**Wave
Science**

Donald J. Jordan

Consulting Engineer

113 Evergreen Lane

Glastonbury, Connecticut

Reproduced with the kind permission of Donald Jordan

**
Non-Breaking Waves**

Scientists began to study waves in the late 18th and early 19th centuries. They
used a flow channel in which they could measure the speed, height, and velocity
of regular waves.

They found that the wave speed and the wave length could be defined by a simple
formula:

Thus a wave with a wave length of 300 ft. will have a wave speed of 39 ft/sec.
(23 knots) and a period between wave crests of 7.7 seconds.

For regular waves the wave height does not affect the wave speed.

These simple relationships help us understand that waves are packets of energy
floating on the water surface. Each wave is similar to a pendulum. The mass
of waters moving up and down is the weight and the wave length is similar to
the length of the arm of the pendulum.

Note that the weight of the water or the weight at the bottom of the pendulum
has no effect on the period of either a wave or a pendulum. In fact the formula
for the period of a simple pendulum is remarkably similar to that of a wave.

Period of a wave = A L
seconds Period of a pendulum = B L
seconds.

Where A and B are constants and L is the wave length and pendulum arm length.

Thus waves formed of liquid lead would have the same speed as water waves

A pendulum would have the same period if the weight were lead or brass. Of course
this is why pendulums were used for clocks.

From these studies we can obtain an effective engineering understanding of regular
waves. However, regular waves do not threaten a well found yacht unless the
yacht is permitted to surf down the forward face and reach a high speed.

**Breaking Waves**

When scientists increased the height
of the waves in the flow channel by moving the paddle more violently they observed
that the waves became very steep and collapsed forming a breaking wave. They
determined that the waves would break when the wave height exceeded 1/7 of the
wave length.

Similarly we know that a pendulum will cease to function if it swings up too
high.

A wave breaks because its crest is too high for the forward speed of the wave.
The water cannot get over the crest, just as a yacht cannot get over.

When a wave breaks, water cascades down the forward face of the wave. Sailors
have described the face of a breaking wave as a waterfall. The falling water
makes a roaring sound, and from ancient times such waves were known as "growlers".

**Worst
Case Breaking Wave Strike **

I have chosen the case of the Winston Churchill in the 1998 Sydney Hobart race
as an example of a worst case breaking wave. The Churchill was a classic wooden
sloop of 25 tons displacement and 55 ft. LOA. Of the experienced crew of 9,
three perished in the accident.

From "Fatal Storm' by Mundle. "A sea came out of nowhere", said
Stanley, " I could feel it from where I was in the aft coach house. It
picked the boat up and rolled it down its face - 25 tons of boat- into the trough
at a 45 degree angle. It was like hitting a brick wall when we hit the bottom".
A crewman below reports that a sudden motion of the ship picked him up and threw
him 7 ft. He observed that 8 ft of the heavy timber bulwark and planking had
been torn off near the leeward shrouds, and the ribs were exposed. . The boat
filled rapidly and sank in a matter of minutes.

This is an unusual type of accident. Although there are records of many storm
casualties, I am aware of no documented instance of a well found yacht of the
size and reputation of the Churchill and crewed by an ample group of expert
sailors, suffering such catastrophic structural damage that it sank in a matter
of minutes. How could this possibly happen? The severity or the storm was extreme
but by no means unprecedented. There are numerous reports of large sailing yachts
surviving hurricanes of the same general magnitude. Although yachts have been
lost in such storms I have been able to find no record of comparable structural
damage.

History shows that the probability of a yacht being capsized and damaged by
a large breaking wave is strongly influenced by the displacement of the vessel.
Yachts under 35 ft. have a poor history while yachts over 50 ft are rarely capsized
and damaged.

The nature and extent of the damage incurred by the Churchill is also most unusual.
The vessel was designed by Sparkman and Stevens and was maintained to the highest
standard. Yet the heavy timber bulwark was shattered, the planking gone and
the ribs exposed.

There is no question of the fact that the leeward bow of the boat was driven
into solid green water at an extremely high velocity, far higher than would
be expected in a simple contact with a breaking wave. We now have a technical
understanding of how such a destructive force can be generated. Observations
from many experienced sailors on a number of the SH yachts provide data which
permit a sound engineering analysis of the performance of the waves and the
boats in the race.

Water forces are applied to the hull of a yacht by two means, buoyancy forces
and dynamic forces. Buoyancy forces are the familiar pressure forces which keep
the boat afloat. They never reach sufficient magnitude to damage a well found
yacht.

Dynamic forces result from the motion of the boat relative to the water, either as a result of the boat velocity or the water velocity due to wave motion. A speeding power boat can be destroyed by striking solid water. Similarly, a sailing yacht can be destroyed if it is accelerated up to a high speed by a breaking wave strike and then impacts solid green water in the preceding trough. This is the fate that befell the Churchill.

To understand this phenomenon we must consider the concept of energy. A moving
car or boat has energy. This form of energy is called kinetic energy. Kinetic
energy is measured in foot-pounds. Kinetic energy can be calculated by the formula
KE=1/2 (w/g) times (v squared). Where w is the weight of the car or boat, g
is the acceleration of gravity (32.2 ft/sec) and v is the velocity in ft./sec.

Thus a 3,000 lb. weight traveling at 30 mph (44 ft./sec.) would have a kinetic
energy of 90,000 foot pounds. Now...and this is very important to our understanding
of the Churchill disaster...if the moving vehicle strikes an object, the kinetic
energy determines the severity of the collision and the extent of the damage.

In addition to energy due to motion, a vehicle can possess energy due to height.
This type of energy, also measured in foot pounds, is calculated simply as the
height times the weight. A 3000 lb car hoisted to a height of 50 ft. would have
150,000 foot pounds of energy. If dropped from 50 ft to a solid surface, the
car would dissipate this energy in damage. If the car was compressed by 2 ft.
the average force during the impact would be 75,000 pounds. If it landed on
its top and compressed four feet (because it was softer) the average force would
be 37,500 lbs. .These numbers (compression and force) are not precise but the
product must be the same to satisfy the energy balance.

Since a car accident is a more familiar event than a wave strike I will continue
with this analogy since it is technically identical to the Churchill event.

**Fig.1** shows a car being dropped from 50 ft. It will impact
the ground at 57 ft/sec (39 mph) and will have a collision energy of 150,000
ft. pounds. It will sustain the appropriate damage.

**Fig. 2** shows the
car on a ramp 50 ft. high. The car rolls freely down the ramp and strikes a
tree. The velocity at the bottom of the ramp will be the same as if the car
had been dropped vertically, that is 57 ft/sec. Thus the collision damage will
be comparable to that of the vertical drop.

Now we come to the key element in our study of storm damage. This explains why the crew of the Churchill felt an impact similar to that of striking another boat.

**Fig. 3** Here we assume that the entire ramp is mounted on wheels
and is propelled toward the tree at 30 m.p.h. The moving ramp simulates the
front face of a large breaking storm wave. The car is released from the top
of the ramp and is permitted to roll down the face. The " increase"
in speed while descending the ramp is the same as when the ramp is stationery,
39 m.p.h.. Thus the final speed of the car as it leaves the ramp and strikes
the tree is 30 plus 39 or 69 m.p.h..

However since the kinetic energy
(collision energy) varies as the square of the speed, the kinetic energy (collision
energy} is 480,000 foot lbs or over 3 times as much as if the ramp had been
stationary. There is no other wave - boat interaction which can generate such
destructive loads.

The wave in this event acts as a sling shot, hurling the vehicle, car or boat
forward at a high velocity. This is the mechanism which destroyed the Churchill
and the same mechanical system that David used to destroy Goliath.

With this understanding we can design a simple system to decelerate the boat
before it strikes the solid water in the trough.

**An Experiment
**

The sling shot concept can seem arcane. Actually it is simple.

It can be accurately observed with no special equipment. All it takes is a shovel
with a curved blade and a golf ball.

Place the golf ball in the center of a garage or cellar with a level floor.
Walk across the cellar at a constant (approx.) speed pushing the shovel towards
the ball. Adjust your walking speed such that the ball is picked up and ascends
up about 2/3 of the shovel height.

Maintain your walking speed constant as the ball rolls down the blade and proceeds
to outrun the shovel. Except for friction effect, the ball will leave the shovel
at twice the speed at which you were walking. When it strikes an object it will
have 4 times the collision energy of a ball moving at shovel speed.

The Loss of the Winston Churchill

We now have enough information that we can apply the same analyses to the Winston
Churchill.

We can estimate the speed of a breaking wave (but not a non-breaking wave) if
we know the height of the wave. The breaking wave that destroyed the Churchill
was estimated by several observers to have a height of at least 45 ft. Such
a wave would be moving at about 30 mph. Therefore, when the boat had been picked
up by the wave it would be moving at that speed..

As the Churchill slid down the face of the wave on its side, there would be
very little friction or drag, because the water supporting the boat would be
moving at the same speed and would accelerate with the boat. With no friction
the boat could reach a speed of 67 mph by the time it reached the trough. If
we assume only half of this speed increase, the boat would strike the green
water in the trough at over 50 mph.

This velocity is equivalent to a free fall from over 70 ft. This clearly explains
the sequence of events which destroyed the Churchill. A boat striking green
water at this speed can incur a force of over 200,000 lbs

Winston Churchhill with drogue

It is not feasible to design a drogue which will prevent a boat from being picked
up by the wave and carried up to wave speed. The loads would be prohibitive.
Therefore it is necessary to design a drogue which is capable of decelerating
the boat to a low speed before it plunges into the trough.

**Fig . 4** shows the Churchill in the trough of a 45 ft breaking
wave. A series drogue has been deployed and the boat is dead in the water. The
wave face is moving toward the boat at over 30 mph. The drogue device consists
of 164 5in. diam. cones concentric with the towline and attached to 348 ft.of
double braided nylon line tapered from 7/8 to ¾ to ½ in.diam.
A 30 lb. weight, usually a length of chain is attached to the end.

**Fig. 5** shows the
boat as it reaches the wave face. A heavy boat such as the Churchill is not
thrown ahead of the wave but is caught up by the wave and brought up to wave
speed. The loads on the boat when struck by the crest are not high enough to
cause damage. The boat rides up the face and is near wave speed when struck
by the moving water at the crest. In the more than 15 years that the drogue
has been at sea, no boat has ever been damaged. In particular the rudder, transom,
cockpit and companionway doors have all been unscathed.

At the position shown in Fig. 5, the drogue has picked up a load of approx.
5000 lbs.

This is sufficient to avoid yawing and broaching but not sufficient to prevent the boat from being driven up to wave speed.

**Fig. 6** shows the
Churchill surfing down the face of the wave. The crest has broken and the surface
water is moving with the wave. Without a drogue the boat would accelerate rapidly.
However, at this point the drogue has straightened out and is reaching the peak
load, approx. 25000 lbs or half the displacement of the boat. The boat now decelerates
and reaches the trough at a moderate velocity and with little roll or yaw..
No high loads are imposed on the hull or rigging.

**Fig. 7** shows the
Churchill without a drogue impacting the trough at a speed of over 50 mph. This
is why the crew reported that "It felt like we had struck another boat".

The wave characteristics discussed
here and shown on these figures are taken from a computational fluid dynamics
simulation. Although actual storm waves will have local surface variations,
the energy level and dynamic behavior of large waves such as those that struck
the Churchill are now well understood and predictable for engineering purposes.

have a load of 900 lbs. The series drogue will protect both the monohull and the multihull in a survival storm.

I would be glad to answer questions via email and to provide supporting documents where feasible.

Donald J. Jordan, Consulting Engineer

Glastonbury, CT

.