### HYDRODYNAMICS IN FINNING AND GLIDING AND ITS IMPORTANCE IN FREEDIVING WITH BI-FINS

by Jeremy Meyer, July 2010

### Introduction

Hydrodynamics is the study of the motion and action of water and other fluids. In freediving we tend to use the term “hydrodynamic” when we really mean “hydrodynamically efficient”. The study of hydrodynamics has much in common with aerodynamics, which is the study of motion and action of air. I will introduce the physical terms and the issues involved in the part of hydrodynamic study which are relevant to us and then show how they should influence our choice of equipment and our divingtechnique. The focus of this study is mostly concerned with the use of bi fins in freediving, although most of the concepts discussed apply equally well to monofin or unassisted diving.

### Basic Physics Terms

The understanding of forces and how they work is fundamental to hydrodynamics, so we should be aware of some of the basic terms.

#### Newton's Laws of Motion

Using Newton's simple laws of physics, (where force is measured in units called newtons) here are some rules about forces which most of us should remember from school. It is useful to remind ourselves of these when understanding the forces at play in hydrodynamics. Possibly the most useful for the freediver is the third law, “for every force there is an equal and opposite force”. Simply put this just means that if you push against a wall with a force of 50 newtons, it is pushing back on you with the same force.

Illustration 1:

This is important because when we move in the water, our fins or hands or feet apply force on the water, and it is the opposite, or “reactionary” force which propels us forwards.

### Component and Resultant Forces and Vectors

A force is what we call a “vector” quantity, which just means that forces have magnitude (how much force) and direction (where they are being applied).

Illustration 2:

Sometimes a force is applied at an angle, or deflected so that not all of the force acts in one direction. This means that a force can have a “component” in two different directions. This is easy to picture if you imagine yourself pushing a lawnmower. The handle is angled such that as you walk along, you are pushing both down and forwards. If you are applying a force to the handle, of say, 60N, you might be applying a downward component of 30N and a forward component of 30N.

Illustration 3:

Sometimes two or more forces are applied on an object. These add together (or cancel each other out) to produce a single, resultant force. If you imagine two men in a tug of war competition, applying a force on a rope of 1000N in a Northerly direction and 1005N in a Southerly direction respectively, the resultant force is 5N in a Southerly direction and the men and rope will move in that direction.

Illustration 4:

To re-visit the previous example, if you are applying a downward component of 30N on the lawnmower, and the weight of the lawnmower is effectively already applying a 100N force downwards, the resultant downward force is 130N.

#### Inertia and Momentum

When a body is at rest, it will have resistance to being moved. This force is inertia. Imagine moving a heavy box along the floor. You will need more force to get it moving initially. When a body is moving, it will resist being stopped, this is momentum. Imagine pushing a heavy supermarket trolley. You need to apply a strong force to stop it.

#### Work

Work is more or less simply defined as an amount of force applied over a certain distance. So Force X Distance. This is fairly intuitive. If we move 5 bricks 10 metres, we have done some work. Two do twice as much work we could move 5 bricks 20m or 10 bricks 10m. In Freediving we can consider work done to be roughly proportional to oxygen consumed, bearing in mind that the body always does some “work” by keeping itself alive.

### Hydrodynamic Terms and Definitions

#### Angle of Attack

Illustration 5:

The angle that a surface (a paddler or a hand or fin) holds when it moves through water.

#### Lift

Lift is the resultant force caused by a surface applying a force in a fluid. To put that simply, if you move a paddle or a fin through the water at an angle, the surface of the blade will exert a downward pressure on the water. By Newton's law above, this will create a resultant force in the opposite direction, which is the lift. (It is even called lift when it is not exerting the force upwards). In freediving, the forward thrust comes from the lift generated by the fin and is proportional to the angle of attack and the surface area of the paddle / fin / wing.

Illustration 6:

#### Drag

Not when a male freediver wears a female freediver's suit. Drag is the general term applied to the force that the water applies to any object which is moving through it. Drag is the most significant adverse force that we experience when moving through water. This is reinforced by the fact that the drag force increases with the square of the velocity. This means that if a diver doubles her speed through the water, she is multiplying her drag by 4, if she multiplies her speed by 4 she is multiplying her drag by 16, and so on. Reducing drag is the way that we can make the most difference to the performance and efficiency of any craft or body moving through the water. Drag is caused by a variety of different factors and can be sub-classed into different types.

1) Parasitic Drag is undesirable as it does not provide a useful component force to the object moving in the water. In freediving we are mostly concerned with two forms of parasitic drag: Form drag, the drag caused by the shape of the object and skin friction, drag caused by the rough surface of an object.

2)

Illustration 7:

3) Induced Drag or Lift Induced Drag is the drag caused when an object moving in the water creates lift by changing its angle of attack to assert a lateral force on the water. This angle effectively creates the surface area and thus the drag will increase as the angle increases. Since this drag can be the resultant force of a fin stroke, we don't consider it parasitic.

Illustration 8:

Turbulence

Turbulence is a break up of the smooth flow of water around an object. This can create vortices, or miniature whirlpools which exert a drag on the object. The smoother and more streamlined an object is, the less likely it is to form turbulence on its trailing edge (the back edge).

Illustration 9:

### Hydrodynamics and Finning

Now that we have defined the terms and some of the concepts in hydrodynamics we can apply them to freediving, for the purposes of both choosing equipment and improving our technique.

#### Type of Fins

Rigidity

Consider a completely rigid fin (such fins are not actually sold), it would be an efficient wing or paddle, but because it would maintain a constant angle of attack relative to the foot, the fin would generate a component of lift or thrust in the water in the wrong direction, unless the knee is bent on the forward stroke. This would cause us to move backwards. Also, the drag in the water would be greater relative to the forward thrust. This means that for the the initial part of the fin stroke, to overcome the inertia and gain momentum would be a hard, high intensity muscle action and would tend to create anaerobic fatigue.

Illustration 10:

Fins should be supple enough that they flex with the fin stroke. The suppleness allows two things:

Firstly it allows the pressure of the water to bend the fin, creating an angle of attack on the fin surface which produces forward thrust. Secondly it converts some of the finning energy into bending the fin to have a smaller form drag (than a stiff fin) at the beginning of each fin cycle, reducing anaerobic strain on the muscle, allowing some momentum to be built up and some of the spring of the fin to provide a final propulsive force at the end of the fin stroke.

Illustration 11:

An overly flexible fin will create a very small angle of attack in the water, generating very little lift. The curve will have less form drag than stiffer fins because the surface area will be smaller relative to the direction of the fin stroke force. This means that inertia will be smaller and fins will feel easier to use, but energy is wasted. The spring of the fin provides little or no work at the end of the kick cycle as little energy is stored.

Illustration 12:

Shape

Straight ended fin tips will tend to create turbulence and hence more drag. A variety of different fin shapes have been tested by the various manufacturers and found to reduce turbulence. Most commonly a split in the fin allows the fin to flex to either side, streamlining it and reducing turbulence. In some fins, a tapered end reduces surface area in contact with water at the end of the fin. In the case of a very thin taper, or “tongue”, this might also respond first to the reactionary force from the water, starting the bend of the fin earlier in the stroke, creating the correct angle of attack earlier and making the fin stroke more efficient without requiring much more effort.

Thickness

Fins which have uniform thickness will tend to bend in water pressure in a semi circle, creating similar problems to a fin which is too soft. A fin which tapers in thickness towards the tip will tend to bend in a parabolic curve, keeping the last third or so of the blade at an angle of attack which will generate useful power.

#### Finning Stroke

Since a good freediver depends on moving efficiently through the water so that he or she may gain the maximum speed for the minimal effort, we need to consider the different forces and how to optimise them with our finning style.

Use of Knees

Bending knees will reduce the angle of attack relative to the direction of finning force, in extreme cases to zero, pulling the fins through the water along their length, creating no drag or lift. Bending the knee at the beginning of the stroke will reduce the initial inertial force, and if straightened during the fin stroke or kept rigid, may still present a good finning technique. Changing the angle of the knee by bending during the finning stroke will tend to reduce the angle of attack as above and will lead to an ineffective fin stroke with no propulsion. The top part of the thigh will also generate a parasitic drag in the direction opposite to the diver's travel.

Illustration 13:

Larger fin strokes

Small strokes with long fins will not allow the fins to flex enough from the water resistance and will not create a useful angle of attack.

Body and Head Position whilst Finning

The diver should maintain a straight body position, with chin tucked in so that the body has the minimum form drag possible relative to the desired direction of travel. Use of the hands or arching of the body to change direction with bi-fins, creates additional form drag which wastes energy and thus uses more oxygen.

A fin with the correct flex, used with the correct stroke, has a lift component in the opposite direction to the kick, (see Illustration 11) so finning harder (or with larger strokes) to the front, will tend to push the diver backwards and finning harder (or with larger strokes) to the back will do the opposite. The diver can thus control his position in the water by using the fins alone and maintain the correct body and head position.

Illustration 14:

#### Finning Speed

Finning in the water creates drag in two areas. The finning motion generates drag against the fins and legs (parasitic and non-parasitic) and the forward propulsion created by the finning produces form drag on the body, particularly head and shoulders. Drag can be calculated by a somewhat complicated formula which takes into account the density of the fluid, the speed of the object and the drag coefficient (based on the surface area, skin friction, etc.) The most important thing for us to remember is the relationship between drag and speed as mentioned above. The drag increases by the square of the speed, so doubling your speed will multiply your drag by two times two, which is four. e.g. if you are finning at 1metre per second, against a drag force of 5N (the equivalent of lifting a 0.5kg weight on dry land), then increasing your speed to 2m per second will increase your drag to 25N (the equivalent of lifting a 2.5kg weight on dry land). This effectively means that in this case, you would have to do 5 times as much work to gain twice as much speed.

It is easy to see that if we minimise drag as much as possible, we can reduce the impact of this squaring relationship. It is also easy to see that speeding up at the end of a dive is most likely to be counter productive. For example, if you were to be working against the forces in the example above, and doubled your speed from 1m/s to 2m/s in the last 20m of a dive, you would be cutting 10 seconds off your dive time and therefore your breath hold. But, since work is calculated over distance, not time you would still be multiplying your exertion by 5 times for the last 10 seconds because of the drag. Assuming a linear relationship between oxygen consumption and work done (which will not be completely accurate, but can serve as a rough estimate or benchmark) we have:

Where W is work, and F is the force due to drag,

at 1m/s W1 = F * 20 = 5 X 20 = 100N/m
at 2 m/s W2= 5F * 20 = 25 X 20 = 500N/m

Which means we are comparing the use of x amount of O2 in 20 seconds with the use of 5x amount of O2 in 10 seconds. In other words, by doubling our speed for the last 20m, we may effectively be adding the equivalent of 30 seconds to our dive time!

### Hydrodynamics and Gliding

As stated above, the glide phase of a dive saves oxygen because the diver is not expending any energy. This means that a way to extend our dive times and our depth as freedivers is to improve our glide position and speed. The force which propels us down on a glide is gravity, minus our buoyancy, so although we are not finning, the forces which work against us are the same.

The increase of drag caused by speed is less important in gliding than in finning because although it causes slowing of the glide, it does not use energy. It does use time, however, and so it is still an important factor.

Resistance in Wetsuits

Since skin friction is a measurable force, it becomes more significant over a larger distance, or at greater speed. A smooth skin wetsuit will obviously have the least skin friction and is preferable for gliding (and finning).

Buoyancy in Wetsuits

A thicker suit will tend to increase the form drag of the diver and hence slow down the glide. It is hard to calculate whether or not this minor increase makes a significant difference to the glide, (like the material of the suit or the position) but all else being equal, a thinner suit will glide better. Thicker suits will also compress more, so the difference will tend to decrease with depth.

Illustration 15:

Gliding Position

The position of our body and fins is really the only way we can adjust our drag. Fin position is the most important factor because the fins have the largest surface area and are flat, hence their minimum and maximum drag ranges from being almost zero to being greater than anything that other parts of our bodies could exert.

Most fins have a blade mounted at an angle to the foot, to make the angle between the lower leg and the fin as close to 180 degrees as possible. Even with a pointed toe, the blade is usually not quite 180 degrees and so is not a perfect continuation our leg. Keeping the body and legs absolutely straight actually can lead to a slightly angled fin which creates a large form drag with a backward component which tends to push the top of the fin back. The trailing edge of the fin is also diverting water flow, so creating more turbulence.

Illustration 16:

Bending the legs slightly (by the same angle that the fin makes with the foot) creates a smaller form drag on the backs of the calves but close to zero drag on the fins themselves, making an overall significant reduction.

Illustration 17:

### Conclusion

Understanding the physical forces at play when we are freediving will help us to make educated choices when selecting our freediving equipment and refining our finning and gliding technique. Being aware of the relationship between drag, surface area, angle of attack and velocity is important when considering the right body positioning and style, and may cause us to rethink some incorrect assumptions about our diving.

References;

Drag and Turbulence:
http://en.wikipedia.org/wiki/Drag_%28physics%29

Anaerobic vs. Aerobic Muscle Activity
http://www.members.shaw.ca/bodybu ilding/Muscles/structure.html
http://www.dynamicchiropractic.com/mpacms/dc/article.php?id=31599
http://en.wikipedia.org/wiki/Anaerobic_exercise

Hydrodynamics in Turbines

G.Boyle “Renewable Energy – Power for a sustainable future 2nd Edition”

Finning Techniques

Pelizzari, Tovaglieri “Manual of Freediving- Underwater on a Single Breath!”