Fysik og matematik-timen

Hold da op det er længe siden der er sket noget her. Redaktionen er delvist lockoutet og den anden del sidder tilbage og måber over processen. Men nu skal alting ikke gå i stå bare fordi skolerne er lukket. Som nødløsning etablerer vi hjemmeundervisning her på siden og vi starter med matematik, fysik og engelsk – om hvordan vi kan forholde os til wavepiercing og skrogfacon. Vi har valgt at differentiere undervisningen således at hjemmeundervisningen i denne omgang primært er til nørderne. Imens må de andre gå på fodboldbanen.Vi har tyvstjålet indlægget fra ‘carbonicboats’ – det beder vi om tilgivelse for.

Glæd dig allerede nu til næste lektion i historie

We are receiving many questions about the pros and cons of so called wavepiercing bows. There seems to be much debate among sailors partly fueled by unsubstantiated claims from manufacturers.

As our regular followers and clients know, at Carbonicboats we do not make dogmatic proclamations about what our products will do. Instead we explain the reasoning that leads us to each design choice.
We aim to demystify the principles at work acknowledging that in most cases there are tradeoffs involved. Sharing the process is a way to communicate our passion for the art of design.

So let’s look at modern bow shapes. Unsurprisingly the ‘piercing vs conventional’ debate is founded on a false dichotomy. The obvious visual character of a bow profile is in fact almost incidental. It is driven by something more subtle: the distribution of volume in the cross sections.

Each cross section shape naturally comes together to give a characteristic bow profile.
To understand how this works, look at the following illustrations.

The port and starboard hull halves are shown in different colours and the cross section lines are in yellow. By extending each hull half past the centreline you can clearly see that the way the two sides intersect defines the centerline profile of the bow.

So now when you look at a bow profile you will be able to read the section shape.
It follows that wavepiercing bows are not just conventional bows with the excess freeboard removed. They are simply a consequence of a particular section volume distribution.
It doesn’t make sense to say that they are inherently more or less susceptible to burying as is being claimed by certain parties.
The question instead becomes: ‘what are the pros and cons of different section shapes?’

As we have seen in previous posts, conventional hulls resist bow down trimming forces by immersing more volume forward. This shifts the centre of buoyancy forward. If the centre of gravity remains stationary or moves aft, the resulting separation gives a bow up righting moment.

Tornado style ‘conventional’ raked bow profiles indicate flared hull sections. Meaning the sections get wider moving up, resulting in more volume at the top of the bow. Such additional volume in the upper part of the hull is what we mean by ‘reserve buoyancy’.

Compare the two IOR maxi bows in the foreground with
the modern VO70 bows in the background. The hollow profile of the red bow (Steinlager II) reflects progressively widening flare in the topsides. In some cases the bow rake is made less extreme by ‘cheating’ the natural intersections of the two hull halves with a variable radius between the two surfaces. Image source

Downwind

Conventional bows seek to marry a fine waterline entry with extra volume that only becomes immersed when needed.

Inherent in this mechanism is a need for significant bow down trim in order for the reserve buoyancy to take effect.

On a conventional multihull this is not a problem: As the bow is pressed down, the boat will keep sailing horizontally along the surface as the bow immerses. The additional volume going into the water at the front will shift the CB forward and a new equilibrium will be reached. A few degrees of bow down trim has no adverse effect.

The limiting factors in this case are bow freeboard and additional hull drag due to the progressively blunter entry of the trimmed immersed shape.

Freeboard limits the absolute amount of reserve buoyancy available.

Additional drag limits acceleration which in turn affects apparent wind (accelerating downwind reduces pressure in the rig, relieving bow down trimming moment).

Multihull evolution has seen reserve buoyancy move down, progressively closer to the normal water level. Meaning sections have developed from being ‘V’ shaped to more ‘U’ shaped. It is no coincidence that this trend occurred at the same time as the advent of angled/curved foils.

Imagine a conventional Tornado style hull with angled or curved foils. When reaching at speed the foils would be providing significant vertical force helping to keep the bow up and slightly reduce effective displacement.

Now imagine this hypothetical boat encountering a gust: The rig would power up and press the bow down. Since the reserve buoyancy is some distance above the water, bow down trim would initially increase to bring the reserve buoyancy into play.

But at the same time the bow down trim would reduce the angle of attack of the foils, possibly even bringing it below neutral.

The boat would not tend to follow the water surface. Instead it would want to follow the chord line of the foils. This would create a feedback loop where bow down trim would increase bow down trimming force…

Having reserve buoyancy low down in the bow sections makes it immediately available. This is desirable when pitch attitude is critical such as on foil assisted boats.

When things get out of shape, the wide flat deck of a conventional hull abruptly increases drag at the very point where reserve buoyancy runs out.

A carefully shaped ‘upside down’ bow brings the water flow back together cleanly above it, giving the boat a better chance of accelerating and shedding water to allow the bow to pop back up.

Image source

But this is not the exclusive preserve of radical inverted bows. More moderate shapes such as the Boyer MkIV A Cat still benefit from this effect.
This brings us back to the premise that ‘wavepiercing bow’ is too generic a term to be indicative of behaviour or performance.
The vertical location of the maximum section width is the feature that tells you the most about the design priorities of a particular boat.

The bow profile is an indication of this vertical volume distribution.

We saw in Part 1 and Part 2 that generalised statements about the handling qualities of ‘wavepiercing’ bows miss the point that bow profile is a reflection of sectional volume distribution which is a much more useful indicator of design priorities.

Multihull bow sections have recently tended to carry volume lower down rather than above the water ‘in reserve’. We saw that this makes maximum buoyancy available at smaller bow down trim angles. These shapes are inherently slab-sided so tend to come together in upright stem profiles.
Such sections combined with peaked foredecks designed to shed water easily characterise modern bow profiles though there is still considerable variation in the details. Generally it can be said that such shapes behave more lineally: Gone is the sudden ‘tripping’ effect generated by a wide flat deck suddenly becoming submerged.

So far we have concentrated on downwind bow burying conditions. However the choice of bow shape must also take into account more common cases.

Image source

Straight Line Sailing

As we saw in our look at the A Cat state of the art, multihull volume distribution must consider the doubling in displacement of the leeward hull as the windward one leaves the water. As flying a hull has become more common, limiting immersion or ‘sink’ of the leeward hull has become more important. Another reason for more U shaped sections. In this respect the decision must take into account the relative importance of wetted area and cross sectional area, values that can to some extent be traded.

As average speeds have increased prismatic coefficients have grown, making the ends fuller. This has led to very interesting findings about the sharpness of forward waterline endings. The concept of a fine bow ‘cutting’ the water has been replaced by more sophisticated ideas that have more in common with aerofoil leading edge theories. Fuller bows have evolved into more bulbous elliptical entries that are less sensitive to changes in the angle of the oncoming flow.

Image source

Pitching

Dynamic periodic motion is a complex subject but the simplified rule of thumb is that the damping effect of fuller extremities is greater than their contribution to pitching moment. This is the one context where ‘wavepiercing’ is an apt description. Meaning the upper part of the bow does not contribute to pitching moment as there is no upward component to the hydrostatic pressure. On the contrary, there is a small cancellation with the lower part of the bow. Interestingly stern flare helps with pitch damping as the dynamics there are slightly different.

Conclusion

Modern bows come in a variety of profiles reflecting different design choices in section shape. Rather than bundling all these types into one sweeping category and then drawing generalised conclusions, much understanding can be gained by looking a bit more carefully at the underlying section shape.
This should enable us to make a good educated assessment of the priorities driving the design choices in each individual case

Skriv en kommentar

Skriv et svar Annuller svar