* NOTES,
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CONCEPTUAL ANALYSIS OF STATIC AND DYNAMIC
STABILITY OF 420
PROBLEM
When the boat capsizes, the masthead is immersed
and water begins to intrude into the hollow core of the mast
extrusion. This progressive flooding causes an increase in capsizing
moment and the boat eventually turtles. When the boat is righted,
the added weight of water must be lifted clear of the surface. Once
the mast reaches horizontal, the water begins to flow toward the
step. The reduced capsizing moment quickly drops well below the
applied righting moment and the boat snaps through vertical, often
to capsize again on the opposite tack. This could result in the crew
becoming trapped under the sail.
SOLUTION
The solution is to prevent flooding of the mast.
The Junior fleet has done this by inserting closed cell foam.
Another variation is familiar to Laser sailors, who have a
completely sealed top mast section.
HOW TO DO IT YOURSELF
You need to get closed cell pipe
insulation. We ordered ours from McMaster Carr (www.mcmaster.com).
It is specified by its inside diameter (3/8”) and thickness (1/2”).
To insert it into an existing mast, you need to get it past the
fasteners on the forestay. You could remove and re-install them, but
we simply scored the insulation. First, unscrew and remove the
masthead fitting. Push one section of insulation into the mast,
rotating it as necessary when you contact the fasteners. You will
feel it line up. Then use the second as a pusher to force the first
piece down to the spreaders. Finish the job by re-installing the
masthead fitting. Total cost about $6 per boat. Here are some
pictures of the operation:
Duct tape added for visual clarity.
RIGHTING TECHNIQUES
The volume of water displaced is about 0.6 pounds
per foot while the mast weighs about 0.85 pounds per foot so the
mast will not float! We have reduced the righting
moment required to lift the mast almost in half. This should allow
standard scoop or walkover recovery techniques to succeed. If you
need outside assistance here are some suggestions.
If the mast comes horizontal but won’t lift out
of the water try turning the bow into the wind. The wind will fill
in between the mast and surface of the water creating a lifting
force just like a board sailor’s water start. Once the sail clears
the water, it will swing behind the mast reducing the righting
moment just when less is required to prevent rollover.
If you still have trouble, have the rescue boat
gently pull your bow painter to windward at dead slow speed and
for only 1-2 boat lengths. This pulls the sail out from under the
overlying water so it can drain off astern as the boat rights.
Repeat as necessary (see Cautionary Note below).
If you still don’t have enough righting moment,
have the rescue boat grab the windward shroud and
lift while moving hand over hand toward the hounds. You should
lift the mast until it is slightly above horizontal. You should
see and/or hear water escaping near the step. Give it time to
escape! As it does, the load will get lighter. Start moving hand
over hand back down the leeward shroud, which allows
the rescue team to control the tendency to swing past vertical and
rollover.
CAUTIONARY NOTE
It is very important to understand the size of
the forces involved in righting a boat. A prime rule to teach your
juniors is to UNCLEAT THE SHEETS. Even boats as small
as a Laser need to move large masses of water to come back upright.
If the sheet is cleated tight and the boat is simply rolled back
upright, you would need to move almost 100 tons of water out
of the way! It is far easier to slice through the water at an angle
of attack regulated by how tight the sheet is cleated. Anyone who
has righted a boat has observed that it tends to move forward as it
comes up and the water flows off the leech. That is why we recommend
towing forward with the rescue boat. As you pull forward the angle
of attack of the sail minimizes drag as the boat rolls. The water
flows off the sail just as the wind does when upright.
Address your questions to
ccycjuniors@hotmail.com
Attention: Bruce
Thompson:
NOTES AND COMMENTS
Here is a photo of the masthead fitting as originally supplied
(1994) showing the hole through the base and a view of the foam
inserted into the mast extrusion. See discussion below.
The foam has a nominal wall thickness of ½”, but
as received it had a wall thickness of 3/4” making the outside
diameter of 1-7/8”. We recommend asking your supplier to confirm
outside diameter as there appears to be some manufacturing
tolerance.
Our URL has been distributed to US Sailing
Regional Training Directors and posted on
www.sailingscuttlebutt.com #1561 .
Dave Kirkpatrick of Vanguard posted his own
comments
http://www.sailingscuttlebutt.com/archived_Detail.asp?key=2794
He states that newer boats (1996 onward) have a masthead without the
hole. You can see their parts sheet
http://teamvanguard.com/boats/c/cnt/down/C420Locator8-5x11.pdf
showing P/N 20046. He also indicates that the mast should not leak
too much and he prefers to save the weight of the foam.
We believe that having a sealed masthead and foam
is even better and that the weight and cost penalty is quite minor.
Scuttlebutt posted our reply:
“I agree with Dave Kirkpatrick ('Butt 1562) on 2
points:
1) Our 1994 vintage 420s have a large, hidden hole in the base of
the masthead fitting allowing water to flood the mast. 2) Even with
a solid fitting, the mast will leak. This is proven when lifting the
head of a flooded mast above horizontal. The water rushes to the
step and sprays out. Given point 2 above, the conclusion is that the
mast will completely flood given enough time (say waiting for a
thunderstorm to pass). This is where the foam shines. By filling the
void, it prevents most flooding.
The cost is a very small increase in heeling moment, less than a
pint of water! The foam weighs ounces, a pint is a pound the world
around. I would support owners using both a sealed mast and foam.
This "belt & suspenders" approach maximizes safety. It's a decision
left to the owners to make. The question is whether a class
dominated by kids could benefit from some adult supervision. Is it
best to sacrifice the last measure of boatspeed for increased
safety? We'll find out. “
There are several permutations of masthead and foam. Our boats
had been modified by the previous owner to plug the masthead, but
some plugs failed. This allowed water in, but restricted it going
out. The foam really helped control the flooding! We will reseal the
mastheads to ensure watertightness.
CONCEPTUAL ANALYSIS OF STATIC AND DYNAMIC STABILITY OF 420
AUTHOR’S NOTE: The angles and moments shown are
conceptual, not measured. The kids are in school and the water is
46º F. Testing will have to wait.
Below is a chart showing the general form of a
static hydrodynamic stability chart. The boat is statically stabile
when the vertical axis is zero. These three points are upright,
inverted and an intermediate point called the angle of vanishing
stability. For a centerboard boat this is about 80º, for a keelboat
it is about 120º. Starting at the left, zero heel, the curve starts
to rise due to the center of buoyancy shifting to leeward faster
than the center of gravity does. The slope of the curve is positive
in the direction of greater heel. The curve peaks when the leeward
rail starts to submerge, about 40-45º. The curve trends downward
until the boat reaches vanishing stability at about 80º.
Capsize!!!!!
At this point, the righting moment of the hull
just balances the heeling moment of the mast. At 90º the heeling
moment of the mast reaches a maximum and begins to decrease. At
about 100º, the center of gravity of the hull crosses the center of
buoyancy and it begins to add to heeling moment. The heeling moment
continues to increase mostly due to the hull and decreasingly due to
the mast. The heeling moment peaks roughly when the top of old
windward tank hits the water at 150º. The slope of the curve
gradually decreases until it reaches zero at 180º.
The susceptibility of the boat to dynamic
transients can be inferred by the slope of the curve in the
direction of the changing heel angle. For the upright part of the
curve (0 – 90º), a sharply positive slope indicates a damping effect
due to an increasing reaction force. A horizontal slope indicates a
neutral effect. A sharply negative slope indicates positive
feedback. The boat will be increasingly unstable. [While some
positive feedback can be useful with the presence of negative
feedback of other terms, only positive feedback is unstable. Think
of an addiction, it feels good so you want to do more until you’re
out of control. A steady diet of only positive feedback leads
children to become brats!]
OBSERVATIONS
- The boat is dynamically stable at two points, upright and
inverted. At these cusps, the slope changes sign and the absolute
value of moment rises in either direction.
- Once the boat passes vanishing stability, it will continue to
seek static stability. It will turtle.
- When the sails hit the water they induce a transient impulse
due to hydrodynamic drag through the water. The maximum speed is
at the first impact and the impulse can be quite high since the
drag is exponential to the velocity. This force only exists due to
movement, so it cannot provide a righting force. It just slows the
rate at which the boat turtles. A 420 without sails will turtle
much quicker than one with them.
- The time for the crew to try going over the side and onto the
centerboard is the range from 45-80º. The impact impulse is the
last best chance before the crew slips into the water. A crew on
the board will add righting moment. A crew in the water will have
no effect.
- When the crew tries to right the boat, they will experience a
maximum heeling moment from the mast at 90º. This will be greater
than the heeling moment during the capsize if the mast has leaked
and is now full of water. There is also a need lift the sail up to
let the overlying water flow off the sail over the leech.
- Note that as the boat rises above the angle of vanishing
stability, it begins to add righting moment. Slowly at first, it
begins to increase rapidly as the angle reaches 40º and the slope
turns negative. The boat tends to snap upright.
- The righting moment of a 100-pound crew out 3 feet on the
centerboard is 300 foot-pounds. The righting moment at zero heel
is 275 foot-pounds (half the beam times 100 pounds) less whatever
buoyancy immersion of the legs provides. So while the boat is now
upright, there is still a large righting moment due to the crew
causing it to swing over on top of him. This is why we recommend
the scoop recovery. The second crew is lifted out of the water to
provide a counter-balancing moment in the nick of time.
- Having water in the mast means more righting moment, which
could require both crew on the centerboard and preclude a scoop
recovery. No water is best!
