Hydrodynamics of Surfboards

Scotts Head, NSW, 1974

Thesis by Michael Paine

for Bachelor of Engineering (Mechanical),  Sydney University 1974

This was a fascinating research project involving
• riding waves with an instrumented surfboard (a pitot tube and pressure gauge for speed measurement) - measured speeds ranged from 5 to 10 m/s
• observing surfboard riding and taking speed measurements from the shore (similar results)
• reviewing ocean wave theory - deep ocean waves, solitary (cnoidal) waves and breaking waves
• developing an early (punch card!) computer model of a shoaling breaking wave
• reviewing and adapting theory for planing water craft - including stability problems (porpoising) and lift/drag/trim data from seaplane research.
• designing, constructing and operating an experiment which generated a standing wave in a flume tank. The resulting wave was about 200mm high (flume 1.2m wide, flow rate 0.37 cumecs)
• constructing model surfboards and experimenting with them on the standing wave.
• (unsuccessfully) trying to model a human spring mass system to dampen the instability of the models (this was essentially a 2D flow - it turns out that a 3D flow would probably have eliminated the instability - see the paper by Hornung and Killen).
• recommending some design changes for surfboards: sharp trailing edges and a stepped front to eliminate the strong tendency of the convex front of a surfboard to nosedive (I later built such a surfboard - although it performed as expected on a wave its non-planing drag was high and this made it much more difficult to paddle than a conventional surfboard and this made it impractical)

• 31 Jul 24 The Conversation: Anatomy of a wave: what makes the Olympic surf break at Teahupo'o unique.
  
• July 2024 Cosmos Magazine: Surfing Science - but I do not agree with this description of a breaking wave: "When they come in contact with the seabed near shore, it exerts frictional force on the base of the wave, turning the orbit of molecules elliptical, until the top of the wave is moving faster than the base, causing it to break." (the diagram shows the ellipse becomes more vertical).
  
• Firstly, waves slow down due to the reducing depth of water (see formula on page 9 of my thesis: wave celerity (speed) is proportional to the square root of water depth). Being a liquid, there is no significant friction in the process of a shoaling wave, other than very close to the seafloor.
  
• Secondly, the near circular motion of wave particles in deep water is squashed into a horizontal ellipse as water depth decreases - see Figure 4 on page 9 of my thesis. This effect means that water particles on the crest of the water move towards shore faster causing the wave to become steeper until the wave breaks. In fact, as a follow-up to my thesis I wrote a Fortran program (using punch cards!) that simulated this steepening effect and I found that the wave "broke" - the angle of the free surface near mid-height went past the vertical! 
  
• 17 Feb 04: As part of its Sports Exhibition, the Powerhouse Museum in Sydney has built a superb interactive surfing display with a 300mm high tubing wave, based on Peter Killen's work. Here is a picture of the display. Click on the picture for a movie clip (3Mb).
• Reaper Cheat - inflatable rash vest. A clever design that featured on The New Inventors in 2004. The Sydney agent is: Canoe Sports, 2/6 Taronga Place, Mona Vale  NSW  4922,  Ph: (02)99794911
• 26 Feb 05: Swansea University Research into Fins and Surfboards (SURFS) research group
• 30 Jun 05 New Scientist: Surf's up, down at the swimming pool
• ASR “Amalgamates Solutions and Research” - [Design of] Multi-purpose artificial surfing reefs + Nature ($): Creating the perfect wave (p997)
• 21 Aug 08 BBC: Bournemouth makes waves with surf plan.
• June 2009. Watching a few big-surf movies, it seems that some of my ideas might be ready to try out. In particular, tow-surfing allows surfers to catch huge ocean swells and my calculations in 1974 showed that this was feasible. "It is theoretically possible to surf ocean waves of height greater than 16ft. An initial velocity of 40ft/s (approx 35km/h) is required to catch the wave". I had no idea how this might be achieved - but that was way before jetskis. I also noted that "the sanity of a person riding waves in mid-ocean would have to be questioned" - this still stands! Also the extremely bumpy ride suggests that a stepped hull might be useful for improving stability, since the paddling drag is no longer an issue.
• 22 Nov 17 The Conversation: Walter Munk, inventor of the surf forecast, turns 100.
• 12 Apr 18 ABC Science Show: Blimp used to spot sharks - Kye Adams from Uni of Wollongong has be trialling use of a blimp to spot sharks and distressed swimmers (not necessarily at the same time!) at Kiama Beach. It is a great idea because a blimp can stay in the air, at the same spot, all day. Drones need frequent recharges. Seems to me to be a much better alternative to shark nets and would actually cost a lot less than paying contractors to deploy and maintain the nets (i.e. remove dead dolphins and turtles).
  

I have scanned most of the (typewritten!) pages of my thesis and created a 400K PDF file. To save space I have not included several of the photos so save them as images from this page if you need them. No copyright but acknowledge and/or a link would be appreciated.

Here is the table of contents:

CONTENTS

Acknowledgements.
Notation.

Introduction.

Previous Work.

Chapter l Theory.

Principles of surfboard riding.
Ocean wave theory.
Typical Sydney waves.
Planing hull theory.

Chapter2 Hydrodynamics of surfing.

Initial case,surfing deep water waves.
Hydrodynamics of surfing across a breaking wave. -

Chapter 3 Experimental Work.

Field experiments;
Measurement of wave and peeling velocities.
Surfboard speed measurement.
Performance of the equipment in the surf.
Results.
Hydrodynamics laboratory experiments;
Creating a standing wave.
Design of the equipment.
Initial results.

Chapter 4 Stability of surfboards.

General stability.
Porpoising;
Theory.
Discussion of the theory.
Stability of an actual surfboard.
Human response - the effects on stability.
Effects of the curved free surface.

Chapter 5 Conclusions

Effects of waves on planing craft
Some design suggestions for surfboards
A concluding note

References

Appendix

I. Deep water wave computer program.(Fortran!)
II Adaption of NACA model test data
III Wave profile measurement

Images

Tip: To view the image full size from Netscape right click the mouse and select View Image.

1.Use of sluice gate to generate a standing breaking wave


2. Layout of flume tank


3. Nosediving at the bottom of a wave (more of a problem with surf skis and surfboats)


4. Planing craft trim data from NACA seaplane experiments in the 1930s


5. Pitot tube and pressure gauge mounted on a surfboard for estimating speed


6. Panoramic view of one of the field experiments
(Scotts Head, New South Wales North Coast)



In a shoaling wave the water particle orbits become ellipses

Footnote

Thanks to my thesis supervisor, Bob Halliday, and the staff of the old Hydro Lab.

One year later Peter Killen (URL updated 7 Nov 06) undertook a similar, but more sophisticated thesis at the Australian National University. Peter used a plough shaped barrier to produce a 3D peeling breaking wave. The work was published in the Journal of Fluid Mechanics in 1976 (see below). Peter kindly cited my thesis work in that paper.

Peter subsequently built a full size standing wave system which he could ride with a surfboard at the Department of Mechanical Engineering, University of Queensland (circa 1979).

J. Fluid Mech. (1976), vol. 78, part 3, pp. 459-480

A stationary oblique breaking wave for laboratory testing of surfboards

By H. G. HORNUNG AND P. KILLEN

Department of Physics, School of General Studies,
Australian National University, Canberra
(Received 7 May 1976)
 

Abstract

A surface gravity wave obliquely incident on a sloping beach is broken near the   beach and has a smooth surface further out. Viewed in the frame of reference of   the transition from the smooth to the broken part, the flow is steady, and the   wave is oblique to the free stream. By placing a suitably shaped obstacle in a   flume operated at high Froude number, such a wave can be generated. Experiments in which a wave of 18 cm height was generated are described and the wave   shape and some of its characteristics presented. In particular, the dividing   stream surface separating that part of the flow which curls over into the break   from the part that flows smoothly over the obstacle is discussed.

Model surfboards can ride this wave unsupported, provided the correctly   scaled weight loads them at the right centre-of-mass position. This makes it possible to determine the forces on the board without a balance. A comparison   of the measured forces with estimates, particularly of the drag, indicate that viscous and surface-tension phenomena introduce only small scale effects in the   Froude number modelling. While the results are not sufficiently accurate to draw definite conclusions about the effects of surfboard shape, they indicate clearly   that surfboard flows may be modelled with quantitative success in the laboratory.

Images from the J. Fluid Mechanics paper

Cross section of the laboratory wave


Desirable wave shape!


Picture of the laboratory wave with a model surfboard

 

• Site map (graphic)