Ai Weiwei's wave

 

Ai Weiwei is an engineer's artist: he makes towers out of bicycles, polygons out of wood, and surveillance cameras out of marble. His work comments on the impact of industrialisation on culture and the environment; he uses electronic communication as part of his art. 

Seven key principles for converting wave energy

1.  Provide a point of reaction. Power is captured when wave induced motion is damped. The force resisting the motion results in an equal force in the opposite direction. This has to be opposed by something; no sky hooks allowed.
    
2. The DoF where power is extracted must have a restoring force. There must be a way to restore the change in position due to wave induced motion. Gravity is the simplest method; buoyancy does the job for heave, pitch and roll motion. If power is captured from surge, sway or yaw motions, a restoring force must be supplied by mechanical springs, or by coupling to a motion that has buoyancy. 
    
3. Radiated waves capture waves. When the power take off (PTO) system is run in reverse (motoring), the waves generated indicate the potential for capturing ocean waves. Good performance results from radiation of waves that have the same direction of travel, the same amplitude, and the opposite phase, as the waves you want to capture. These are the waves that the incoming wave splits into once it reaches the device: the waves reflected and/or transmitted by the wave energy converter.
    
4. Get the level of damping just right. Like baby bear’s porridge.
    
5. Match natural period to wave period. Radiating a wave which is out of phase with the waves you want to capture is important. At resonance the phase takes care of itself. The options are to design for a natural period that equals the design wave peiod, to have a range of operating modes with different natural periods, or to use the PTO force to trick the system into behaviour with the desired natural period.
    
6. Size matters. The smaller the device, the narrower the bandwidth of the capture curve, and the lower the natural period. These disadvantages trade off against cost, so clearly size is an important cost of energy consideration.
    
7. Manage losses. Reduce losses (PTO, overheads) in low energy seas; shed loads and power in high energy seas.

Can a photo demonstrate percentage of wave power absorbed?

Photo of Duck in action, by Jamie Taylor, the University of Edinburgh

This conundrum puzzled me for a while, so I'd like to share it with you. The question is whether it is possible to determine what percentage of wave power was being absorbed by the Duck in the time lapse photo.

 

About this photo 

This photo has an interesting history behind it: it was presented as proof to the British public (and funding bodies) that the Edinburgh Duck was capable of absorbing 96% of the power in a wave. Yet the story told by this photo is not as simple as it first seems.

Standing wave visualisation

Code showing standing wave due to terminator absorbing wave power

I've discussed how reflection results in a standing wave. It can be useful to visualise how complete and partial reflection look.

At some point I'll make this into something more fun and user-friendly. For now, if you are really curious to visualise how a standing wave looks when 96% of the energy has been absorbed, then paste the following into Octave (Matlab will do), and change Ar to 0.04:

clear;
close;
Ai = 1; %incident amplitude
Ar = 0.9; %amplitude of combined radiated and reflected waves - try varying between 0 (full absorption) and 1(no absorption).
NumWaves = 2;
wtmax = NumWaves*2*pi; %maximum time to plot to give NumWaves # of cycles

kx= 1:100;
wt = 1:wtmax/(20*NumWaves):wtmax %discretisation: 20 points per wave
for ii = 1:length(wt)
     wi(ii,:) = Ai*sin(wt(ii)+kx);
     wr(ii,:) = Ar*sin(wt(ii)-kx);
end

ws = wi+wr;
plot(ws)