The proposed wave energy converter consists of a floating tube filled with water and power units inside. As waves pass, the water level inside the tube fluctuates up and down, causing buoys attached to the power units to move. This motion is converted to electrical energy via gear systems and generators. The design aims for low cost production and maintenance to produce electricity at around €0.05/kWh. Key aspects are its modular structure, ability to withstand storms by sinking below waves, and potential organization into zig-zag farms for efficient energy capture and transmission. Experimental testing is needed to validate the power generation capabilities and viability of the concept.

2. Introduction
 The proposed converter is a linear attenuator
 Its operation is based in the mediation of water
between sea waves and a chain of power units (PU)
 Power units and water are inside a floating tube
 The water is the working substance acting as an
interface between the sea waves and the power units

3. Concept requirements
 Low manufacturing and maintenance cost in order the
device to meet the cost requirements (≈ 0,05 €/Kwh)
 Long device viability
 High capability of capturing wave power flux
 Modular structure
 Environmentally friendly

4. Main components
A Power module with m (=1, 2,...,m) PU’s and the
generator compartment in the middle.
(1) Flexible and durable floating tube reinforced with
metal rings. The tube is tightly closed.
(2) Power unit,
(3) Generator compartment hermetically closed
(4) Articulated axis with Cardan joints

5. The power unit
(1) Pair of cylindrical buoys
(2) Gear systems
(3) Protective cage
(4) Shaft
(5) Cardan joint
(6) Buoy supporting arm

6. The pinion system
(1) Arm supporting buoy I, rotating
freely around the shaft
(2) Arm supporting buoy II, rotating
freely around the shaft
(3) Pinion mounted on arm 1 performing
rotation with center on the shaft
(4) Pinion mounted on arm 2 rotating
around the shaft, coupling pinion 3
with pinion 5
(5) Pinion coupled to the shaft through a
ratchet (not shown in the figure)
(6) The shaft. A ratchet (not shown)
couples the shaft with the pinion 5

7. Function of a power module
The floating tube is filled with water by half, another 30% of the tube approximately is
occupied by the power units and the generator compartment and the remaining 20% is
free space. Buoys, in a trough contained water, move upward, while buoys on a
crest, move downward by following the receding water. The water in the tube is
denoted by blue color, while the dot line stands for the sea wave. Tube sections in wave
troughs sink deeper relative to tube sections on wave crests. This is the Hug effect. If ζ
and C the sea surface and tube axis deviations correspondingly, then
Hug ≡ ABS(ζmax–Cmax)

8. Power flow associated with a sea wave
Let Fw the wave energy flux through a vertical plane of unit
width perpendicular to the wave propagation direction, then
Fw = E 0 c g
Where, E0 the wave energy density E0=ρw g Hs2/16, cg the group
velocity of the wave in deep-water approximation, cg=
g/2ωp, Hs the significant wave height, Tp the peak wave period
of the Pierson-Moskowitz spectrum and ωp = 2π/ Tp. Making
the replacements ρw≈1000 Kg/m3 and g≈10 m/s2 we obtain
Fw ≈ 0,5Hs2 Tp Kw/m

9. According to Pierson-Moskowitz spectrum
Hs=0,021U2 and Tp ~0,73U
U the wind speed at 19,5 m high so,
Fw=2,5 Hs5/2 and Tp=5,04Hs1/2
Fw Kw/m
Tp
Fw

10. Power capability of the converter
The figure shows a cross-section of a
power unit
D: floating tube diameter
R: buoys radius
r: polar distance of the buoy center
q: polar angle of the centers of the
buoys
h: maximum vertical distance
traversed by buoys centers

11. It is easy to prove that maximum work per stroke is obtained if
R = 0,2D, then r = 0,3D, h= 0,447D & -0,841 ≤ q ≤ +0,841 rad
If we take Z=1,5D and W the buoys weight, then
Wmax = 1,65D4-0,8944WD/1000 KJ/PU (per power unit)
Ppuc=(1,65D3 - 0,8944W/1000)D/T Kw/PU (per power unit)
1. Assume a sinusoidal wave with T = Tp
2. Neglect the weight term as very small compared to
buoyancy
3. Divide by the PU length (=2D), then we obtain
Pc ≡ 0,825D3/Tp Kw/m
the relation above is the definition of the power capability of a
converter.
Pc is a reference quantity for determining the efficiency of
a converter under real sea conditions

12. Equations of motion
Torques associated
with a PU
Buoyancy torque per buoy
Tb(t)=0,018ρgD4(U-sinUcosU)cosq
Weight torque per buoy
Tw=-0,3WDcosq
Driving torque per couple of
buoys:
Tbw=2(Tb + Tw)
Damping torque per couple of
buoys
Td =a(dq/dt)
Inertia torque per couple of
buoys
TI =-0,18(WD2/g)(d2q/dt2)
Equation of motion:
TI+Tbw+Td =0

13. Equation of upward motion:
0,18(WD2/g)(d2q/dt2)=Tbw-a(dq/dt)
In the downward motion we neglect inertia term as negligible and the
damping term (a=0) since the buoys fall freely following the water
level, then Tbw=0 and consequently
U-sinUcosU - (0,3/0,018)W/ρg D3=0
The solution is denoted by Uw. The downward motion starts when the
normalized water level Q≡Y/D takes the value Qw given by
Qw=0,3sinqmin– 0,2cosUw
The normalized distance Hw ≡ H/D of the buoy center from the water level
Qw is given by
Hw≡ (ymin-Ymin)/D = 0,3sinqmin-Qw=0,2cosUw
The buoys follow the descending water Q, while Hw remains constant during
the downward motion so,
Equation of downward motion may be written as follows,
q=Asin((0,2cosUw+Q)/ 0,3) (Asin stands for the inverse sin)
Equations of motion are solved numerically.

14. Power considerations
The dissipated power by a damper is given by
Pd = Td(dq/dt) = a(dq/dt)2 w/PU
Similarly the power yield of the converter is given by
Pyld = Tbwdq/dt = a(dq/dt)2 w/PU
For very low or very high values of a, Pd → 0, so there
is an optimum value of aopt for which Pd becomes
maximum. we determine aopt, we introduce it into the
eq. of motion and solve it numerically. The maximum
power yield per power module meter is given by
Pyld = (10-3Tbw/2D)dq/dt Kw/m

15. Water Fluctuation Factor: WFF is an important quantity
, defined as two times the standard deviation of Q(t), i.e.,
WFF ≡ 2<Q(t)2>1/2
WFF is strongly dependent on Hs and D and characterizes
the water behavior inside the floating tube. WFF is a factor
requiring measurement in the concept validation
experiment.
Efficiency Coefficient: This coefficient characterizes the
performance of a power module and is defined as follows,
e ≡ <Pyld>/Pc
Our simulation model shows strong dependence of e on WFF

16. Application
Solution of eq. of motion
for a regular sinusoidal
wave
Wave parameters:
Hs = 3,02 m, Tp =8,76
sec, Fw=40 Kw/m
Power module parameters:
D=3 m, Hug= 0,43
m, Pc = 2,54 Kw/m,
Solution: WWF=0,71%,
<Pyld>=2,44 Kw/m, e = 96%,

17. Tbw vs q Tbw vs Ω
the inscribed area is equal to the work Negative values of Ω, corresponding to
produced by the buoys per cycle downward motion, have been neglected

18. Further analysis gives the following interesting results

20. Irregular wave-fully developed sea

21. Plots of Tbw vs. q and Ω for various D’s - Wave characteristics (Hs,Tp, Fw) are fixed

23. In Figs Tbw vs. Ω, we have omitted negative values of Ω for reasons of clarity. On the
other hand the downward motion is not of particular importance. Looking at the
plots of Tbw vs q we observe the pattern to shift to higher values of q with
Increasing D. In other words the buoys tend to move to the upper half of the
floating tube and their activity is limited to narrower range of q’s. Similarly, the
Plots of Tbw vs. Ω (=dq/dt) show that the buoys activity tends to be confined in the
vicinity of a straight line as D increases.

24. Irregular
• In the case of the specific irregular wave Pyld, e > Pyld , e corresponding to the regular wave for all D’s. The
reason is that in the sea wave there are more numerous time-intervals < Tp between successive troughs or
crests than time-intervals > Tp.
• Also, in the irregular wave, e increases slightly for 1 ≤ D ≤ 3 m and then decreases for higher values of D, while
e, corresponding to the regular wave, always decreases as D increases. This is due to two competing factors.
One is the increasing e-width with D, responsible for the increasing of e and the other is the decreasing of
WWF with D, responsible for the decreasing of e. The influence of WFF seems to prevail for D>3 m
• The behavior of WFF as D varies is almost the same in both kinds of waves, having only slightly lower values.

25. Discussion
So far we have developed an innovative concept aimed
to a low cost electric power production. Based in the
cost of fossil fuels, the target is about 0,05 euros /Kwh.
However, we must point out that two important factors
are missing from this estimate, the cost of
environmental destruction and the finite amount of
fossil fuels on the planet. On the other hand the energy
consumption in heavily industrialized countries is less
than 1% of solar energy reaching the surface of these
countries. That alone makes comprehensible the need to
utilize, in every possible way, the primary and secondary
solar energy offered to us profusely and for ever.

26. Among a number of important technical issues we choose
some basic ones to discuss below:
a. We have made the assumption that the internal water
level follows the inverse sea level motion. This is not
totally true. Actually, the internal water tends to follow
the troughs, but we do not know the exact way. This is an
issue which requires thorough investigation under various
waves in the beginning of the experimental work.
b. The right and the left buoy must remain in the right and
left side of the power unit always since if they interchange
position, the power unit stops producing work. This may
be achieved by introducing a reset buoy on the top of the
power unit to reset the unit in upright position, as shown
in the figure below. Shown also the limiters of
upward/downward buoys motion, as well the electric
power cable.

27. External flexible/durable tube
Reset buoy
Limiter of upward Protective cage
buoys motion
Left Buoy Right Buoy
cable that runs through the unit
resulting in sockets at the ends Limiter of downward
of the power module buoys motion

28. c. A farm may be developed in a zig-zag formation for
efficient capture of the wave energy. The zig-zag
arrangement ensures yet the direct connection of internal
wires between adjacent devices.
Loose anchoring
Tight anchoring
Wave Front

29. The zig-zag farm is allowed to orient in the direction of the wave
propagation, thanks to the flexibility of the tubes, if the ends, opposite to the
incident wave front, are tightly anchored, while the other ones are loosely
anchored.

30. d. A very important issue is the protection of the farm against storm
conditions. Only devices that can withstand the strongest storms will
survive. Already, the flexibility of the device and the farm as a
whole, the matching of the wave with the device, at any time, by
equalizing weight and buoyancy along the tube, as well as the
mobility of the internal water remove the risk of accumulation of
strong stresses in individual points. On the other hand, the forces
developed inside the tube by the weight of the accumulated water
and the buoyancy of the buoys in the troughs of the wave (action-
reaction) are distributed over a large area of the floating tube walls
and thus result in the pursuit of relatively low pressure on the
walls, i.e. this is a kind of self-protection.
However, under conditions of large scale storms, each device of the
farm must be able to sink below the surface of the sea. One idea
would be the buoys and the floating tube to be filled with water.
Technically, this is achieved if the buoys consist of perforated solid
outer wall with an air-bladder inside.
To achieve immersion, we pump out the air of the buoys and we
pump into the floating tube and the buoys sea water.

31. e. The Concept Proof is a necessary experimental procedure and
consist the starting phase for the validation of the concept, before
the submission of a proposal, aiming to a commercial device, for
financial support from European programs, or/and from the private
sector. The latter would concern the next phases as: the Engineering
design model, the Process model, the Prototype model, and
Demonstration model.
The experimental device for the concept proof should be about 10
meters long and 0,4 meters in diameter. The experiment might be
performed in two steps:
Step 1: Measurement of the two important factors (WFF and hug) in
a simplified variation of the device, free of complex mechanical
parts. The values of the above factors are determinative for prooving
the theoretically expected power yields. This is a very low cost step
and it is decisive one in order to proceed to the next more costly
experiment.
Step 2: In this step the power yield, the buoyancy of the device and
the forces exerted upon it, as well as the mooring tensions
developed for various kinds of waves.

32. Main characteristics
I. Low cost electric power production
 Very simple design leading to low manufacturing cost.
 Most parts of the device float in the sea and are much lighter than
most of the competitive machines. Therefore, a device can be
transferred near the sea in parts and be assembled in the sea with
consequent cost reduction.
 The structural flexibility of the device, the movement of the water
inside the tube to positions of minimum potential energy and the
consequent hugging of the wave minimizes unwanted loadings,
securing long viability.
 The zig-zag layout allows the installation of the main electrical
conductor inside the tubes along the farm line and from there to
the mains in the mainland reducing this way the total length of the
conductor and consequently the cost of the energy transfer. This is
compared with farms with scattered formations of other devices
 A low cost converter would be very appropriate for low wave
potential seas. In such seas, the viability of a converter would be
rather high, lowering even more the operational cost of the farm.

33. Main characteristics (continued)
II. Friendliness to the marine environment
 There are no turbines and high pressure pumps
which operate with non-ecological liquids.
 There is no any external protective paint.
 It is not noisy.
 The farms are low profile and there are no horizon
blocking gigantic structures. Installed a few
kilometers away from the coastline they are not
being visible from the coast.

34. Inventors
 Alexandros Anastassiadis, Physicist, Ph.D. Columbia
University N.Y., alexandrosanastassiadis@gmail.com
 John Anastassiadis, Engineering Science: B.S. The City
University of New York, johna@ath.forthnet.gr
 Dimitrios Papageorgiou, B.S. in Economics and Business
Management at SUNY Stonybrook, M.B.A. in Finance &
BPR, Athens Laboratory of Business Administration,
dipapageor@cosmote.gr
Patent: In the process of publication