIUI). There are 2 interesting bucket rig variations
though, including one with all 4 on one side together in the middle of
the boat.
Kit
Greg Doyle
is a basic high school physics problem. 20 minutes tops for the
average 16-18 year old to write out the various permutations.
Walter Martindale
No kidding. The first published discussion of this of which I'm aware
was in our text book for "mathematical applications in sport" - My
books are currently all piled up in storage so I can't pull out the
exact citation but it was published some time in the 1970s.
Walter
Mike De Petris
"He also goes on to show that unbalanced boats in which there are
unequal numbers of oars on each side, can also be wiggle free if the
spacing between the rowers can be altered. As an example, he shows how
a Three could have a zero transverse moment."
:-)
anyway, I've seen model "d" eights in my youth, nothing new, and "a"
is clearly a nonsense, even if modern materials may allow it.
Peter Ford
Only the comical one (4 rowers on the same side in the middle) is new,
certainly. I can't spot any photos of the rig with 67 and 23 tandems
immediately, but I'm almost sure I've seen one raced; in addition, we
considered racing it a couple of years ago. For most crews, with
gearings and ratings that are common, either of the 'old' rigs will
cause problems due to stroke rowing in bow's puddle at race rates; it
seems that an even number of tandems is a good idea.
Having read the paper now, it seems to have various other flaws. One
obvious one is that they seem to think an uneven boat is straightened
out on the recovery by inwards forces on the gates, rather than by
e.g. a rudder; this is a trivial (to the maths) misunderstanding, but
a bizarre.
Peter
carolinetu
Caroline
Rob Collings
> How many coxless eights have you seen? (see end of paragraph 2)
>
> Caroline
I've seen some that might as well have been, do they count?
:-)
Rob.
Carl Douglas
I thought your problem right now was more to do with coxless pairs, Rob,
although I recognise that's a sore point.
I think this paper is great fun, but unless my eyes are deceiving me the
author may have omitted a not insignificant force component from his
analysis.
Dealing with the oar as a foil, you have to consider not just the
approximately perpendicular (the the shaft axis) reaction. There is
also a smaller, variable but not negligible component of fluid drag as
the water flows along the blade (except in the stalled mid-stroke phase.
That drag component resolves itself along the shaft axis & can be
considered as acting through the pin. So it will add extra moments
which ought to be considered.
AFAIK, no work has been done on progression of axial drag forces on an
oar throughout the stroke. Obviously this is an added drag component
which is not normally considered by anyone tempted to investigate
sources of drag in rowing. As well as its possible further influence on
the twitchiness of the boat, it could provide a nice little research
project for someone.
Cheers -
Carl
--
Carl Douglas Racing Shells -
Fine Small-Boats/AeRoWing Low-drag Riggers/Advanced Accessories
Write: Harris Boatyard, Laleham Reach, Chertsey KT16 8RP, UK
Find: http://tinyurl.com/2tqujf
Email: ca...@carldouglas.co.uk Tel: +44(0)1932-570946 Fax: -563682
URLs: www.carldouglas.co.uk (boats) & www.aerowing.co.uk (riggers)
Tinus
> approximately perpendicular (the the shaft axis) reaction. There is
> also a smaller, variable but not negligible component of fluid drag as
> the water flows along the blade (except in the stalled mid-stroke phase.
> That drag component resolves itself along the shaft axis & can be
> considered as acting through the pin.
But are these forces of such property as possible to be cancelled? If
every pin experiences a torque in the same direction along the axis
from starboard side to port side than they can't cancel because they
aren't in opposite direction as is the case with the torques around
the axis perpendicular to the water surface. Any torques around the
axis along the length of the boat should cancel if the spans are the
same for starboard and port.
BTW. the article should be written as a short snack for the author
(who is not a pure mathematician but also/originally a physicist or
astronomer) and not much serious. I wonder however... I was always
under the impression that rig d is much more common than rig c. The
centre block from rig a is how I have the people which I coach
practice in the rowing tank.
Tinus
> oar throughout the stroke.
I forgot to mention in the previous post. Isn't it such that some
older oars used to be made of a single carbon helix which only twisted
in a single direction such that the stiffness, to axial forces, of the
material is not symmetric for port and starboard oars. This would
cause asymmetric differences in the angles of the blades. I can
imagine that there must have been done some work on that topic.
Carl Douglas
Tinus -
I see a few typos in what I wrote - sorry, more haste, less clarity :(
The drag force on a blade which is generating hydrodynamic lift creates,
at a first approximation (straight shaft), no torque about the pin. By
convention that drag lies directly along the blade's major chord, is due
to surface friction generated by the flow along the 2 faces of the blade
& hence passes straight through the pin. But it does generate moments
on the boat as a whole.
Well, we know the oar bends, so the drag force passes in reality
through a line (depending on load) aimed somewhat astern of the pin.
All of which means that even in the simple case there may be little hope
of relating the couples generated by the fluid drag on the blades to
those generated by forces perpendicular blade. In any case, everything
depends on how blade loads vary through the stroke between crew members.
Yes, the article seems intended to stimulate and entertain active minds.
Cheers -
Carl
--
Carl Douglas Racing Shells -
Fine Small-Boats/AeRoWing low-drag Riggers/Advanced Accessories
Write: Harris Boatyard, Laleham Reach, Chertsey KT16 8RP, UK
Carl Douglas
I have no information on that, Tinus. I believe some of the early
carbon-tube oar-shafts did develop a twist over time, but AFAIK that's
no longer a problem. And I doubt it is relevant to that boat-wiggle
article.
FWIW:
If the original layup combined axial fibres with fibres spiralled in
only one direction, that might not twist differently in use between
sides if there was good cohesion between the 2 carbon alignments - for
small deflections the spiral winding would be equally stiff in
compression (for one twist direction) & tension (the other twist
direction). Problems of permanent twist could arise if, as the resin
aged, it underwent small dimensional changes which altered the original
separation of the 2 alignments.
Walter Martindale
Ok... Found the citation - haven't found the book.. (it's somewhere
here...)
Brearley, M. N. Oar arrangements in rowing eights. in: Lanady, S. P.,
and R. E. Machol (eds.) _Optimal Strategies in Sports (Studies in
Management Science and Systems; v. 5), elsevier North-Holland, inc.
New York. pp 184-185, (1977).
Remarks that when the oars are at the catch in a standard rigged 8+,
the side of the boat that is "bow" side (i.e., normally starboard, but
if it's a starboard stroked boat, it's port side) has a leverage
advantage pushing away from the boat, causing the bow to push towards
portside. When the blades are past "perpendicular" they still have a
mechanical advantage, but they are pushing in toward the hull, hence
pulling the boat towards bow-side (starboard). The easy way to fix
this is to have a tandem rig where "bow side" and "stroke side" are
the same side (making the terms bow side and stroke side seem silly).
Brearley essentially does an easy leverage calculation based on the
distance of all of the oars from the tiller. A standard rigged boat
will have 2, 4, 6, 8 on port, and 1, 3, 5, 7 on starboard. On port
side, then, stroke seat (8) is 1 unit of distance from the tiller, 6
seat is 3 units of distance from tiller, etc., giving a sum of
distances from the tiller of 16 on port. On starboard, 7 seat is 2
units of distance from the tiller, 5 seat is 4 units of distance from
the tiller, etc., giving a sum of distances from the tiller of 2+4+6+8
= 20. When everyone is at the catch, assuming similar force curves,
the boat has a turning moment pushing the bow towards port.
A tandem rig where the sums on boat sides are the same (e.g., portside
at 1, 3, 6, 8, and starboard at 2, 4, 5, 7, gives sums of distances
from the tiller of 8+6+3+1 (18) and 7+5+4+2 (18), respectively,
meaning equal leverage with respect to the tiller, and a better chance
of having a straight boat during the drive.
It's old news that people who train in pairs a lot develop different
force curves - stroke with a stronger force uptake at the start of the
drive - which tends to keep the boat straight. If you're forming a
crew from a bunch of pair rowers, it may be no advantage to tandem
rig because all of the stroke siders (usually port) will have learned
to keep the boat straight, but if you're forming an 8+ or 4- (or 4+)
from a bunch of scullers, then it may be to your advantage to tandem
rig.
Of course - it may just work better one way or the other with or
without the wobble.
If I manage to find the book I'll scan, OCR (or PDF) it and post the
article with a link...
W