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<P ALIGN="CENTER">ESTIMATING HYDROFOIL MOVEMENT OVER WAVES</P>
<P ALIGN="RIGHT">W.R. Frank, <BR>
87 Staincross Common, <BR>
Barnsley. B75 6NA <BR>
tel: 382272</P>
<P>In the open sea, a sailing hydrofoil is moving at nearly 90 degrees to wind and
parallel with waves, which reach forward and rear foils at nearly the same times.
There is no pitching moment at exactly 90 deg., although heave is accompanied by
secondary pitch. Foils feel the wave frequency. When waves approach from other directions,
the same estimating procedures may be used, but it is more complicated. The mathematics
applies exactly, when foil lifts are proportional to angles of attack and to depths
of immersion. When otherwise, plot lifts against angles and depths, and use the tangents
to replace terms like R/ ,, and R/D.</P>
<P>Complex behavior may be split up, each separate behavior estimated, and then the
results combined. We may illustrate by an imaginary experiment:</P>
<P>Imagine a model hydrofoil tested in a tank. Its movements are due to waves, but
it also resists movements. So do one test over flat water, another over waves.</P>
<P>Over flat water, the model is caused to heave by a mechanism which applies a force
at centre of gravity G. Heave Y. sin w t, requires force F. sin (w t + a - ß).</P>
<P>Now repeat over waves A. sin. w t; but with G hinged to a slider on a horizontal
rail parallel with the waves. The model can pitch, but not heave. Measure the hinge
force Fw. sin.(w t + a).</P>
<P>For amplitudes only; Y requires force F. Yx Fw/F would require force Fw. A requires
force Fw. So A will cause heave of amplitude Y x Fw/F. To bring in the phase angles,
use the rules below. A causes heave of phase angle (w t + a - ß).</P>
<P>We could do a pitching experiment at 90 deg. to waves, length between foils equal
to half a wavelength, so that G does not experience wave generated heaving force;
although there will be secondary heave due to pitching.</P>
<P>In the mathematics, for different headings, the wave heaving action is separated
from the wave pitching action. All this seems complicated; but in the mathematics,
all we have to do is put the sum of moments zero to get heave; put the sum of forces
zero to get pitch. For pitch, first estimate pitch if foils were not to vary depths
of immersion. The maths. provides ratios which are used to multiply the 'geometrically
calculated' heave and pitch. We need formulae for wave frequencies, lengths and speeds.</P>
<P>(page 19)
<HR>
</P>
<P>Using rotating vectors</P>
<P>Forces, moments, displacements, velocities, etc., are all cycling at tines frequency
felt by foils, f. On heading parallel to waves, foil frequency f = wave frequency
w. Each may be represented by a rotating 'crank.' One vector is taken as datum, and
the positions of other vectors measured from this datum. A diagram is a 'snapshot,'
which freezes the rotation. I have used anti-clockwise as positive, and horizontal
pointing to the right to represent time t = 0. We are not concerned with instantaneous
values; only with amplitudes and their phase angles.</P>
<P>There is one complication. In the algebra, there are sine and cosine terms. We
could replace cos. (w t + y ) by sin.(w t + 90 + y ). The cosine zero datum is the
vertical through 0. Cos.w t = sin.(w t + 90.).</P>
<P><U>Vector rules.</U> <BR>
To add, draw to scale, and measure from 0. Draw a parallelogram and measure its diagonal.
<BR>
To subtract vector B from vector A, reverse B by rotating 180 degrees; draw a parallelogram
and measure the diagonal. <BR>
To multiply. A sin(w t + a) x B. sin.(w t + b) = AxBxsin. (w t + a + b). <BR>
To divide. A sin (w t + a) divided by B sin (w t + b) =(A./B.) sin (w t + a - b).</P>
<P><U>Negative vectors.</U> These can be made positive by rotating 180 deg., and
adding 180 to the phase angle.</P>
<P><U>Changing phases. </U>Fig. 5. Vectors at phase y and (90 + y ), have to be altered.
Draw the resultant and then resolve it into the new directions.</P>
<P><U>Mass and inertia.</U> In the experiment, mass is involved in the flat water
test, since G oscillated, but mass is not involved in the heave wave experiment,
when G is not oscillating. Moment of inertia comes into both experiments. In the
calculations, mass is put zero in the wave generated force formulae.</P>
<P>On heading parallel with waves, foil frequency f rad/sec = wave freq. w. Vertical
displacements of {FORMULA} G = y = Y. sin w t. Vel = dy/dt = w.Y. cos w t. accn -
w 22 Ysin w t.</P>
<P>Angular displacements = {FORMULA} G sin(6Jt + ~ . Angl vel.~ . ~.cos(~Jt + /).
Accn - GJZ ~. z</P>
<P>Mass accl force, - M.w2 .Y.sin w t.</P>
<P>Inertia acceln moment = -I. Q .sin (w t + y ). w2</P>
<CENTER>
<P><IMG SRC="p20.gif" WIDTH="555" HEIGHT="200" ALIGN="BOTTOM" BORDER="0"></P>
</CENTER>
<P>(page 20)
<HR>
</P>
<P><U>Calculations for heave.</U> G is given linear oscillation Y sin w t. Secondary
pitching is Q. sin (w t + y ). Anti clockwise made positive. Force F is applied externally.
Moment is zero. The estimates, when the force is generated by waves, replace oscillation
of G by wave vertical oscillation. G is then prevented from heaving, but can pitch.
The only difference in calculations is that in wave force calculations, the mass
acceleration force is omitted.</P>
<P><U>How the external force F varies.<BR>
</U>When a foil force increases, external force F decreases and vice versa. Note
that when the hydrofoil tilts positively, anti-clockwise, that both foils lose lift.</P>
<P><U>DAMPING FORCES.<BR>
</U>When water moves vertically past a foil, upwards, it increases the foil angle
of attack. If the water velocity is u, the foil velocity is V, then angle of attack
is increased by (u/V), and foil lift increased by<BR>
R.x(u/V) / a.</P>
<P>When the foil moves, the water being stationary, then the force opposes. <BR>
That requires increase in the externally applied force.
<HR>
<BR>
<U>THE SUM OF THE EXTERNALLY APPLIED FORCES, THROUGH G, is:</U></P>
<P>(Formula)</P>
<P>+ ~ .sin(~ t + /).( -b.Rb/Db + a.Rs./Ds. + Rb./o~b. + Rs./c~s.)</P>
<P>+ ~ .cos(~ t + ~).x(~ /V) x ( -b.Rb./r~(b. + a.Rs./ots.)
<HR>
</P>
<P><U>THE SUM OF THE MOMENTS OF THESE FORCES IS ZERO IN HEAVE.</U></P>
<P>(Formula)<BR>
+</P>
<P>+ ~.sin(b~t + t). (( b . Rb/Db. + a~ .Rs./Ds. - b.Rb./~ b. + a.Rsky~s) _ .I.)</P>
<P>+ ~ .cos(~ t + g). (CJ/V).( b}.Rb/~ b + a .Ra./o~ s.)
<HR>
</P>
<P>When a foil is not surface piercing or feeler controlled, omit the /D term.</P>
<P>Use the moment equation to find the ratio, Q/Y., and the value of angle y , then
use these in the force equation to replace Q by Y. Solve by drawing vector diagrams.
In pitch calculations, put the sum of the forces zero.</P>
<P>
<HR>
</P>
<P>These formulae are for instantaneous values of y, whereas vector diagrams are
pictures of vector 'crank' positions. When 'sine( w t)' is used, it means a 'crank',
horizontal and pointing to the right. When 'cos ( w t)', that means a 'crank'. pointing
vertically upwards. These 'sine' and 'cos' positions are the zero angle datums, and
phase angles are measured from them anti clockwise plus. 'Cranks' are manipulated
using ordinary trigonometry.</P>
<P>(page 21)
<HR>
</P>
<P><U>EXAMPLE.</U> Hydrofoil 20ft between foils. a=12ft. b=8ft. V=20ft/sec. Wave
frequency 2 rad/sec.= freq. felt by foils on heading parallel to waves. The bow foil
has angle of attack 0.15 red; the stern foil, 0.10 red. Bow foil is surface piercing,
and lift is proportional to depth of immersion. The bow foil is immersed lft., the
stern foil is totally immersed, and Rs/Ds terms are put zero. Mass is 20 slugs. The
weight of 6441b is partly carried by the outrigger. The forward component of wind
force transfers some weight from stern to bows. Bow static reaction Rb = 3001b. Stern
Rs = 2001b. Moment of inertia in pitch, I, is 1000 slug ft2.</P>
<P>( w /V) in damping terms is 1/10. Mass acceleration force is -20.2 .Y. = -80.Y.lb.
Max 2<BR>
Inertia acceleration moment is - 1000.2 . . = - 4000 Q . lb.ft. Max</P>
<P><U>COEFFICIENTS.<BR>
</U>A=300. B=4000. C=400. D= -8000. E= -3600. F= -8000. G=35,200. H= 416,000.
<HR>
</P>
<P>Instantaneous values for applied force F.sin( w t:+ ? ). Figs 5 and 6</P>
<P>((300 - 80).Y.sin w t. + (4000/10).Y.cos. w t.) + (400. Q .sin.( w t + y ) - (8000/10)
Q .cos.( w t + y ). --------3.
<HR>
</P>
<P>Instantaneous values for an applied moment. In heave, this moment is put zero.</P>
<P>(-3600.Y.sin w t.- (8000/10).Y.cos. w t.)) Fig 3 +(( 35,000 - 4000).~ . sin. w
t + Q )) + (416,000/10). Q . cos ( w t + y ).) Fig 4
<HR>
</P>
<P>The 'cranks' in diagrams are maximum values of the oscillating quantities. In
figure 3, the combined moments due to OT and TR are represented by OR. In fig 4,
the combined moments due to OP and PQ are represented by OQ. Fig 4 is reduced in
scale 1/14.1 , and OP put in line with OR. The sum is zero. This ratio, 1/14.1 and
phase angle = -40.6 degrees,are then used in the force balance diagrams to replace
Q by Y, and to give y a numerical value. The vectors at phase angle y, have to be
'phase shifted' to zero phase; done by drawing in fig. 5. Then add these resolved
vectors to the original Y vectors in fig. 6.
<HR>
</P>
<P>Figure 6 resultant is the maximum value of the applied force, at phase angle 58.8
deg. from the applied heave oscillation Y.sin Wt. Left hand diagram. <BR>
<U>Wave generated forces.</U> Tank test. G held against heaving, but the hydrofoil
is free to pitch. The applied heave oscillation amplitude Y, is replaced by the vertical
water oscillation A.sin w t. The only difference is that there is no mass acceleration
force. So, if we add 80 to the horizontal vector, we get force Fw due to a wave amplitude
Y. We want Fw due to wave amplitude A, so multiply by A/Y. But Y is unknown. We do
know that the wave generated force Fw has to equal applied force F.</P>
<P>(page 22)
<HR>
</P>
<P>Refer to fig 6. To increase the amplitude of force F up to Fw, the original heave
Y has to be multiplied by Fw/F, and its phase altered by 8.9 deg.</P>
<P><U>So wave amplitude A causes heave of A.Fw/F.sin ( w t - 8.9 deg).</U></P>
<P>These phase angle concepts are confusing. But the procedures and arithmetic are
simple. For other frequencies, copy this example. For other hydrofoil speeds, coefficients
are re-calculated. For other headings, some information about waves is required.
Otherwise, put the sum of the forces zero to get pitching.</P>
<CENTER>
<P><IMG SRC="p23.gif" WIDTH="435" HEIGHT="600" ALIGN="BOTTOM" BORDER="0"></P>
</CENTER>
<P>(page 23)</P>
<P><A HREF="101.html#contents">Return to Contents</A></P>
<P>
<HR>
</P>
<DIV ALIGN="RIGHT">
<P>St Andrews, <BR>
Fife Scotland <BR>
April 1985</P>
</DIV>
<P><A NAME="Wind turbine"></A>Dear Mr. Ellison,</P>
<P>You may like to have the enclosed paper on the Vertical-Axis Turbine/Propeller
for Ship Propulsion, if you do not already have Wind Engineering; the windmill builders
are now linked with a group considering ship propulsion, so you may have seen it.</P>
<P>You may be able to put me right over my notion that I am the first to expound
the principle of the vertical-axis machine as a device for both stream-bending and
stream-accelerating or decelerating. Have you come across any evidence of this being
anticipated ? I am too old to start a campaign to have such a machine built; it would
be a satisfaction to have priority recognized - if I have it. Although I have sent
xerox copies of, the paper to several people who should, I thought, be interested,
I have had no response. Now that I have the proper reprints I shall be sending out
a few more.</P>
<P>To change the subject completely, there is another thing that I wanted to ask
you. When my triscaph "Trion" was built in Cowes in 1955 for the speed-trials,
we had the floats tested in Saunders-Roe's seaplane tank, and there is a nice set
of experimental figures which has never been published. There is such a shortage
of genuine measurements on anything comparable that I feel they should appear. The
man who paid for the testing is long dead, and Crago, who did the testing, sees no
objection. Would you like it for an AYRS issue ? The triscaph configuration could
be useful for a rescue craft, for example: with the floats trimmed bow-down in the
displacement mode, a low-power outboard would give cruising speed of 4 or 5 knots,
while the system for changing trim to planing attitude would automatically immerse
a big outboard for the 30-knot stuff.</P>
<H4>References</H4>
<OL Type="1">
<LI><B>H.M. Barkla.</B><I> "Downwind Faster than the Wind' AYRS, Vol. 98, 11
9Dec. 1983): (Amateur Yacht Research Society).</I>
</OL>
<OL Type="1">
<LI><B>A.B. Bauer.</B><I> "Faster than the Wind' Proceedings of the First AIAA
Symposium on the AeroHydronautics of Sailing {1969).</I>
</OL>
<OL Type="1">
<LI><B>A.B. Bauer.</B><I> "Sailing all Points of the Compass' Proceedings of
the Third AIAA Symposium on the Aer/Hydronautics of Sailing {1971).</I>
</OL>
<OL Type="1">
<LI><B>H.M. Barkla.</B><I> "The Linear Wind/Water-Mill/Propeller' Proceedings
of the Twelfth AIAA Symposium on the AeroHydronautics of Sailing (1982).</I>
</OL>
<OL Type="1">
<LI><B>R.C.T. Rainey.</B><I> "The Wind Turbine Ship," "Symposium on
Wind Propulsion of Commercial Ships." RINA 1980.</I>
</OL>
<OL Type="1">
<LI><B>J. Wellicome.</B><I> "A Broad Appraisal of the Economic and Technical
Requisites for a Wind driven Merchant Vessel," RINA Symposium "The Future
of Commercial Sail," 1975.</I>
</OL>
<OL Type="1">
<LI><B>N. Bose.</B><I> "Windmills - Propulsion for a Hydrofoil Trimaran,"
"Symposium on Wind Propulsion of Commercial Ships," RINA 1980.</I>
</OL>
<OL Type="1">
<LI><B>N. Bose and R.C. McGregor.</B><I> "The Wind Turbine Boat - Construction,
Performance and Control," RINA Conference "Advanced Rigs for Advanced Craft"
1983.</I>
</OL>
<OL Type="1">
<LI><B>H.A. Madsen and K. Lundgren.</B><I> "The Voith-Schneider Wind Turbine,"
Aalborg University Centre 1980.</I>
</OL>
<P>Hugh Barkla</P>
<P>(page 24)
<HR>
</P>
<DIV ALIGN="RIGHT">
<P>Michael Ellison <BR>
10 Boringdon Terrace <BR>
Turnchapel, <BR>
Plymouth, PL9 9QT</P>
</DIV>
<P>Dear Mr Barkla,</P>
<P>Very many thanks for your letter of 9th and the enclosed paper on Vertical-Axis
Turbine/Propeller.</P>
<P>Two members are active on their own in this field. Joseph Dusek, who lives in
Sydney recently took out a patent on a vertical axis windmill. His idea is to use
the wind 'lift' on the upwind sweep of the blade to give power via hydraulic or an
air pump. He has done a lot of research on his own and builds models and a full size
hydrofoil craft "Dalibor" on which he has tried various rigs. Not similar
to your idea but I am sure he would be very pleased to read your paper.</P>
<P>The second member, Douglas Hannan, is an ideas man in New York who makes a living
from after dinner talking and drawing cartoons. He has sent many ideas for savonnus
rotors (reversible) and other inclined rigs. He tries these on models but I have
never seen any maths to indicate performance or possible power outputs and so I assume
that these have never been measured.</P>
<P>Of course there are many other members like George Chapman, Reg Frank and Harry
Morse who will study the sums. I am sure these people understand all that we publish.
A few years ago I made a big effort to understand the patent papers by Anton Flettner
for his rotors. He had I gather ordered the construction of a vertical axis windmill
powered craft when he went on holiday. On his return he stopped work and changed
to his rotors. The later ones using power fans and slots were never tried at sea.</P>
<P>I would be very pleased indeed to have the "Trion" test figures for
publication. I feel that one of the biggest things we could do to help design progress
would be to publish such information, not only for special craft but for "ordinary"
fast racing craft as well. As we are not trying to sell anything honest figures could
be published - even just towing a range of craft at various speeds could be helpful.</P>
<P>At the end of June I shall move to Plymouth, I have bought an old terraced house
near the harbour plus a small building to use as an office. Hopefully this will help
us get back into growth and action again. BBC Television spent two days in Plymouth
recently making a programme about A.Y.R.S. to show in June or July (one of "Making
Waves" series). A U.S.A. magazine "Nautical Quarterly" are publishing
a feature article about us in May with a foreword by H.R.H. Prince Philip and I hope
this will bring in some more overseas members.</P>
<P>(page 25)
<HR>
</P>
<P>It is strange that around the whole world so very few people are building and
trying out new ideas. Those that do try get very little encouragement! I also notice
that recently "peoplet" have almost stopped buying our back numbers. Anything
published more than two years ago is regarded as being of historic rather than future
research. The time will come when we will have to use video film to distribute our
information, I fear that this will be quite soon.</P>
<CENTER>
<P><IMG SRC="p26.gif" WIDTH="366" HEIGHT="362" ALIGN="BOTTOM" BORDER="0"></P>
</CENTER>
<P>(page 26)</P>
<P><A HREF="101.html#contents">Return to Contents</A></P>
<P>
<HR>
</P>
<CENTER>
<P><A NAME="vertical axis mill"></A>VERTICAL AXIS WINDMILL</P>
</CENTER>
<P>The present invention relates to the above device in the form of vertical axis
windmill to produce power from the wind. The device consists of windmill mounted
on vertical shaft, helicopter fashion, and unlike similar windmills that produce
power by using drag of reclining blades off the wind, the device stated above uses
aerodynamic force of advancing blades into the wind which flip upwards.</P>
<P>In order that the invention may be better understood and put practice preferred
forms therefore are hereinafter described, by way of example with reference to the
accompanying diagrammatic drawings in which Fig. 1 is a view which describes invention.
The device consists of windmill mounted on hollow vertical shaft (1) helicopter fashion.
The windmill operates on principle that exposed area of reclining blades is pushed
off the wind while</P>
<P>advancing blade into the wind rotates 85 degrees and projects small front section
of the edge of the blade into the wind. Blades of the windmill (2) are attached through
bearings (4) to short beams which are hinged to the hub and shaft. This system enables
blades to not only rotate along their horizontal axis 85 degrees, but also to flip
upwards producing additional aerodynamic force which is extracted by means of pneumatic
pumps (5) or any other mechanical, electrical or hydraulic systems. The power from
systems is transmitted through hollow shaft (1). On movable plate (6) under the rotor,
rolling small wheels (7) connected by short arms to axles of blades. By moving plate
up or down output of windmill is regulated or shut down in high winds, or when not
in use. Upper curved dish (8) supports trailing wheels in flip-up mode.</P>
<DIV ALIGN="RIGHT">
<P>J.T. Dusek</P>
</DIV>
<CENTER>
<H4>LATE EXTRA</H4>
</CENTER>
<CENTER>
<H4>VERTICAL AXIS AEROGENERATOR (VAAG)</H4>
</CENTER>
<DIV ALIGN="RIGHT">
<P>PETER A. RICHARDSON</P>
</DIV>
<P>Rotaboat MayFly</P>
<P>A VAAG/Screw driven craft. Using data tfom a tunnel tested Musgrove VAAL a fibre
composite has been constructed. A trimaran hull 5m LOA X 3m bean has been tailored
to the turbine. Pedal power from a bicycle crank-set with fixed sprocket provides
initial rotation of the turbine. SEE SOUTHAMPTON SHOW 1985.</P>
<DIV ALIGN="RIGHT">
<P>NINE BOLD PLACE, LIVERPOOL, Ll PDN.</P>
</DIV>
<CENTER>
<P>Compiled and edited by Norman Champ.</P>
</CENTER>
<P>(page 27)
<HR>
</P>
<CENTER>
<P><IMG SRC="BCa.jpg" WIDTH="337" HEIGHT="232" ALIGN="BOTTOM" BORDER="0"></P>
</CENTER>
<CENTER>
<P><IMG SRC="BCb.gif" WIDTH="334" HEIGHT="234" ALIGN="BOTTOM" BORDER="0"></P>
</CENTER>
<P>(Back Cover)</P>
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