# Slingshot Resonance for Ocean Wave Energy Conversion

- 19 Downloads

## Abstract

The slingshot effect and its application to converting ocean wave energy are discussed. It is shown that, owing to the large inertia transported by ocean waves and their periodicity, the slingshot effect can result in the transmission of significant kinetic energy to a puck colliding elastically with a pusher plate driven by ocean wave motion. A simplified geometrical model is used to demonstrate that, despite the stochastic nature of the collisions (whereby collisions occur at random times in the wave cycle), head-on collisions occur more frequently, yielding a net average gain of energy. However, the most promising configuration for applying the slingshot effect to ocean wave energy conversion is that which matches, through appropriate design, the travel time of the puck between collisions with the wave period. Then, only head-on collisions occur, resulting in a significant magnification of the puck kinetic energy. Further research will be required before this slingshot effect can be practically implemented for ocean wave energy conversion.

## Keywords

Ocean wave energy conversion Slingshot effect Resonant cavities Electromagnetic wave converters## Abbreviations

*b*Damping coefficient

*B*Magnetic field

- \(c_{\text{d}}\)
Drag coefficient

- \(C_1\)
Constant

- \(C_2\)
Constant

- \(D_c\)
Slingshot cavity diameter

*E*Energy

*F*Forces

*g*Gravity

*h*Cavity length

*H*Wave amplitude

*l*Wire length

- \(m_{\text{p}}\)
Puck mass

*N*Number of turns in the wire loop

*P*Power

*R*Load resistance

*t*Time

*T*Wave period

*u*Puck velocity

*v*Ocean wave velocity

*X*Parameter, Eq. (34)

*Y*Parameter, Eq. (35)

*z*Vertical length co-ordinate

## Greek symbols

- \(\beta\)
Total damping parameter

- \(\beta _{\text{f}}\)
Damping parameter due to friction

- \(\beta _{\text{c}}\)
Damping parameter due to the converter

- \(\delta\)
Phase difference between the puck and the wave

- \(\rho\)
Atmospheric density

- \(\omega\)
Wave frequency

- \(\Gamma\)
Net gain in the resonant mode

## Subscripts

*c*Converter

*d*Downwards

*f*Friction

*r*Resonant

*s*Stochastic

*u*Upwards

## Notes

### Acknowledgements

This research was supported by the Spanish Ministry of Economy and Competitiveness under the fellowship grant Ramon y Cajal: RYC-2013-13459.

## References

- 1.D. Ross,
*Power from the Waves*(Oxford University Press, Oxford, UK, 1995)Google Scholar - 2.B. Drew, A.R. Plumer, M.N. Sahinkaya, A Review of Wave Energy Converter Technology. Proc. IMechE Vol. 223, Part A: J. Power and Energy (2009)Google Scholar
- 3.E. Rusu, F. Onea, A review of the technologies for wave energy extraction. Clean Energy
**2**(1), 10–19 (2018)CrossRefGoogle Scholar - 4.H.T. Benbouzid, M. Benbouzid, An up-to-date technologies review and evaluation of wave energy converters. Int. Rev. Electr. Eng. Iree
**10**(1), 52–61 (2015)CrossRefGoogle Scholar - 5.K. Budal, J. Falnes, A resonant point absorber of ocean-wave power. Nature
**256**, 478–479 (1975)CrossRefGoogle Scholar - 6.J. Falnes,
*Ocean Waves and Oscillating Systems*(Cambridge University Press, Cambridge, 2002), pp. 1–275CrossRefzbMATHGoogle Scholar - 7.J.N. Miles, Resonant response of harbours: an equivalent circuit analysis. J. Fluid Mech.
**46**, 241–265 (1971)CrossRefzbMATHGoogle Scholar - 8.J. Engströma, V. Kurupath, J. Isberg, M. Leijon, A resonant two body system for a point absorbing wave energy converter with direct-driven linear generator. J. Appl. Phys.
**110**, 124904 (2011)CrossRefGoogle Scholar - 9.M.E. McCormick,
*Ocean Wave Energy Conversion*(Dover Publications, Inc., Mineola, 2007)Google Scholar - 10.Y. Masuda, Wave Activated Generator. Proceeding, International Collowium on the Exposition of teh oceasn, Bordeaux, France (1971)Google Scholar
- 11.K. Budal, J. Falnes,
*Power from Sea Waves*(B. M. Count, Academic Press, London, 1980)Google Scholar - 12.J. Falnes, Int. J. Offshore Polar Eng.
**12**(2), 147 (2002)Google Scholar - 13.A. Babarit, G. Duclos, A.H. Clement, Comparison of latching control strategies for a heaving wave energy device in random sea. Appl. Ocean. Res.
**26**, 227 (2004)CrossRefGoogle Scholar - 14.M.P. Schoen, J. Hals, T. Moan, Wave prediction and robust control of heaving wave energy devices for irregular waves. IEEE Trans. Energy Convers.
**99**, 13 (2011)Google Scholar - 15.J. Engström, M. Eriksson, J. Isberg, M. Leijon, Wave energy converter with enhanced amplitude response at frequencies coinciding with Swedish west coast sea states by use of a supplementary submerged body. J. Appl. Phys.
**106**, 064512 (2009)CrossRefGoogle Scholar - 16.J.J. Candido, P.A.P.S. Justino, Modelling, control and Pontryagin Maximum Principle for a two-body wave energy device. Renew. Energy
**36**, 1545 (2010)CrossRefGoogle Scholar - 17.T. Omholt, A wave Activated Electric Generator. Proceedings, Ocean 78, Marine Technology Conference, Washington, D.C, pp. 585–589 (1978)Google Scholar