Post by PetePost by Henry LawLet's say the rudder is 100mmx50mm (that seemed about right, sitting in
my front room): 0.005m^2. 2000m in 5 min would be 40m/sec (surely too
high). I think I see that to a very rough approximation the force on a
rudder is around speed x cross sectional area, given in Kg force when
dimensions are in meters. So 40*0.005 = 200g force. Can a rudder not
sustain that amount of load? And I think this calculation is for a
flat plate normal to the flow of water, i.e. stalled, which no rudder
ever should be with a good cox aboard.
Your calculation isn't in the right units, therefore clearly wrong.
Apart from anything else, it thinks that the resistance is the same in
air and water. Also, your minutes seem to contain 10 seconds...
Force on a rudder can be pretty high; it's got to be, in order to move
most of a ton around. That said, it shouldn't break rudders whoever
you put in the boat.
Pete
The forces on rudders are not at all high, so do I hope that all the
hi-falutin' tosh that is spinning off this latest urban myth can be
promptly laid to rest.
The fact that an eight might weigh nearly a ton has little bearing on
the rather small forces needed to swing its stern. A decent rudder
operating within ~2m of the stern of a 16m boat will generate a large
turning moment, even though it is lightly loaded.
Eights fitted with conventional rudders never turn rapidly because those
rudders are so hopelessly inefficient, & their rudders remain very
lightly loaded, whatever the steering input. When the design is mere
crap, the turning force is crap & so, too, is the hydrodynamic force on
said crappy rudder.
Now let's re-run Henry's calcs:
Rudder face area = 0.1 x 0.05 = 0.005 m^2
Boat velocity = 2000/(5 x 60) = 6.7 m/s
(& that's more of an extreme sprint speed than head race cruise!)
Density of water = 1 tonne/m^3
Assume:
1. rudder perpendicular to uninterrupted water flow (an alignment which
no rudder should even remotely approach)
2. drag coeff, Cd, = 1
Force on rudder = area x velocity^2 x density x Cd/(2 x g)
where g is acceleration due to gravity, = 9.81 m/s^2
So:
Force on rudder = 0.005 x 6.7^2 x 1 x 1/18.8
= 0.012 tonnes force
= 12 kgf or 26lbf
[Actually this is far too high, since a typical eights rudder operates
well within the slowed & disturbed flow of the hull's boundary layer. A
more realistic velocity would be around 5m/s, giving a force on a
fully-stalled rudder plate of about 6.6kgf or 14.6 lbf]
Now consider the loads on the rudder pin:
Assume:
1. centre of load acts at middle of rudder plate, e.g. at 50mm from end
of pin.
2. take that length as the lever arm for the application of the force to
the rudder pin
So:
Pin bending moment = 0.012 x 0.05
(BM) = 0.00085 tonne force.m
= 6.2 Newton.m
Assume
1. pin is of 6mm diameter type 316 stainless steel
2. 0.2% proof stress of that steel is ~200 MPa (= 2 x 10^8 Newton/m^2)
(don't even want pin to deform, but ultimate tensile stress is 2.5
x higher)
Extreme fibre stress in a 6mm diameter rod under bending load is:
S = BM x R/(pi x R^4/4)
Bar radius, R = 3mm = 0.003 m
S = 8.3 x 0.003/(3.142 x 0.003^4/4)
= 2.9 x 10^8 Newton/m^s
Now that _is_ an interesting result (if my maths is correct)! Just
supposing the rudder was turned at 90 degrees to the fullest flow while
at top speed, there could be enough pressure on it to _slightly_ bend a
6mm pin. However, the pressure would still only be about 50% of that
required to completely bend it flat. And, as soon as the pin starts to
bend, the load reduces.
One could suppose that if, a) cox were so unwise as to apply 100% rudder
at full speed (but why would she want to subject her crew to a sudden 12
kilogram drag penalty?) & b) the quality of welding was poor, then it is
possible to imagine a rudder breaking off.
This does not allow anyone to attribute these multiple equipment
failures to the strength of the crew. That crew was marginally faster
than those it beat &, while that margin was enough to enable it to win
convincingly despite the lack of adequate steering, it was insufficient
to drastically increase rudder loadings.
Now let's consider how a rudder, any rudder, works & how it is supposed
to be used.
The rudder's function is to generate controllable side-forces, acting at
right angles to the direction of the boat. Those side forces, which
pull the stern sideways causing the boat to change direction, should be
generated through induced hydrodynamic lift, whereby the placing of a
"foil" at a (small) angle to a flow generates substantial (lift) forces
on the foil perpendicular to that flow while incurring almost no fluid
drag. They should achieve this without significantly increasing fluid
drag, & they do not work, as some think, by creating drag.
As with aircraft wings, efficient rudder has are of so-called aerofoil
shape - long (top to bottom) & of approximately teardrop cross-section.
Such shapes induce flow to follow their surfaces cleanly, even when
under high loads, without "separation" (tearing away).
Furthermore, the rudder should act in undisturbed flow! The water
layers flowing close to the hull of a rowing shell are highly disturbed
& being dragged along as a result of fluid friction. So it is axiomatic
that any rudder or any part thereof that is set close to the skin, &
which thus lies within this disturbed "boundary layer", will be
relatively ineffective & inefficient.
Finally, a rudder should be part of joined up thinking on boat steering,
not an afterthought. By that token, if you have a large fin, then
tacking a little bit of metal just behind it, & inside the boundary
layer, & asking it to act as a rudder, is rather pathetic: while the
fin does its level (but often rather poor) best to keep the boat running
straight, the poor little tab of metal you call a rudder is struggling
to deflect enough flow to produce some sort of turning effect. No
wonder that convention fin-&-rudder systems are, shall we say, a touch
slow to act & uncertain in performance?
In short, typical rowing rudders are rather ridiculous. Yet crews
happily race each other carrying equally hindering systems, oblivious of
the drag penalties they thus incur. Those drag penalties come from
several sources:
1. the common plate-fin/appended-rudder devices have high drag because
flow conforms poorly to flat plates with sharp leading edges, even when
they aren't a bit bent. Non-conforming flows separate from the fin
surfaces & spin energy off into vortices - all loss & drag.
2. when cox tries to use the silly little rudder, it fights the fin. The
steering result is just the crumbs left over from that fight - the rest
is lost energy that slows the boat.
3. because conventional systems are uncertain, the boat is constantly
changing direction under wind loads & varying blade loadings, even if
cox is not trying to correct the last over-correction. So the boat
follows a slightly but significantly meandering course (watch boat
courses on a filmed multilane event). Every meander sets the boat
slightly sideways to the direction in which it is moving. Shells incur
the least drag when going the way they're pointing, & drag rises rapidly
when they're even slightly out of line.
There is _one_ truly effective & race-proven steering system - AeRowFin.
We invented it. We designed it. And we make it (see our website).
It is an undoubted race-winning tool. It costs less than one new oar.
It works precisely, & it truly empowers the cox. It doesn't break off
when you steer with it, even when you make an urgent steering correction
to avoid collision ;) .
More recently, AeRowFin has been ripped off (badly) by Empacher. You
could say, as some do, that imitation is the sincerest form of flattery.
Personally speaking, I think it stinks. Incredibly, just a few months
ago Empacher got very rattled by my occasionally pointing out what they
had done. They sent me an email in which they had gall to threaten to
sue me if I continued to tell the truth on this matter. Quite stunning
cheek, you might think. In explaining my disdain for this thuggish
threat I also reminded Empacher how pissed off they were when they
complained to FISA, at a boatbuilders' meeting in St Catherines '99,
about the Chinese ripping off "their" hull shapes. I was very
sympathetic with them at the time. I'm a lot less sympathetic now.
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: ***@carldouglas.co.uk Tel: +44(0)1932-570946 Fax: -563682
URLs: www.carldouglas.co.uk (boats) & www.aerowing.co.uk (riggers)