# Surfboard Geometry and Design

Image Source: http://wikimedia.org

Surfboard Design has a number of different geometries associated with the overall size and shape of the surfboard and its underside fins.

For a high performance board capable of doing very tight turns, and spectacular skateboard like manoeuvers, there is a specific geometrical setup of the component parts of the board.

Here is a short two minute video of World Champion Kelly Slater showing some spectacular modern day manoeuvers on a very basic small wave at Bells Beach in Australia.

In this lesson we look at Modern Surfboard Design, and its associated mathematical geometry.

First we look at the main types of Surfboards, and then we examine the specific geometries of the component parts. We also look at computerised shaping and manufacture of surfboards.

Types of Surfboards

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For a large Poster of the Main Surfboard types, click the poster image below to enlarge it to full size on a new screen.

Image Source: http://sandiegosurfingschool.com

The Surf Science website at http://www.surfscience.com/ has the following classification scheme for types of Surfboards:

Shortboard
Fish
Longboard
Fun Board
Gun
Hybrid
Other

In the sections which follow, we examine each of these surfboard types.

The Shortboard

Image Purchased by Passy World from Dreamstime.com

The shortboard surfboard design reinvented high performance surfing in the 1970s, and continues to allow surfers to push the boundaries of the sport.

The shortboard is usually found at a length of under seven feet long.

It has a greater amount of “rocker” curve on its top deck, which allows it to surf in critical sections of the wave.

It is most commonly seen with sharp noses, thins rails, and either three or four fins.

The Fish

The Fish design became popular in the 1970s and originated from the knee-board.

It is typically found shorter and wider than the shortboard, and because of this it works very well in small mushy surf.

A fish is a relatively flat surfboard with only a small amount of rocker deck curve, allowing it to paddle very well and carry speed through flat sections of a wave.

It also has an angular swallow tail which helps disperse bumpy water away efficiently.

The Longboard

Image Source: http://surfingaustralia.com

The Longboard is the oldest and most traditional surfboard design.

Longboards typically range from 8 feet to 12 feet long, at least 2.5 inches thick and twenty inches wide.

This extra volume allows them to paddle incredibly well and catch waves with ease.

A beginner should start on a longboard shape to learn wave selection, paddling technique, and turning basics.

Longboards are great boards for small 1 to 1.5 metre high waves, (3ft to 5 ft surf).

Expert longboarders are known for their smooth style, surfing in a very smooth and fluid manner on waves they can ride right into shore.

Another exciting aspect of longboards is running up and down the board and “nose riding”, or “hanging five” and “hanging ten”.

The following six minute video shows some brilliant longboarding by local surfers at Maresias in Brazil.

The Funboard

A funboard is a larger surfboard with a lot of volume via its thickness and length, but not quite as much as a longboard.

They typically range from 6 feet to 8 feet long.

The funboard is a perfect for surfers who want to transition to a smaller board, while still maintaining additional paddling power and stability.

The funboard is similar to the “Malibu” and can come in a variety of tail shapes, nose shapes, and foils.

The Gun

Original Image Source: http://wikimedia.org

The Gun is the surfboard that needs to be used when the waves are huge.

A typical gun ranges in length from 6 ft 6 inches to 10 foot.

The extra length allows a surfer to gain enough speed while paddling to catch the huge and fast moving waves, (eg. 10 foot, 15 foot, and higher waves).

It is designed for big drops and handling very high speeds with good control.

A gun will have a great deal of rocker, (eg. the deck curves dramatically upwards), and will most likely have three of four fins.

There is a very good article about Gun boards at the following link:

http://www.grantmillersurfboards.com.au/boards/gun

The Hybrid

Image Source: http://surfingaustralia.com

A hybrid surfboard design mixes a few design elements from different board types.

One typical hybrid is a larger and wider version of either the Shortboard or the Fish.

Other hybrids mix characteristics and performance of a shortboard with the stability and tail design of a fish.

This is a great board for medium size days or even just a heavier surfer who wants to surf a smaller style board.

Other Types / SUP

Original Image Source: http://www.seabreeze.com.au

Other Types of surfboards mainly include the “Stand Up Paddle Board” or “SUP” design, as well as the “Tow In” board.

Some other less common surfboard designs are the “Bonzer”, “Mini Simmons”, and “Alaia”.

Each of these types excels in specific conditions.

The Stand Up Paddle Board can catch waves that normal surfers cannot, because using its big paddle produces a 4:1 ratio of paddling power compared to a surfer paddling with their arms.

Think of the types of Surfboards, as being like types of cars.

The Gun is like a big long cigar shaped high speed Drag Racer, the Longboard is like a big stable slow turning 4WD, the Hybrid is an SUV like the Ford Territory, the Shortboard is like a high performance sports car, and the Fish is like a rally car suited for good performance in bumpy conditions.

Choosing a Surfboard

The correct surfboard for your body is usually the one that is one hand palm above your head in length.

Choosing a board also depends on your weight, heavier people need a longer and wider board so that the foam volume is greater.

In addition, choosing a board depends on the type of waves and surfing you want to do, as well as your experience/commitment level.

For example, if you are a casual surfer who rides small-to-medium waves at your local beach break, you can choose to use a longboard or a funboard/malibu.

However, if you are an experienced serious surfer, who wants high manoeuverability, you can use a Fish or a Short Board.

Here are some sizing tables for a range of different board types.

Original Image Source: http://www.surfertoday.com

There is a great sizing table for all board types at the following link:

http://www.surfertoday.com/board-size-chart/surf

The following video talks about choosing a surfboard.

This next video is a great video about the types of boards beginner surfers should choose.

After carefully selecting the right size and design, it is important to know the main features of a surfboard.

A rounder template/outline will create wider turns with longer curves and more laid-back surfing.

Width and length are very important issues. Wider boards offer more fluctuation and are the perfect choice for very small fat waves.

Wider boards also have more stability, which is important for beginner surfers.

Rocker (the upward curve of the deck) is considered the most important feature in a surfboard, by many shapers who design and make boards.

For small mushy surf, people often use “Fish” type boards, which are a flat looking board with very little rocker.

In terms of tail shapes on surfboards, the rounded pin tail, round tail, and squash tail are very common because they hold the surfboard quite well in all-round surf conditions.

These component parts: Rocker curve, Tail shape, and so on are discussed in detail in the next section.

Parts of a Surfboard

Image Source: http://www.renesas.com

The component parts of a Surboard are:

Nose, Rocker Rails, Stringer, Fins, Tail, Bottom Contour, and Deck.

In the sections which follow we investigate the Geometry associated with each of these component parts, and how this effects the board’s performance characteristics.

The Nose

Image Source: http://surfboardexchange.com.au

The nose is the very front of the surfboard.

It’s Geometric shape plays a significant role when dropping into waves.

Noses vary in width, curvature and thickness.

There are two basic types of surfboard nose: The “Pointed Nose” and the “Round Nose”.

The Pointed nose is found on most high performance boards, like short boards and fish.

The pointed shape adds more rail curve compared to a round nose longboard, which is handy for dropping into big waves, and paddling through chop.

It is also easier to duck dive under a wave with a pointed nose because the nose is lot smaller and less buoyant than a round nose.

The Round Nose allows for the front of the board to have more surface area, giving the board more stability.

Round nose boards make it easier to paddle, glide, and plane on the surface because it helps to keep more of the surfboard out of the water.

Longboards typically have a round nose for the purpose of allowing the surfer to nose-ride.

The Rocker

Image Source: http://www.konaboys.com

A Surfboard has a bow or upward bend in it; eg. the deck is not flat along the entire board.

This bow, or upward banana-shaped curving, is called “The Rocker”.

Actually there are usually two Rockers on a typical board – the Nose Rocker and the Tail Rocker.

The in between part in the middle of the board, which includes most of the board’s deck is essentially flat.

The “Fish” design has a very flat deck, and so do most longboards; but other boards have a larger amount of curving upwards, (or more “rocker”), on their decks.

The Stringer

Image Source: http://www.hydroflex-surfboards.com

Traditionally, all surfboards required a stringer (stiffener) placed down the middle of the board to strengthen the core and add rigidity.

Without a stringer, the core would be too flexible and too prone to breakage.

Stringers have usually been wood, but carbon fibre has been used for some boards in recent times.

The Stringer has the two sides of the board foam laminated onto it, and comes as part of the initial “blank” that a shaper builds a board from.

Parabolic Stringers

This is an additional stringer system where two stringers are placed along the perimeter of the rails.

They are typically made of wood or carbon fiber and create “memory flex”, which dictates how quickly the shape can bend and bounce back to its original shape.

“Memory Flex” from Parabolic Stringers increase the board’s handling, and enable faster and tighter turning.

The added flexibility on the perimeter of the board allows you to lean into the stringer in turns as opposed to the foam.

This bends the stringer and shoots you out of the turn as it flexes back.

This results in more speed, acceleration and torque through each turn.

Multiple Stringers

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Longboards often have multiple stringers for the purpose of adding strength.

This is needed in a lot of cases because the larger surface area of a longboard can flex and wobble too much.

Additional stringers will minimize this effect.

Stringerless Boards

Some surfboards have no stringers.

Epoxy and Carbon Fiber boards often have a stringerless design.

Their materials and sandwich construction give the board added stiffness so a stringer is not needed.

http://www.tactics.com/info/epoxy-surfboard-construction

Surfboard Rails

Rails are a critical part of surfboard design and are the edge of a surfboard, where the deck and the bottom meet.

“Soft” rails are rounded with no hard edges. The transition from the rail to the bottom of the board is very smooth.

A “Hard” rail, (also called a down rail), is more squared off, sloping down in a more distinct manner and may form a corner or edge with the bottom.

The softer the curve of the rail, the more the surfboard will hold its “track” in the wave, but with reduced turning ability.

Softer rails are found on more traditional long-boards, but harder edges can be used in certain places for drive and manoeuverability.

Hard Rails produce boards which do a tighter turns and have explosive acceleration.

Modern short-boards have a combination of both soft and hard railing, and they are kept lower to disguise the thickness and give better turning.

Because the thickness of the board varies from nose to tail, forming the rails along the edge of the board can be quite complex, as shown in the following cross-sectional measurements diagram:

Image Source: http://www.swaylocks.com

There is a great detailed article all about rails at the following link:

http://www.surfscience.com/topics/surfboard-anatomy/rail/ignore-the-rail-at-own-risk/

Tail Shapes

Original Image Source: http://www.surfertoday.com

The different tail shapes on surfboards are: Squash, Square, Thumb, Rounded Pin Tail, Pin Tail, Swallow Tail, Bat Tail, and Wing Tail.

Tail shape influences the hold and release on the surface of the wave.

Water is a “sticky” liquid, and follows the lines of the board when it flows off the back of the board.

The basic hydrodynamics are that rounded curves hold water flow, whereas corners allow water to break away.

A round or pin tail will hold the water longer, making it stable in bigger surf and it also allows rounder and smoother turns.

A square or angular tail releases water quickly, making it looser, skateier and snappy.

Angular shaped tails like the “Wing”, create more pivot, which allows for sharper turns.

The Square tail is typically found on “Longboards” and historically is the earliest surfboard tail design. The square tail is wide and helps ad stability to a surfboard.

The Squash Tail is a square tail with an edgier shape which allows for quick release. This makes the board very responsive and easier for sharper and looser turns.

The Squash shape allows for more width, which increases the surface area in the tail. More surface area means more lift, or easier to plane and maintain speed.

This makes the Squash Tail good for slower spots of a wave, and is the most common type of tail found on “Shortboards”.

The Swallow Tail is ideal for smaller waves, which is why “Fish” boards typically have a very pronounced swallow tail.

Pin tails are typically found on big wave “Gun” boads. This is because tracking and control in high speeds is far more important than manoeuverability when dropping down the face of huge waves.

There is an excellent article all about Surboard Tail Types at the following link:

http://www.surfscience.com/topics/surfboard-anatomy/tail/basic-tail-shapes/

Surfboard Fins

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Underneath every surfboard there is as least one “fin”.

(They are called a “Fins” because they look like Dolphin and Shark Fins).

Fins are required to turn the board, to stop sideways slipping, and to hold the board onto the face of the wave.

In the early days of surfing, boards just had one reasonably large fin to enable the board to follow the line you wanted (“tracking”), and not slide out sideways underneath you when you turned.

In today’s high manoeuver surfing of tight turns, 180’s, snap backs, and skateboard type tricks, fins and the number of them underneath a board has become a far more complex matter.

Today there is a lot of engineering and design that goes into making surfboard fins and configuring them onto different types of boards.

Fins have flex built into them to cushion their action, and are “foiled” or curved like an aeroplane wing to create pressure differences on each side of the fin.

The idea of the pressure difference, is to have the fin have a low pressure side next to the wave, so that the board is sucked onto the face of the wave and has “grip” as it tracks through the water.

The following seven minute video provides a good tutorial about the properties and behaviour of surfboard fins.

Fin Characteristics

Original Image Source: http://www.surffcs.com.au

The key characteristics of surfing fins are the following:

– Base Length
– Depth
– Surface Area
– Sweep or Rake
– Foil

Base is the length between the leading and trailing edge where the fin meets the board.

Base Length is primarily linked to drive. Fins with a longer base length offer substantially more drive and acceleration.

Depth is the distance the fin penetrates into the water. Depth directly relates to hold.

The greater the depth the more hold, the shorter the depth the more a board will slide and release.

The Depth of the fin cannot be excessively large, or else the fin will create excessive drag and slow the board down.

Area is the total surface area of the fin.

Longboards have the option of installing a large rounded rectangular fin which has a large surface area, and provides stability for nose riding.

Sweep and Rake

Surfboard fins typically are heavily raked or swept back from the vertical, but there is a raking limit.

Sweeping back encourages downwash, the situation in which water flows from one side of the fin to the other.

Heavily raked fins tend to stall during hard turns, cause the fin tip downwash creates a large vortex behind the fin as it travels though the water.

Fins with a large rake give the surfboard a tighter turning radius, but don’t offer as much stability.

Fins with a small rake, like a longboard fin for nose riding give the surfboard more stability but a larger turning arc.

A balance needs to be made, determined by the type of waves the surfer usually rides and the style of board they have.

Rake is discussed later in this lesson in the Fins section.

Foil is associated with the curve of the exterior surface of the fin along its sides.

Foil is discussed in detail in the next section.

Foil on Fins

Original Image Source: http://magicseaweed.com

Foil refers to the shape and geometry of the inside and outside faces of the fin.

Foils directly affect the flow of water over the surface of the fin.

The above photo diagram shows the manoeuverability effect of using fins with different foils.

There are four main types of foils: “Flat”, “Inside”, “50/50″, and “70/30 or 80/20″ foil.

Information from the FCS Fins webpage describes these foils as follows:

FLAT FOIL: A flat inside face combined with a convex outside face. The traditional flat sided foil offers an even combination of drive, pivot and hold and provides a very consistent, reliable feel over a wide variety of conditions.

INSIDE FOIL: A sophisticated hydrodynamic foil consisting of a convex outside face, a rounded leading edge and a concaved inside face. Inside foil increases the efficiency of water flow over the surface of the fin adding lift and reducing drag. The result is a fin with more options through increased hold and speed.

50/50 FOIL: A symmetrical foil used on all centre fins where both sides are convex. Even water flow on both sides creates stability and control.

70/30 or 80/20 FOIL: Combines the performance of a centre and side fin offering increased speed, smooth rail-to-rail transitions and a consistent feel in a variety of conditions. (Ideal for all board types and rear fin placements)

The following diagrams compare the manoeuverability of a surfboard across the wave face for a three fin board, and a four fin board, when different foil profiles are present on the fins.

Original Image Source: www.fcs.com.au

Click the above Image to view full size

The following thirty second video explains FCS Fin Ratings in terms of Drive Speed, Turning Pivot, and Wave Hold/Release.

Flex and Cant on Fins

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Flex refers to the distortion of the fin from its original shape, caused by lateral pressure during a manoeuver.

This is effectively how much side to side movement the fin makes when the tip of the fin is pushed or pulled.

Eg. “Flex” is the amount a fin flexes from the straight line position.

Fins with little flex are more responsive and will have more speed and direct drive.

Fins with flex are more forgiving, easier to use, and offer a “whipping” sensation.

Ideally a fin should have a stiffer base for drive and a flexible tip for release

Cant refers to the angle of the side fins measured from a vertical line perpendicular to the flat bottom surface of the board.

Cant has a direct effect on acceleration and manoeuverability. Less cant produces faster acceleration and a stiffer feel.

More cant will increase manoeuverability and gives the board a loose feel.

The Angle the fins make with the centreline of the horizontal stringer is called the “toe”.

Detailed Fin Measurements

Specifying the Geometrical Design of a Fin requires marking in quite a few measurements:

Image Source: http://wavegrinder.com

Click the above image to go full size.

The above diagram compares a standard surfboard fin with a radical “Wave Grinder” winged keel type fin.

http://wavegrinder.com/

Bulbous Bullet Fin

Image Source: http://www.bulletfins.com

The design of this fin draws on lessons learned from the marine engineering of ship bows.

On ships they build a spherical “bulbous” lump onto the ship’s bow below the water line, this makes the ship cut through the water easier by creating its own out of phase wave to negate bow waves.

Just as with the bow of a non-bulbous ship, the traditional surfboard fin creates a wave as it displaces the water in its path.

The resulting turbulence places drag on the surfboard, which slows the board down.

The bulb of the Bullet Fin design greatly reduces this drag by creating a new (primary) fin wave in front of the original (secondary) wave.

This new bulb wave is designed to be nearly 180 degrees out of phase with the original fin wave to subtract its turbulence thus reducing fin drag.

The result is a fin that gets more efficient as you approach the surfboard’s optimal hull planing speed.

http://www.bulletfins.com

FCS are an Australian company who leads the world in surfboard fin technology.

Over 40 World Titles have been won on surfboards with FCS Fins, and world champion Kelly Slater has used them for several years.

This first four minute video discusses what has changed in Fins between 1993 and 2011, and how FCS was born.

The next video shows two new products that FCS have released that may look simple, but took up a lot of design and testing hours to get production ready and reliable.

The previous video showed a figure 8 type curved fin mounting insert, which is a break away from the traditional rectangular shaped fin box.

This new shape appears to give greater strength, as demonstrated in this next three minute video.

Fin Configurations

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Surfboard fins come in a variety of configurations, ranging from a single fin on a longboard, to three or four fins on a modern high performance short board.

The five fin box mounts setup is used to enable either a tri fin, or a quad fin, setup to be used.

The characteristics of the common fin configurations are as follows:

Single Fin: One long, wide fin that is usually set up at the back center of the surfboard. Almost always used on long boards.

A single fin rides great in directional surfing. They preform well if the take off is not too steep and can really hold a line in a tube.

Twin Fin: Two smaller fins mounted on either side of the rear. A twin fin works well in mushy, powerless surf.

There is usually very little or no entry rocker, and these are typically used on Fish type surfboards.

Thruster: Three fins of the same size, with two mounted slightly toed-in and canted outwards.

These two fins are on the sides, about 10 to 12 inches from the rear. The middle fin is straight, and mounted three to five inches from the rear.

This is standard of today’s pro-surfer and the recreational surfer as well.

Trifins can make tight turns, they are usually lightweight short boards, and require pumping down a line, to gain speed, and can be manoeuvered like skateboards.

There is also a Trifin “2 + 1 Setup” which is basically the same as the thruster set up, but with a larger middle fin and smaller side fins.

The middle fin is not the same size, as the twin pair of outer fins.

The “2+1″ setup is used in modern longboards. It gives boards of this size good down the line surfing, with a lot move manoeuverability.

Quad: Four fins, two on either side of the back of the board. This fin set up give the surfboard a looser feeling in the tail, which allows make tighter turn towards the curl (cutbacks) and other top to bottom manoeuvers.

This fin set up has gained in popularity over the past few years.

Note that for multifin boards, the fins are not always parallel to the direction the board goes in.

Outside fins have their angle offset from the centre line, and they point outwards. This angle is called “The Toe”. The front edge of the fins pointing towards the nose are angled in towards the center stringer and this alignment is called “toe in”.

In multifin setups, only the Trifin-Thruster centre fin is parallel to the centre line, and perpendicular to the surfboard bottom.

Bottom Contour

Image Source: http://www.surfline.com

Bottom contours are associated with the shape of the bottom of the surfboard and influence how water travels under the surfboard.

Some common surfboard bottom contours are:

– Flat Bottom
– Concave Bottom
– Double Concave Bottom
– Vee Bottom
– Multiple Channel Bottom

Image Source: http://www.shapers.com.au

Flat surfboard bottom design is a fast bottom shape but one that can be difficult to control in larger/faster waves.

Flat bottom is good for small, mushy waves, where you need lots of speed.

Concave surfboard bottom design helps to prevent water being released under the rails giving the surfboard lift and speed.

A single Concave is often used in the front section of Longboards to aid noseriding.

On short surfboards a concave bottom will need increased rocker to allow the rider to retain good manoeuverability.

The Double Concave is seen on the majority of modern mainstream surfboards.

It is the most common contour of boards bought it straight off the rack in surf shops.

Generally the board will have a single concave from the nose which will gradually fade into a double concave towards the tail.

The single concave provides a good planing surface, giving the board drive and accelaration.

The double concave splits the water into two channels through the fins and creates a much looser ride, which allows great flowing manoeuvers.

Vee surfboard bottom gives a flat planing surface on each side of the surfboard that makes the surfboard fast through turns and easy to change direction.

A Vee surfboard bottom is not as fast as other boards when going in a straight line.

Multiple Channel bottom design can have up to 8 channels running along the bottom of a surfboard and there are a number of variations.

Their basic purpose is similar to a concave bottom i.e. To direct the water from nose to tail giving increased lift and speed.

If they are deep, long and have hard edges they may do this too well and make the surfboard prone to wanting to stay in a straight line “track”.

Information Source: http://www.shapers.com.au/

The Surfboard Deck

Image Source: http://vimeocdn.com

The deck is the top surface of the surfboard.

Because it is normally slippery fibreglass, it either needs to be thickly waxed, or have rubber grips put onto it.

The most common designs are domed, flat, and step decks.

A number of companies now offer soft top surfboards. These lower the chance of injury and are very durable without sacrificing too much performance.

Making Surfboards

Image Source: http://www.surfertoday.com

The traditional way of making surboards is to start with a foam “blank”, which is a rough cutout of a surfboard shape, with a stringer down the centre.

A “Shaper” is a person who turns this blank into a proper surfboard, using cutting and sanding tools, along with fibreglass and resins.

Image Source: http://b.vimeocdn.com

The customer orders their board in a surf shop on an order form, and then the shaper works from blueprints to carefully measure and remove material from the blank to create the required surfboard.

Original Image Source: http://www.hollowsurfboards.com

Click to enlarge the above image to full size.

The following five minute American video goes through the process of hand making a surfboard, starting from a foam blank.

There is an in depth technical article on how to build your first surfboard at the following link:

http://www.surfersteve.com/design.htm

Shaper Measuring Tools

Original Image Source: http://www.foamez.com

There are a number of specialised measuring tools used by shapers to check the geometry of the board, the fin placement, and the symmetry.

These include the “Fin Angle Finder”, the “Marking Gauge”, the “C-Caliper”, and the unique “E-Z Square Pro”.

The Fin Angle Finder is is a Plastic Protractor and Angle Finder with articulating arms that make it very simple to reproduce or mark out the appropriate cant angle required for the fin system.

The Marking Gauge is a tool for making marks on the blanks for various steps of the shaping process. It is also helpful in drawing the outline prior to masking tape decks and bottoms for air-spraying.

The “C-Caliper” is Used to measure the thickness of blanks and finished surfboards. Thickness is vitally important, as the board volume, expressed in total litres of foam for correct buoancy, is dependant on correct thickness.

The “E-Z Square Pro” is a clear plastic sheet overlay measuring / template tool. It can accurately measure the nose, width, and tail dimensions of a surfboard, and also has the ability to mark fin placement.

The following five minute video shows how to the “EZ Square Pro” foam measuring template tool can be used for marking out a blank that is going to be shaped into a surfboard.

For complete information about the measuring tools discussed here, check out the following webpage:

http://www.foamez.com/shaping-surfboards-surfboard-measuring-devices-c-2_28.html

If you want to know all about shaping Surfboards, then watch the “EZ Foam” videos collection at the following link:

http://vimeo.com/user6626751/videos

Computer Design and Manufacture

Image Source: http://borstdesigns.wordpress.com

There are computerised shaping machines with the ability to reproduce existing “master key” board designs ten times faster than the average shaper.

These machines are able to successfully capture the integrity of any proven board up to ten feet long, which can then be manipulated by computer to any specified dimension.

“Borst” in Southern California, is one such company at the cutting edge of automated surfboard manufacture.

The “master key” foam blank is either made manually by a master shaper, or computer designed and cut, and then checked and finished by a master shaper.

The “master key” board is then scanned using a 3D image scanner so that all vital geometry and size measurements can be captured.

Image Source: http://borstdesigns.wordpress.com

The surfboard’s shape is captured into sets of “Parametric Geometrical Equations” that use three dimensional X Y and Z Coordinates. Simple 2D parametric equations are the y = x^2 Parabola, and the x^2 + y^2 = r^2 Cirle Equation. Parametric Equations allow the board to be “morphed” into larger or smaller sizes. Eg. “Upsizing” a board is more than simply applying a common scale factor to all key measurements.

Once the surfboard’s shape has been captured, it can then be adjusted in a computer designing app to any standard length, and then manufactured the the surfboard maker machine.

This two minute Borst music video shows how a raw blank is machine shaped into a board that is then ready to be fibreglassed.

The finished computer manufactured products look like this:

Original Image Source: http://borstsurfboards.com

http://borstsurfboards.com/

Another site worth checking out is by a guy called Louis Robert who built his own shaping machine so he could increase his surfboard production capacity.

http://www.revolucionsurfboards.com/

Louis Robert’s machine automatically cuts out the blank from a block of foam with hot wires, as well as then being able to be tooled up to do auto shaping.

Here is a short two minute video showing how this is done.

Original Image Source: http://www.firewiresurfboards.com/

Companies like “Firewire” Surfboards, have developed online web apps that allow surfers to design their own boards, and view them in rotational 3D.

The following video shows this application in action, as well as discussing the mathematics and geometry associated with computer design.

If you would like to try out the Free Firewire Design App, then click the link below:

http://custom.firewiresurfboards.com/custom/intro

Computers and People

Original Image Source: http://www.revolucionsurfboards.com

What happens in a lot of cases these days is a “best of both worlds” combination of computerised manufacture, and traditional handshaping.

Australian companies such as “Burford Blanks”, supply blanks of surfboards which are precut to a basic shape by computerised manufacturing, and then a Shaper can finish the board off for you to your own custom design.

These blanks can even have the “rails” precut as a polygon shaped profile that then just needs to be rounded off by the Shaper.

The Shaper can even store your designs on computer, so that when you want your next board, there is your history available as a starting point.

Surf Aid Mathematics Resources

Image Screen Captured from Surf Aid Website

Surf Aid is a not for profit organisation sponsored by Billabong with a kean interest in the preservation of Mentawai in Indonesia.

The Mentawai Islands are a chain of about seventy islands and islets off the western coast of Sumatra in Indonesia.

The Surfaid website can be found at this link:

http://www.surfaidinternational.org/schoolsprogram

Downloadable Free Units which are in ZIP and PDF format which could be of use to Mathematics Teachers are the following:

AUS Maths 12-14

Mathematics – Connections through Surfing

Technology

Destination Mentawai Islands

The Economics Of Aid

Crossing The Divide – Primary

A Typical example might be the following questions about travelling to surfing locations on various Islands:

“If the motor launch can manage an average speed of 15knots, calculate the journey time between each
location. 1knot is 1 nautical mile per hour. You can assume there is sufficient sailing staff to keep moving 24h
per day. Round up your answers to the nearest day and complete worksheet 5.3.

If you move 10º around the equator how many nautical miles have you travelled?

What angle around the equator (change in longitude) corresponds to 1 nautical mile?”

Another activity we looked at was all about “Planning an Overseas Surfing Trip”.

Eg. Costs, Savings Plan, Items needed and their Cost, and so on.

It was very surfing orientated and might alienate non-surfers and female students, but could easily be adapted to be a group of friends planning a Bali Holiday, and undertaking various tours and activites whilst in Bali.

We will be going through all of the Surfaid Materials, and seeing what could be incorporated into some middle school mathematics, even though the school Passy works at has a tiny minority of students who have ever been Surfing.

We suggest you could easily do the same for your classes.

The following is a list of stand out resources which we found on the Internet while researching this lesson.

Surfboard Design

http://www.surfscience.com/topics/surfboard-design/

http://www.edsinnott.com.au/Surfboard%20Design/

http://www.hydroepic.com/technology.php

http://www.surfertoday.com/surfing/7124-the-effects-of-surfboard-design-in-wave-performance

CAD and Surface Meshing to Design Ultimate Surfboard Performance

http://www.sharc.co.uk/html/case_surf.htm

Surfboard Fins

http://blog.surfride.com/surfboard-fin-guide/

http://www.surfertoday.com/surfing/8993-what-are-the-best-fins-for-your-surfboard

http://www.surfertoday.com/surfing/8993-what-are-the-best-fins-for-your-surfboard

http://wavegrinder.com/surfboard-fin-science/

http://www.surffcs.com.au/community-story/community-blog/2013/03/01/a-guide-to-fcs-fins

http://www.surffcs.com.au

http://www.tactics.com/info/guide-to-surfboard-fins

http://surfcabarete.com/surfing-caribbean/different-types-of-surfboard-fins/

Surfboard Bottom Contours

http://www.shapers.com.au/pages/Contours.html

Manufacturing Surfboards

http://borstsurfboards.com/

http://surf.transworld.net/1000074167/features/surf-science-modern-mechanics-of-boardmaking/

http://www.edsinnott.com.au/Surfboard%20Design/

http://www.firewiresurfboards.com/

Image Copyright 2013 by Passy’s World of Mathematics

I have been a keen Surfer for over 20 years, and have surfed all along the East Coast of Australia, all around Indonesia, as well as visiting Fiji and Hawaii.

I was sidelined from serious surfboard Surfing around 6 years ago after a spine operation to repair cumulative damage caused by Surfing and Bike Riding accidents. However I still body surf and boogie board surf whenever I can.

My son is a keen body boarder, and that is him first learning to surf in the bottom right hand corner photo.

MAV Conference PowerPoint

To download the PowerPoint Presentation from the Mathematics Association of Victoria Conference, click the link below and save the file to your computer.

Surfboard Design and Geometry

http://passyworldofmathematics.com/MAVconfPPTs/SurfGeomDesignPPTv3.pptx

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