Stern Lines

[Roger Long]

I just remembered that there was some discussion of stern lines a while back and I promised to add to it after my boat was in the water. I’ve had some nice sails, she’s ready for a cruise up to several hundred miles whenever I feel like it and the damn dog woke me up at 5:00 so here goes.

Water is incompressible and somewhat thick so, when a boat moves forward, it pushes up a hump in the water around the bow. The water level is higher in this hump so water pressure on the hull under the hump is higher than normal and is pushing back on the hull. This is a major component in wave making resistance.

The hump, as it falls back down due to gravity, turns into a wave. When operating near hull speed, the next crest of this wave is at the quarters. The water level around the stern is higher so water pressure on the run is elevated. In crude terms, the boat’s own wave system is pushing forwards on the stern. A more elegant way to say it is that the hull is recovering some of the energy it expended making the waves at the stern. It’s only getting back a small portion of the effort expended in getting the wave moving but it is enough to be a significant factor in overall resistance.

Now consider the flow of water over the hull. It follows the hull fairly closely along the bow lines and around the midsection. Aft of the midsection, the water has to close in around the hull again and, if the flow lines are too steep, it can’t do this. The flow will then separate and kind of design a new “hull” for itself, leaving a space of turbulent water between the main flow and the hull that is largely moving along with the hull.

Why should this separation be a problem? In the air, separation is often promoted as in the dimple on golf balls to reduce resistance. If the water isn’t flowing over the hull, there is less frictional resistance. The answer is in the wave train and the energy recovery from it.

The wave train can not “push” on the stern and energy can not be recovered from it through a zone of separation. The stagnant and turbulent water under the separated flow insulates the hull from the higher water pressure of the wave train. Waterline length is such a significant factor in boat speed because of how it is related to the dynamics of wave making resistance. The boat’s length essentially ends at the point where a significant degree of separation begins. A 30 foot waterline vessel with a full stern and steep flow lines might then actually be only a 25 foot waterline craft. This is why double enders are often slow.

This is not an absolute thing. There is always some degree of separation and some wave energy is recovered through a separation zone. The amount of energy recovery drops off very quickly as the zone thickens. It’s like hull speed, not a line but a region on the graph where the curve turns quickly upwards.

Significant separation begins to occur over a fairly narrow range of flow angles regardless of size. That’s why there are tow testing tanks. The exact angle is influenced by factors such as surface roughness and the shape of the lines forward but will generally be in the 12 – 15 degree range. The flow angle is relative to the axis of the vessel’s motion. The diagonals on a lines plan, if they are drawn to cross the stern station lines as closely to perpendicular as possible, will most closely approximate the water flow. If you draw a line at 15 degrees to the centerline on which the diagonals are drawn and move it up and down, the points at which it becomes tangent (just touches at one point) each diagonal is a good indication of where separation will begin in that region of the hull. The middle of the points found is essentially where the vessel’s waterline length should be measured to for predicting hull speed.

Here is an example of a hull drawn to maintain this 15 degree angle in the diagonal lines:



There has been a lot of discussion about weather helm recently. The aspect of this that is almost never discussed is the effect of these dynamics on the rudder. The wave train is not the same on each side of the boat nor are the flow lines and the degree of separation. The pressure differentials on the rudder, which are felt by the helmsman, are heavily influenced by these factors. Those rare boats which have magically neutral helm owe this fact more to the shape of their sterns and hard to predict pressure patterns rather than having exactly the right amount of “lead” in their sail plan.

[PeterSibley]

Roger , thank for taking the time to set this out , could you however rephrase this for the thick amongst us (me ) .I can't quite get your meaning .

"If you draw a line at 15 degrees to the centerline on which the diagonals are drawn and move it up and down, the points at which it becomes tangent (just touches at one point) each diagonal is a good indication of where separation will begin in that region of the hull. The middle of the points found is essentially where the vessel’s waterline length should be measured to for predicting hull speed."

[Roger Long]

I can't quite get your meaning .

Set a pair of parallel rulers at 15 degrees to the centerline of the lines plan and move one in and out until it just touches each diagonal at one point. Tick those points, and you will have identified the places on the hull where significant separation is likely to begin.

You can also do it with a pair of drafting triangles by sliding one against the other.

[PeterSibley]

Ah ! thanks !

[PeterSibley]

Could I ask you to compare this drawing and yours above Roger .You would say that the buttock lines on this rise too fast towards the wl or have I misunderstood ?

[huisjen]

Thank you Roger. That was very helpful.

I'm trying to envision how heeling is going to change things. My current little paper hull model (4-panel plywood hard chine 15'4" hull, 24° deadrise, almost no twist to the bottom panels, 1:24 scale) seems like it might run smoother when heeled.

It hardly seems worth drawing diagonals on a flat panel hull. What should I be looking at in this case?

Should we mostly ignore buttock lines and concentrate on diagonals when considering hydrodynamics?

The deeper diagonals on Peter's drawing (post #5) have some hollow and go to greater than 15° at the end. Is there a rule of thumb for when you can do that relative to the rest of the curve, in order to maintain laminar flow? I've seen some drawings for a truck cap that mimics the back end of a Prius, and supposedly changes the coefficient of drag from .44 to about .33 for the average truck. The notes say it starts sloping down from the top of the cab at 9° and finishes at about 15°, which seems to agree with what you said above, regardless of the fluid in question or reynold's number.

Dan

[Roger Long]

would say that the buttock lines on this rise too fast towards the wl ?

It is the diagonals you want to look at. Some craft appear to have very full sterns if you look at the buttock lines but easy flow when you look at the diagonals. You'll see this most often in hull forms like large sailing ships of the clipper type.

It would help in this drawing if the upper diagonals were a bit more perpendicular to the station lines.

[Roger Long]

The 'Inga" provides a good example of the principle. Here are the lines with the 15 degree diagonal tangents indicated by the small circles. As far as wave making resistance and the length in Speed/Length ratio are concerned, she is essentially the equivalent of a boat with the strange transom indicated on the lines plan. You can think of everything aft of that as being just something that provides additional buoyancy.



You wouldn't think of building a boat with a stern that ended like that because it would look slow. Double enders, if not very carefully designed, are slow for exactly the same reason. It's just not apparent. Once the flow lines exceed the critical angle, it doesn't much matter what they are.

Hull speed for "Inca" at a S/L of 1.25 would be 6.25 knots based on the measured waterline and 5.59 knots based on the effective waterline.

These are fuzzy numbers because factors like surface roughness will effect the exact point at which separation begins. 12 degrees is probably a better angle in theory but, in studying lines of vessels that needed carrying capacity as well as speed, the 15 degree angle is almost universal in craft the have evolved through trial and error development. For a smooth bottom racing craft, you would use 12 or even a bit less.

It's often better to keep the flow lines shallow and then give them a quick tuck right at the stern. This looks un-streamlined to those of us who grew up in the aviation age but delays separation. You will see this kind of stern lines in many traditional craft. It's also the reason powerboats usually have immersed transoms even if they are not intended to plane.

[paladin]

Damn...roger...chop off the stern overhang on your 23 footer and it'll pretty much like a 21 1/2 footer that I am about finished with. Nice looking pile of kindling.

[Roger Long]

Nice looking pile of kindling.

Thanks. Full plans here:

http://www.rogerlongboats.com/Boats.htm#23Cutter

[willmarsh3]

This is a very fascinating thread. I have wondered why hull speed is what it is.

I'm looking at the drawings in post #1 and #8 and see the diagonal lines in the head on view. At first glance they appear to be 45 degrees but on closer inspection they are not. They instead appear to be approximately perpendicular to the station lines. How is the angle of these lines defined?

[Wayne Jeffers]

Thank you very much for this, Roger.

I have in hand a set of plans for a popular double-ender, which fails your 15* diagonal test. I've been concerned about rumors that she performs not so well as would be expected.

You've likely helped me avoid an expensive mistake.

Thanks again!

Wayne

[L.W. Baxter]

Very interesting and clear exposition, Mr. Long.

Regarding the difference in top hull speed you mention between measured and effective waterline, what effect does that have on acceleration and speeds lower than hull speed? In other words, is that difference notable and detrimental at lower speeds?

[Roger Long]

How is the angle of these lines (diagonals) defined?

They are just arbitrary. Designers who are using them only as fairing lines will take less care to get them to cross as many stern station lines as close to perpendicular as possible. Designers who are using them to assess afterbody flow will try to get them as close to the flow lines as possible.

[Roger Long]

In other words, is that difference notable and detrimental at lower speeds?

At very low speeds, resistance is almost all skin friction. This resistance increases at a fairly steady rate as the boat goes faster. Wave making resistance, increases exponentially. There will be some intermediate speed at which resistance is half skin friction and half wave making. At hull speed, it's mostly wave making.

Boat's with terrible flow lines and full ends can be very good in ghosting air. The shape that has the least surface area for its volume is a sphere. At very low speeds, the closer a boat comes to that ideal, the less wetted surface it will have for its displacement.

The difference between a hull like "Inga" and a transom stern vessel of the same waterline with good flow lines will be less and less apparent as speed decreases.

[sandingblock]

Hi Roger,

In a similar vein (maybe another thread?).

I was shooting the breeze a few months ago with an owner of a boat that had a very slim bow, similar to some Cavaliers I've seen. There was very little room forward of the main bulkhead, just sail and ground tackle stowage. Back aft was very roomy, with a tunnel going down one side of the cockpit to an aft cabin.

We were discussing the theory that the boat had an effective waterline less than the true waterline due to the fact that the bow wave didn't get really going till quite far back in the hull.

The owner thought that the hole in the water that follows the bow wave was further aft than it would be if the bow was fuller. He intimated that the boat wasn't as fast as he expected, as he thought, initially, that modern boats with a lot of volume aft was a sign of performance.

This was a reasonably laden cruising boat.

Edit: Obviously talking about displacement speeds here, so I've drifted a bit from the original post.

Jonny.

[Tom M.]

We were discussing the theory that the boat had an effective waterline less than the true waterline due to the fact that the bow wave didn't get really going till quite far back in the hull.

Lately I have been thinking about this very thing, and I just can't quite wrap my head around the nuances when it comes to an aysymmetrical hull that's fuller aft. It seems obvious to me that there needs to be some wavemaking displacement up front for speed. (A hulls max speed is determined by it's wavemaking length, not it's waterline length--if waterline length mattered, we'd see retractable knife edge extensions to gain speed, but we all know that doesn't work.) Regarding wavemaking resistance, it seems prudent to make a small amplitude wave. Ok, we can do that with very little displacement forward (but not too little!). But what happens as that small amplitude wave becomes a full boatlength wave? How does it change into a higher amplitude (deeper) wave as water passes over the middle and aft sections that have more displacement? I guess I'm wondering how one can optimize a hull for speed that has a low prismatic forward and a high prismatic aft. It would be nice if I was making this more complicated than it needs to be. Anyone care to take this on, or recommend some reading? Am I even asking the right questions?

[Tom M.]

Upon re reading, I see that I assumed prismatic coefficient related to displacement, but they don't really. Rather, it's an indication of the distribution of displacement. I'll let it stand to show my ignorance in these matters.

[wtarzia]

Then a very skinny hull (as on an outrigger canoe/proa) is efficient partly because nearly all of the length of the hull is under that 15 degree-to-diagonal zone?

I wish someone would explain how and why people draw diagonal lines. I have read stuff, various stuff, but none of it seems to well explain diagonals. I can get all the other slices and curves but diagonals. Then in frustration I study diagonals on plans, and still I cannot see the criteria by which they are drawn -- they start at varying heights on the vertical centerline of the plan, they do not go through any intuitive (to me) angle to the planks.... they almost seem randomly drawn, is what I'm saying. Somebody please explain it to me. The argument that started this thread was very well written and got through to me the way other articles have not -- well done sir! -- can the same be dfone for diagonals? -- begging -- Wade

[Tom M.]

Skinny hulls follow different rules. I wish I knew what those rules were.

Maybe someone else will chime in regarding diagonals. If you want a visual representation, it might help you if you try to visualize the diagonal line painted on a finished hull. In contrast with the boot stripe, a diagonal would begin above the boot stripe forward, fall below the stripe midships and ride again above it aft. Designers provide them so the loftsman can check his other lines if need be. It's like when taking bearings, your fix is more accurate if you take more bearings. And by stroke of luck, as Roger stated, diagonals drawn across the sections a perpendicular as possible closely approximates the actual path of water along the hull. This allows him to measure the 15 degree thing.

[Ian McColgin]

The diagonals are mostly useful for a more accurate translation from the 2D of the plans to the 3D of the boat. They can also give some insight into whether the hull has any odd blips or bumps not readily apparant in the section, station and waterlines. In the bad old days, designing from a half-model covered that issue but in making a lofting, diagonals might still be used as a check against the off-sets.

Skinny hulls don't follow different rules, they just make smaller waves for a given displacement. Take two 20 ton boats - one like Granuaile, an LFH Marco Polo of 53' LWL, 10'B, 6'D compared with a husky ketch of similar displacement that's 45'x15'x6 - No matter how you clean up the bow - and prismatic does matter, you are still pushing water 50% further aside, inevitably making a bigger wave. On top of that, you push the water apart and let it come back together in less length - not just increased push apart but increased drag astern. This may be why when you swim you put your palms normal to the stroke, not in line.

Not different rules, just the same rule but different inputs give different results.

[Tom M.]

What you say makes sense Ian, but when I say skinny hull, I mean kayak skinny and skinnier, like a hobie cat. What's happening there? Why can these hulls far exceed their 1.34 speed? Are they actually making a wave that's a lot longer than the hull?

As well, it stands to reason that a hull with low prismatic forward and high prismatic aft will make an aysymmetric wave in amplitude. True? Is this a stable wave? If not, is it trying to become symmetrical? And if so, does the aft part of the wave try to abhor the amplitude vacuum forward? Does it give the boat a "push"? Is this why aysymmetric hulls are faster? So many questions...

[bott]

What you say makes sense Ian, but when I say skinny hull, I mean kayak skinny and skinnier, like a hobie cat. What's happening there? Why can these hulls far exceed their 1.34 speed? Are they actually making a wave that's a lot longer than the hull?

As well, it stands to reason that a hull with low prismatic forward and high prismatic aft will make an aysymmetric wave in amplitude. True? Is this a stable wave? If not, is it trying to become symmetrical? And if so, does the aft part of the wave try to abhor the amplitude vacuum forward? Does it give the boat a "push"? Is this why aysymmetric hulls are faster? So many questions...

I believe that (in my completely non-expert opinion) those type of craft are really no longer in the same "dynamic category" because of their low displacement. And essentially the high L/B ratio is a expression of this, such that they are no longer operating in the displacement hull form paradigm. This is opposed to the Fife-type plank-on-edge hulls where I believe Mr. McColgin's comment prevail.

[Tom M.]

So maybe the idea with these small displacement skinny hulls is they bypass wave making resistance. Maybe the waves they make are so small in amplitude that they never account for more resistance than friction does...

[bott]

I guess my point/opinion was that they easily get up and over their (very small) bow wave and begin planing quickly.

But, again, I am prepared to be corrected by the other more knowledgeable people in this thread.

[Ian McColgin]

Narrow boats do not in general plane as they haven't the surface area to support them. In Hyannis Port we had a lovely LFH express that was superficially the same envelope as Granuaile - 55' LOA by 10' B. She drew about the prop on shallow V sections. She was repowered in such a way that the engine torque coupled with the prop tended to warp her into a dynamic starboard list that was partly corrected by deployable stern planes.

At speed she, like other old time needle boats such as Turbina, never came out of the water on a plane, but she could go through the water every bit as fast as a lot of planing hulls. A similar phenomenon is utilized to great effect in high speed catamaran ferries that also don't get up on a step, but rather have incredibly efficient hulls moving through, not over, the water.

In these boats, the hole in the water between bow and stern wave was not deep and the boat was not trying to sail uphill the way a boat just moving from displacement to planing mode does.

There are needle boats that plane. Dave Gerr has a few examples. They are quite different, however, from narrow displacement hulls.