Episode 4 - Wave Interference, Wave Rotary Motion, Wavelength to Hull Length Effects

Añadido: 2026-05-19

[00:00:00]Hello and welcome back to the Sailing Technical Channel, where we explore the engineering behind sailing. This is episode four in the heavy weather series and the second episode on waves. If you've made it this far, you are probably in a small group of sailors. I say that because whenever I presented technical talks on sail trim and how sails work, I found only about a third of the audience is comfortable interpreting formulas and graphs. The rest start to shuffle their bums, their eyes glaze over, and they stink out of the room. Interestingly, when I've taught junior racing sailors, high school students tend to engage more openly with the technical material. They may not grasp everything immediately, but they are willing to work through it without being intimidated. As a result, relatively few sailors develop a clear understanding of the forces acting on their boats, and especially in heavy weather. And that's one reason why I created the series with the hope that if I laid out the information that would otherwise be guarded away in text, some sailors with a basic technical knowledge would benefit. To my understanding, no single source consolidates and explains the mechanics of heavy weather sailing, the interaction of wind, waves, and boat response in what I hope is viewed as a clear and structured way. If you follow this series through all seven episodes, you will be among a very small group of sailors who understand the forces at play. And when we finish, you will already be in a position to better interpret forecasts, anticipate conditions, prepare your crew, and possibly avert situations for those with a lesser understanding of wind and wave mechanics. Before we continue, if you haven't watched the earlier episodes in sequence, please go back to episode one because being in demanding conditions requires being able to steer. And unless you have an understanding of how rudders work and that the turning force is proportional to the square of the water speed around them, you will be unable to follow this episode. And with that, let's get started. Wave interference in confused seas. It's time to revisit your grade eight science class. You may remember that theoretical waves have smooth, regular, sinusoidal forms, but you might also recall some of the basic lessons of wave interference. When waves overlap, they can interfere constructively, combining to form much larger waves, or they can interfere destructively, partially or completely canceling each other out, or they can create a mixed interference pattern. In moderate conditions, mixed interference patterns are typically messy, but not problematic. However, as a wind increases, multiple wave systems often develop, leading to irregular, steep, and chaotic seas, what sailors call a confused sea. And when this happens, it usually becomes challenging for sailors cuz the waves can be unpredictable, and some have short wavelengths, and some have very high steepness ratios.

[00:02:34]Mixed interference waves can develop by reflecting and refracting off of hard surfaces like rock shorelines or breakwaters. I understand the 1998 Sydney-Hobart race troubles were caused by a wind-against-tide scenario when the yacht crossed into the Bass Strait. One key takeaway, mixed interference can produce unexpectedly large waves at regular intervals. These occur due to a phenomenon similar to a beat frequency where wave patterns predictably align.

[00:03:05]The result is a repeating pattern of unusually large waves, even on otherwise moderate conditions, and can produce a beat of extra large unpredictable waves within a reoccurring time period.

[00:03:16]Stormsurf is a free website that provides global wave forecasts. The lower right panel is a screenshot I took of the Caribbean. I once made a passage from Saint Martin to the British Virgin Islands aboard a French Jeanneau 53. It was a down-howl run in about 15 knots of wind, conditions that should have been uneventful. However, along the route shown on the upper right insert by the red dotted line, we encountered mixed interference between the southeasterly and northeasterly wave trains. About every 10 minutes, a large wave would constructively form under the boat's wide stern section, lifting it and throwing her on her side. Annoying because it overwhelmed the auto helm, but not dangerous. This was not the case in the 1979 Fastnet race. From accounts, the fleet initially encountered relatively even wave train, but the wind veered and increased producing two sets of interfering waves that were tall, steep, and chaotic. These conditions caused violent accelerations leaving crews incapacitated leading to the abandonment of many yachts that were still seaworthy. And with that, next slide, please. Veritasium video introduction. This video is from the popular YouTube channel Veritasium hosted by Dr. Derek Muller. It is the most comprehensive explanation I could find on the theory and characteristics of water waves. Dr. Muller did his undergrad in engineering physics at Queen's University in Kingston, Ontario and his PhD in Sydney, Australia. I will show only roughly a 12-minute clip here, but I give it as a homework assignment to watch the full episode from the link below. And when you do, as with all the videos, please give it a like, subscribe, and ring his bell because it's the least you can do. As no YouTuber has to pay for its content and this learning experience. Now, with that stern lecture, as we run this video, watch for a couple of points. The orbital motion of waves, which we'll see as yet another reason why downward helming is so difficult. And when you see the examples of wave interference, try to imagine them scaled up and that is your boat instead of the toy shown and judge your chances in such a confused sea. Let's roll the segment now. This regular out there? Correct.

[00:05:20]One of the fundamental characteristics of a wave is its wavelength, the distance from one crest to the next. The first thing most people learn about waves is they transmit energy rather than material from one place to another.

[00:05:33]In this case, as the wave travels to the right, the water molecules themselves basically move along circular paths. And the deeper the water, the smaller this motion. All motion stops at at equal to half the wavelength. This is known as the wave base.

[00:05:51]But even in an ideal water wave, the molecules do drift a bit in the direction of wave motion. And this is because the molecules travel faster the higher up they are. So, they move farther at the top of their loop than they move backwards at the bottom, creating a spiral path.

[00:06:08]This place is perfect for observing properties of different waves. I asked Miguel to show me some waves with different frequencies but the same amplitude.

[00:06:17]>> So, what I'll have him do now is I'll have him stop this wave and this change the frequency.

[00:06:21]Cuz we're at 0.6, we'll go to 0.5, so it'll be a 2-second wave.

[00:06:26]Here, I'm split screening waves with frequencies of 0.67, 0.5, and 0.33 hertz, all with the same amplitude.

[00:06:35]So, two things to notice. Even though they all have the same amplitude, the ones with higher frequency look like they have a greater amplitude because the slope of the waves is steeper.

[00:06:45]And second, the frequency of a wave affects its speed. High-frequency waves travel slower than low-frequency waves.

[00:06:54]In fact, as long as the water is deeper than the wave base, wave speed is inversely proportional to its frequency.

[00:07:01]They have a really cool demo that takes advantage of the different speeds of different frequency waves. You can see it starting here. They send out high-frequency waves first, followed by lower and lower-frequency waves. And because the high-frequency waves travel slower, the lower-frequency waves gradually catch up.

[00:07:21]Whoa.

[00:07:25]And they've timed it so that all the waves meet up at exactly the same time and place in the pool. This causes the wave to break.

[00:07:33]The ocean engineers can do this again and again in exactly the same way, thanks to their precise control over the waves.

[00:07:46]This demo also nicely illustrates the principle of superposition, that when waves meet, they add together. The height of the water is equal to the sum of the heights of the individual waves meeting at that point.

[00:07:58]You can see how much bigger the amplitude is. Those individual waves weren't that big, but when you add them all together, you can make this big breaking wave.

[00:08:09]They can also take advantage of the superposition principle to create standing waves. So, what's coming up next are two regular waves coming at each other.

[00:08:17]What we call the quilt wave. So, we're going to have a wave coming this way and a wave going this way, and it's going to create standing waves. So, there's two regular waves coming out, and if you look at the wave, it looks like a big quilt pattern out there.

[00:08:28]At some places in the pool, the waves always cancel out to zero amplitude, and at other places, the waves add up for maximum amplitude.

[00:08:38]They can even send waves from all directions, so they form circular wave fronts. And then, all the wave energy is channeled into one spot they call the bull's-eye.

[00:08:49]And so, now we're going to run the bull's-eye wave, which is essentially the same thing, but instead of having a line of waves, we're having it all coalesce at one individual point.

[00:08:57]So, you can start seeing the waves are coming from the long bank here. And you can see they're making a spherical wave.

[00:09:03]And then, you have another spherical wave coming from the short bank.

[00:09:06]And this is breaking due to the coalescing waves and the wave height being more than 1/7 of the wavelength.

[00:09:14]We tried throwing some toys into the wave to see what would happen to them.

[00:09:18]Would they get pushed into the breaking wave?

[00:09:21]Even though there's not much net movement of the water, the ducky drifts with the waves and pretty quickly is pushed into the bull's-eye.

[00:09:30]How's the How's the ducky doing?

[00:09:32]He's getting to the danger zone right now.

[00:09:35]It's starting to funnel him right into that breaking wave. Oh, we're Is there >> down up.

[00:09:42]Oh, it swamped it. That's amazing. That was right where we wanted it.

[00:09:49]Now, the real purpose of this facility is not to play with toys or make perfect unnatural waves. It is to replicate on a small scale the types of waves navy ships will encounter in the oceans of the world.

[00:10:02]Research engineers place ships modeled after billion-dollar vessels in the water to see how different designs actually behave in real-world conditions. Right now, this is coming from 45°. It's going to be about a 5-in significant wave height, which if we were to scale it up for this model would be 20-ft waves.

[00:10:20]When we're doing a free-running model like this, we usually run like a racetrack, like a big circle, or a figure-eight track, so we know the headings that we're running in so that we can correlate that to, you know, the full-scale vessel.

[00:10:33]For the model to provide an accurate representation of the real world, a lot of things must be taken into account.

[00:10:40]Is the water Fresh water. Okay, not salty. Nope, fresh water. So, when you're in salty water, you're going to have a lot more buoyancy. So, when we're ballasting our models, we have to make sure that they take into account that buoyancy difference. So, when we go full scale, you know, you're the same conditions.

[00:10:57]For fluid mechanics, I always expect that you have to keep the Reynolds number the same as in the real-world phenomena. But, actually, to get the right wave dynamics, you have to use a different scaling, which is based on the Froude number.

[00:11:10]So, the Froude number is a measure of the ratio of inertial to gravitational forces. It's equal to the flow velocity divided by the square root of the acceleration due to gravity times the characteristic length, like the length of the ship. In this case, the model ship's hull is 46 times smaller than the real thing, which means to get accurate data, it should be traveling at 1 over the square root of 46 times its real-world speed. And to make the footage from the model look the same as that from the full-size ship, you have to slow it down by a factor of the square root of 46, so roughly 6.8 times slower.

[00:11:48]I'm amazed at just how well these shots match. But, of course, that's the idea.

[00:11:53]Scale the model and the waves so the physics are identical to a real ship out on the open ocean.

[00:12:00]Naturally, I asked if I could go swimming in the pool, but they said, very kindly, no way. The closest I could get would be on a little dinghy. This is our boat with a catch.

[00:12:15]It's pretty smooth, uh, smooth sailing out here right now.

[00:12:18]Yep. No waves while we're out here.

[00:12:21]So, I'm assuming no one's ever been out here in waves? Nope. That's one of the no-nos they don't want us to do. Like, I guess it's a risk thing, so This place seems like, uh, I don't know, like, a massive playground kind of like It kind of is for engineers like us where it's we kind of dork out on the science and what we're doing here. It's it's a huge volume. Like, I guess I never understood how deep 20 ft was until they emptied it to put in the new wave makers. It's a large volume that's taken up by this water. Um So, as we come by, these are our sensors right here. We have a bigger array here.

[00:12:58]Um these are ultrasonic sensors, and that's how we measure wave height and period and direction in the basin. So, we want to make measure that to make sure that what we're testing is what we think we have.

[00:13:08]In this pool, they can create all sorts of different wave conditions you might encounter in different parts of the world.

[00:13:15]Most ocean waves are created by wind, and the strongest winds occur in and around storms.

[00:13:22]Five factors affect the size and shape of waves created. These are the wind speed, the wind duration, the distance over which the wind is acting, which is known as the fetch, the width of the fetch, and the depth of the water.

[00:13:39]As waves travel out from a storm, the higher frequency waves dissipate their energy more quickly. So, the waves that travel a long way are the fast-moving, low-frequency waves, which are called swell.

[00:13:51]When those waves end up becoming like hundreds of miles away, like if you have it in the Pacific, eventually you'll get long period swell from them. So, you're no longer near the the the storm, but it created enough energy to make long waves, and that's where you get your open ocean swell. Tell me if this is a good analogy. I feel like with sound, a lot of high frequencies will die off quickly away from a source, but the low frequencies will travel much further.

[00:14:14]>> Correct. So, is it the same thing with the waves? It's like like you're walking away from a concert, and you can hear still hear like the bass, but you can't see any of the high high frequencies.

[00:14:22]>> analogy. Yeah. What's the deal with rogue waves?

[00:14:26]People like to think it's a rogue wave, where it just came out of nowhere and just came up. No, it's usually multiple waves that are meeting up and creating an amplitude that's much larger than what the self-standing wave would be.

[00:14:38]So, when it meets, it's going to break because you have this large wave creating this huge amplitude that the it just can't hold it, and it breaks.

[00:14:46]On a calm day, when you see waves crashing at the beach around 10 seconds apart, that is swell.

[00:14:52]But, because of its long wavelength, swell isn't really a concern for ships out in the open ocean. Uh you know, if you're in a long period swell, your ship's probably just going to heave a little bit. You're more worried about the steep waves and the windy waves that are really moving you around.

[00:15:08]Wind waves are formed in three steps.

[00:15:11]First, as wind blows across the surface of perfectly still water, the turbulent motion of the air creates regions of slightly higher and slightly lower pressure, and this makes tiny ripples with wavelengths of around a centimeter.

[00:15:25]But now the wind can act on these ripples, creating larger pressure differences between the front and the top of the wave crest, pulling them up into bigger waves. And the interaction of the wind with these waves then creates even larger pressure differences and even larger waves.

[00:15:42]The waves are mostly uniform at this point, but as they interact with each other, they create a range of different wavelength waves. And as the wind keeps blowing, these waves begin breaking, transferring their kinetic energy into swirling eddies that dissipate their energy as heat. Once the energy dissipation matches the energy input from the wind, the waves have reached their maximum size, and this is known as a fully developed sea.

[00:16:11]So this is going to be an irregular wave. This is irregular? Irregular wave.

[00:16:15]So the what you saw earlier with the regular waves where one frequency, one amplitude. This is what we call a spectra or multiple frequencies and multiple amplitudes.

[00:16:26]You can see that there's like higher frequency little waves that kind of go travel slower than the low frequency waves. Those low frequency waves will travel fast and overcome them, and that's what's making them look peaky or kind of dulling it out.

[00:16:39]What surprised me is that the different oceans of the world have different mixtures of wave frequencies or different spectra, depending on their geography and the types of storms that occur there.

[00:16:51]For example, the North Sea and other small bodies of water have a peakier spectrum. And this is due to the limited fetch of storms that occur there.

[00:17:00]In the Mid-Atlantic, a broader spectrum best describes the developing or decaying open ocean waves that you'd find there. And in the North Atlantic, the steady wind across an open ocean produces the broadest spectrum of wind waves.

[00:17:15]So when testing, engineers first have to figure out where the ship will be deployed and which spectra best >> for effectiveness downwind with wave orbital flow. Let's return to our helmsman of the far 40 from episode 1.

[00:17:27]He was making constant micro-adjustments as he struggled to keep the boat underneath the sail plan. We now understand that each of those small helm inputs, alternating angle from port to starboard, was effectively sliding the rudder up and down its lift curve, the blue line on the curve shown here. The goal was simple, generate just enough side force and no more to maintain course or risk inducing a rhythmic roll.

[00:17:51]We also now know the magnitude of that rudder force is governed by the equation shown on the lower left, and the dominant variable is a squared function of the water velocity past the rudder.

[00:18:02]In flat water, this velocity is constant and equal to the boat speed through the water. However, that assumption breaks down when sailing downwind in waves due to the orbital flow.

[00:18:12]In waves, the water speed at the rudder becomes the boat speed plus or minus the orbital water velocity associated with each wave. Consequently, rudder feel and control changes continuously as it moves through the oscillating directions of orbital velocities on the crests and in wave troughs. At the wave crest, the orbital flow travels in the same direction as the boat and rudder, but conversely in a trough, the orbital flow reverses and travels against the boat and rudder. This is profound of consequences for helm control when sailing downwind. When the rudder is in a trough, the opposing orbital flow must be added to the hull speed and that increases the relative water velocity over the rudder. Because rudder force varies with the square of the velocity, the rudder becomes suddenly powerful and sensitive. Conversely, when the rudder is perched on a wave crest, the orbital velocity must be subtracted from the boat speed. Then the relative water velocity drops sharply and the rudder becomes much less effective. Therefore, to generate the same turning force, the helmsman must turn the rudder significantly further up the lift curve.

[00:19:14]This alternate sensitivity, over response in the trough, and under response in the crest, is one of the fundamental reasons why sailing downwind in waves is so difficult. The result is often over correction in the trough, and insufficient correction on the crest, leading to a loss of alignment with the wave train, and escalating instability, which can lead to an uncontrolled yaw.

[00:19:35]A quote from Dr. Müller's introduction, and as shown in the upper schematic, the wave orbital velocity decays with depth on an exponential basis. This means that the magnitude of the orbital flow acting on the rudder depends on two factors.

[00:19:49]One, the depth of the rudder, and two, the height and steepness of the wave. In the lower right graph from our High Seaworthiness, we see orbital velocity plotted against wavelength, with curves of different wave steepness ratio. Note that the wave steepness ratios increase from 1 to 20, to 1 to 15, to 1 to 10, and even 1 to 7, orbital velocity increases dramatically. That means that when the boat's rudder is perched on a wave crest of a steep wave, the orbital flow is the strongest, and thus when traveling downwind, the rudder is at its weakest efficiency on a crest, and thus making any boat, sail or powerboat, much more vulnerable to approach. And with that, next slide, please. The flow and yaw induction. First, let's refresh our understanding of orbital flow motion from this short video from the website Small Trimarans Design. It's a good website and you should visit it.

[00:21:55]>> This animation shows the counter flow in a wave trough and the leaf capsize in a miniature breaker as an introduction to the next episode. Please read the comments on the screen. Okay, with that review, let's turn to the upper left diagram. Here we see a boat sailing about 30° to the wave train with a schematic of orbital motion, the clockwise beneath the crest and counterclockwise in a trough. As the vessel progresses, even though the boat speed remains constant, the rudder is repeatedly exposed to rapid changes in relative water velocity caused by this orbital flow. Now turn to the lower right image. Here we see a boat running in waves about twice its whole length with about a 1:6 steepness ratio and its rudder position near a crest. The rudder is immersed in orbital flow moving with the boat, reducing the apparent water speed over the rudder and therefore reducing steering effectiveness. At the same time, the bow is approaching a trough where it experiences boat speed plus the opposing orbital flow. The danger here is that any imbalance in hydraulic pressure on one side of the bow can begin an unexpected yaw. And if the rudder is simultaneously operating with reduced authority, that yaw may develop into a broach. From the mar high curve shown earlier, we saw that for a 200 mile fetch with a steepness ratio of 1 to 16, orbital velocity is about 4.2 knots. And for a 10 mile fetch with a steepness ratio of 1 to 10, orbital velocity is roughly 3 knots. Now, recall our rudder force calculation in episode 1 for the 10-22 sailing downwind.

[00:23:29]We established that rudder force varies with the square of the water velocity over the rudder. Now, place that boat sailing downwind at 7 knots in waves with a 1 and 10 steepness ratio.

[00:23:40]When the rudder is near a crest, the upper portion may be immersed in orbital flow moving at about 3 knots in the same direction. That reduces effective flow over that portion of the rudder from roughly 7 knots to 4 knots. Because rudder lift scales with velocity squared, and because orbital flow decays with depth, this could possibly reduce overall rudder effectiveness by the order of over 40%.

[00:24:05]But when the rudder drops into a trough, the opposing orbital flow adds to the boat's speed.

[00:24:10]Okay, increasing the rudder effectiveness. So, the helmsman experiences a rudder that is overly sensitive and powerful in the trough, but sluggish and weakened on the crest.

[00:24:20]And that alternating behavior can induce over correction, another cause to yaw instability.

[00:24:26]That time of encounter also matters because running downwind at 7 knots while the wave train travels at about 9 knots, the boat is slowly being overtaken. That means the rudder may remain in a sluggish crest condition for perhaps 10 to 15 seconds, followed by a similar interval of heightened sensitivity in the trough. That is a long time for the helm to be relatively unresponsive and over responsive. The takeaways from the slide, rotary wave motion is yet another factor compromising rudder control when steering downwind. And importantly, a boat may be most vulnerable to a yaw at the crest, precisely when the rudder effectiveness is at its lowest. Seconds earlier in the trough, the rudder may have had ample reserve turning force, but if on the crest, the required turning force exceeds what the rudder can generate at the reduced apparent flow speed, steerageway can be lost, and that is where broach can begin. The exact numbers are difficult to pin down because orbital flow depends on the wave speed and steepness.

[00:25:27]It decays exponentially with depth, and rudder lift varies with the square of the local flow velocity. So, the interaction is complex, but the bottom line is simple. Wave orbital motion can undermine rudder authority, and under downwind conditions, may contribute directly to yaw induction and broaching.

[00:25:44]And with that, next slide, please. Wave broaching. We saw the French frigate captain waited to turn around because to do so in waves equaling the ship's length would have been very dangerous.

[00:25:55]Small craft most often encounter waves in their own length when they're entering or leaving bars at an entrance to a harbor. I've crossed a couple of bars with moderate steep waves, and I found a real sense of uncertainty on the ability to maintain a course. There are many videos online showing boats broaching when crossing bars, particularly in Florida and France, where it seems is almost a spectator sport. Now you have a comprehensive understanding of when the hull length approaches the wavelength with high steepness ratios, why this situation is precarious. When you view this clip, the trawler's bow is almost certainly going to experience an unequal pressurization on one side inducing a yaw. And the stern perched on the wave crest, the rudder will have greatly reduced water flow around it, and consequently much less rudder authority to correct the boat from the yaw. The result will be a material loss of steering ability.

[00:26:50]A bad yaw, a wave broach, and a resulting capsize. Now, let's roll this clip.

[00:27:14]Why helm corrections alternate downwind.

[00:27:17]On this slide, we'll look more closely at the type of helm motions required when sailing downwind and why rudder corrections are unavoidable. In Professor Mar High's schematic shown here, we have a boat sailing at 30° to the wave train, a 100-ft wavelength, a boat speed of 7 kn, a surface orbital velocity of 4.2 kn. At position one, on the wave crest, as the boat rudder reaches position one, perched on the wave crest, the orbital flow is moving in the same direction as the boat. And we add the velocity vectors. Boat speed is 7 kn, orbital velocity at 4.2 kn with the boat. The resulting effective water velocity at the top of the rudder is reduced to approximately 3.8 kn. At this point, a correction to port is required, but the rudder effectiveness is low and thus a larger rudder angle is required.

[00:28:07]As the boat reaches position two, midway down the wave face, orbital velocity momentarily approaches zero. Here, the effective water speed around the rudder equals the boat speed. Rudder force and thus feel appears to be normal. The helmsman must make a micro adjustment to keep the rudder towards midships. At position three, the boat is now in a trough, still moving at 7 kn, but the orbital flow is now opposing the boat's motion. The result is an effective rudder flow velocity of approximately 11 kn. At this point, only a small rudder correction to starboard is required. Any excessive helm inputs risks inducing a roll. The key takeaways here, the helmsman is forced into a continuous cycle of larger rudder corrections on the crest, neutral response midwaves, and minor rudder corrections in the troughs. Even with perfect timing, this alternating sensitivity makes precise steering downwind extremely difficult.

[00:29:02]And now you know that, let's go to the next slide. Applying these forces. In this final slide for this fourth episode, let's apply what we've learned about wind, waves, orbital flow, and rudder effectiveness to the photograph sequence shown here. Only the first three photographs are relevant because by the fourth image, the vessel has already lost directional control. In the first photograph, the boat appears largely under control. There is some slack in the boom vang. The spinnaker pole is slightly high and forward. The spinnaker sheet appears marginally eased. At this moment, the boat appears to be sliding down a wave and the stern perched on a crest. If so, the rudder effectiveness is reduced due to the orbital flow or moving or with the boat.

[00:29:43]The skipper may have made a slight overcorrection a small roll to starboard. It's also possible that vortex shedding from the mainsail, along with a slightly larger than required rudder correction, is about to generate a roll to port. In the second photograph, the boat is now rolled to port. The stern appears to be in the trough. The bow is beginning to climb the next wave back. Here, orbital flow is opposing the boat. Effective water speed is higher and thus increased rudder sensitivity. A stronger vortex may have shed from the leech of the main, inducing roll to starboard. While the helmsman now fooled by the higher rudder authority may have made an overcorrection. By the third photograph, now it appears the bow is buried into the wave crest with a hydraulic pressure on the starboard side. The stern and rudder are likely close to or within the crest region. And thus, the sum effective rudder control is likely being reduced. At the same time, the boat is rolled well to starboard, causing the boat's sail plan center of effort to be placed well to starboard at the center of lateral resistance. Yaw, roll, and sail forces are now aligned in the same direction. And at this point, the round-up is inevitable. By the time we reach the fourth photograph, the vessel has already departed the regime of recoverable control. Finally, I've included this graphic of the writing moment for racer-cruiser to help with the sequence of photographs into perspective. This boat, like the Farr 40 shown earlier in episode 1, has rolled to approximately 60° at that angle of heel. Her deck is immersed, and the top of her keel is visible. That would have been exhilarating, but also dangerous.

[00:31:19]Critically, the boom has not yet gybed, and when it does, it will do so with considerable force. At this angle of heel, there is a real risk of the crew.

[00:31:27]Anyone not securely braced or holding on could be thrown from the cockpit and potentially overboard. There are a fair number of videos and photographs online showing sequences of this type of roll.

[00:31:38]What they do not capture is how such an event would unfold at night in a storm with waves of very high steepness ratios, often the result of complex interference patterns. In those conditions, visibility is limited, timing is unpredictable, and the consequences are significantly more severe. In a future episode, we will examine and quantify how the vertical accelerations generated by storm waves can alter writing moment magnitudes and materially reduce the angle of vanishing stability, and thereby reducing the safety margins this yacht is experiencing in relatively flat water.

[00:32:13]And that's the last slide for this episode, and we'll go to the outro.

[00:32:17]If you followed the series up to now, you've spent the better part of 2 hours listening to me talk about heavy weather, and I appreciate that. I received a few comments asking why I used English units instead of SI, and I wanted to address that. Seaworthiness, the forgotten factor, is foundational to this series. The publisher, Bloomsbury, very kindly gave me permission to use this material and frankly if I had not secured that permission, I would not have attempted this series. I have no desire to get sued.

[00:32:44]Frankly, I would have preferred to have presented the series in SI. However, because all of Marhaigh's published works was developed and presented in English units, converting all his graphs and charts into SI would have been a major undertaking, one that I was not equipped to do. That left me with a choice, present both systems or stay with one. After due consideration, it struck me presenting both would be more confusing than helpful. So, I stayed with the English units. I even searched for Sverdrup wave curves in SI with no luck. If any viewers know where they can be found, please post a link in the comments. But, the real takeaway here is not the units, it's the concepts. These concepts should be transparent in any system of units. And you're not going to unlearn them. You'll remember orbital flow and think differently about waves and heavy weather tactics. And if this series help you make safer judgments, then it was worth doing because safety is why I did this. And as far as I know, this information has never been consolidated anywhere else in quite this form. I always thought it was a shame that Marhaigh's work never became part of mainstream sail training because seaworthiness is fundamental to understanding stability and what happens to boats in heavy weather. And perhaps you now appreciate my modus operandi.

[00:34:00]I've gathered disassociated information from books, videos, websites, and research and pulled it together around Marhaigh's work into something sailors will hopefully find accessible.

[00:34:10]And I only did this because frankly nobody else had. I didn't do this to make money. I'm comfortable in my retirement. In fact, every episode and post-production cleanup is money out of my pocket. And as I said before, if this channel ever makes a profit, my intention would be to put that back toward helping underprivileged kids learn to sail. Finally, thanks for the comments, even the critical ones, because it shows you're thinking.

[00:34:34]Because anyone making the effort to take in these episodes, I believe is a more inquisitive and advanced reader sailor.

[00:34:40]Also, please don't forget to watch the Vertasim video on waves. That there's more information there worth knowing.

[00:34:46]And please like and subscribe to his channel. He does great work. Well, take care, sail safe, and we'll see you in episode five.