Hydrodynamics of Surfboards

Scotts Head, NSW, 1974

Thesis by Michael Paine

for Bachelor of Engineering (Mechanical), Sydney University 1974

I have scanned most of the (typewritten!) pages of my thesis and created a 5mb PDF file. No copyright but acknowledgment and/or a link would be appreciated.

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)

Updates

19 Mar 25 URBNSURF offers a friendly, safe and controlled environment for families and kids to enjoy surfing together (how disappointing that an artificial surfing venue has opened in Sydney, just kilometres from some of the best surfing beaches in the world. Part of the attraction of surfing is to be with nature using free, non-polluting energy for sport)
12 Nov 24 ABC: Shark attack study using light ‘decoys’ to fool great whites could lead to protections for surfers - another way that science might help surfers!
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 Sydne 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 mp4).
Reaper Cheat - inflatable rash vest. A clever design that featured on The New Inventors in 2004. The Sydney agent was: Canoe Sports - but the product was discontinued, probably because it couldn't meet mandatory standards that are intended for other sports.
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).

Here is the table of contents:

Introduction.

Chapter l Theory.

Chapter2 Hydrodynamics of surfing.

Chapter 3 Experimental Work.

Field experiments

Surfboard speed measurement

Creating a standing wave.

Design of the equipment

Chapter 4 Stability of surfboards.

Effects of the curved free surface.

Chapter 5 Conclusions

References

Appendix

NACA model test data

Images

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

2. Layout of flume tank
FLUME

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

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

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

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

In a shoaling wave the water particle orbits become ellipses
breaking wave ellipse

Footnote

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

Abstract

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.