Deep V hull and vertical accelerations

[KarlB]

I am part of a group of naval architect students currently conducting a small research on the connection between hull design on high speed planing boats and vertical accelerations due to waves.

We have measured vertical accelerations of two different boats using accelerometers in a variety of wave heights. One boat has a conventional hull design while the other is designed to provide good slamming characteristics according to Savitsky's theory. The latter has a hull with less V-angle and double chines. The purpose of our study is to confirm that this new hull design takes on waves as theory says it should, and also to deny the ongoing trend amongst boat manufacturers to build deeper and deeper V-hulls.

It is clear that deeper V-hulls means better slamming characteristics. Many do not consider, however, the great addition of wetted surface and therefore drag.

And now to the questions.
Why do V shaped hulls decrease vertical accelerations?
What is the effect of chines, and what would you say is a disadvantage of having two chines instead of one?
Is there any method of calculating speed decrease due to waves?
What is the most effective way to reduce slamming, by designing a deeper V-hull or to decrease the hull width?

I am grateful for any links covering this topic.
// Karl B, Stockholm

[u4ea32]

Karl, hopefully your experiments with actual boats will provide some clarity to this issue.

Stavitsky's writings, in particular his most recent writings, do indicate that reducing chine beam has a much larger effect on reducing vertical accelerations than does increasing deadrise. His latest papers suggest accelerations are related to beam cubed, so a 10% reduction in chine beam results in 0.9x0.9x0.9=0.73% as much vertical accelerations.

The "second chine" is then really just a crease in the topsides at the static waterline, so the stability at rest is pretty much unchanged. The angle outside the lower chine must be steep enough to ensure flow separation, so perhaps 45 degrees is OK.

The thing about deadrise is that there is very little increase in resistance going from, say 10 degrees to 24 degrees, yet the reduction in vertical accelerations is very large. I'll leave it to you to find and post the appropriate numerical functions from published works.

[tunnels]

ARE you talking about Chines or strakes ??
to get a hull to go it needs lift but where are you going to get that lift ? What sections of the hull are in the water when the hull is planning .
Strakes are usuall placed at the front and disapated as they go aft and most never get to the back. To me this is all the wrong way round .
Where does a hull slamb? in the bow, in the middle ,or at the aft end . Basicly from the chine at the bow end to the chine at the aft end it can be divided roughly in the 1/3s ,The front 1/3 is where the hull hits waves and needs to part the water !so why have strakes there ,the second third is in combination to the first third and gives lift and carries the hull and all its weight this is where starkes need to start , The very aft third of a hull is load carrying and strakes should be there to give the hull lift and get it up to reduce wetted surface area .
To get the hull up and have a less wetted surface Strakes should be used to give this lift ! . Small strakes like you see on just about every hull are not even worth a mentioning . They need to do what they are ment to do lift! !! so give them width and length . All the way from the transom to about the front third of the water entry section and graduually disapate into the hull shape . I have only seen this on one power boat and it completely makes sense , Fine water entry and a area to carry the boat and all its weight . The pad on some boats is to do just what i have written about .

[tspeer]

Hubert Flomenhoft talks about this problem briefly in his book, "The Revolution in Structural Dynamics," in connection with dynamic loads on seaplanes. The minimum load to decelerate the hull's vertical motion is a constant vertical force on the bottom as the hull is dynamically immersed and the kinetic energy is absorbed. Any other force profile will have a higher peak load to dissipate the same energy. Whether we're talking about a seaplane descending onto flat water or the water coming up to meet the hull, the problem is going to be the same.

Herbert Wagner in the 1920's derived a hull section from the constant-load force profile that was bell-shaped. It had a rounded convex keel that transitioned to concave sections flaring out at the chines. At MIT in 1948, they tested Wagner's profile by dropping cylinders into water tank and improved the section shape. The results were used to design the bottom of the Martin P6M SeaMaster (the first jet-powered seaplane).

I haven't located a good paper that solves this inverse problem - all the ones I can find assume a shape and velocity upon impact and calculate the loads. But this paper might give you some starting points. You may be able to take a method for estimating forces and turn it on its ear to specify the force and calculate the shape.

When I apply a very simple-minded approach based on the idea that the dynamic force on the bottom of an impacting cylinder is proportional to the mass in a circular half-cylinder whose diameter is the same as the width of the hull at the waterline, and the hull is undergoing a constant deceleration, I get the shape in the attached spreadsheet. I make no claims for rigor in this whatsoever, but it does produce a bell-shaped section similar to what was described. If you have no idea what shape you are looking for, it might be something worth trying.

[LostInBoston]

Originally Posted by tunnels

ARE you talking about Chines or strakes ??
to get a hull to go it needs lift but where are you going to get that lift ? What sections of the hull are in the water when the hull is planning .
Strakes are usuall placed at the front and disapated as they go aft and most never get to the back. To me this is all the wrong way round .
Where does a hull slamb? in the bow, in the middle ,or at the aft end . Basicly from the chine at the bow end to the chine at the aft end it can be divided roughly in the 1/3s ,The front 1/3 is where the hull hits waves and needs to part the water !so why have strakes there ,the second third is in combination to the first third and gives lift and carries the hull and all its weight this is where starkes need to start , The very aft third of a hull is load carrying and strakes should be there to give the hull lift and get it up to reduce wetted surface area .
To get the hull up and have a less wetted surface Strakes should be used to give this lift ! . Small strakes like you see on just about every hull are not even worth a mentioning . They need to do what they are ment to do lift! !! so give them width and length . All the way from the transom to about the front third of the water entry section and graduually disapate into the hull shape . I have only seen this on one power boat and it completely makes sense , Fine water entry and a area to carry the boat and all its weight . The pad on some boats is to do just what i have written about .

Strakes seperate the water rise from the hull and divert the spray outward. That is why they are towards the bow.

[u4ea32]

Tom, makes sense for a shape to achieve constant deceleration. The outer flare continues to impart the same deceleration even as the vertical motion almost stops.

Its an excellent analysis, thanks!

If you drive your car like that, you'll hate it: what one does to stop smoothly is to gradually increase the force, then decrease the force again, and not a constant force.

A pure deep V provides this sort of deceleration that is a curve instead of straight line deceleration force. At first the force starts low, and then increases. As the vertical velocity reduces, the force also gradually reduces.

Hence, the simpler deep V results in a smoother feeling ride to the passengers.

Note that some studies, such as those published regarding the Axe Bow, indicate that comfort at sea is a function of sudden, sharp accelerations (e.g., a sudden change in acceleration rate, or the second derivative of motion) and not simply the magnitude of the acceleration.

A constant rate shape, as indicated, would introduce two "infinite" rates of change of acceleration, right when the hull enters and the deceleration begins, and again when the "chine" hits and deceleration suddenly stops. These infinite rates of change of vertical acceleration would be perceived as being very harsh to the passengers.

Hence, this bell shaped hull form mostly died off soon after it was introduced.

It was tried on many boats to generally very poor reviews. For example, the US PT boat trials around Long Island: two designs, one with this bottom design, the other with a prismatic (V) bottom. The bell shaped designs broke, and continued to have structural failures. The british also tried this bottom earlier before adopting the prismatic bottom for the same reason, but in sea trials in the North Sea. The crews regarded the non-V bottom boats as very poor sea boats. Eventually, even the final hold outs such as Huckins and Hargrave finally gave up on the concave chine areas.

Today we only see this shape bottom by designers who don't study history and are therefore doomed to repeat it, and by those who are intentionally recreating specific historic boats.

[u4ea32]

Originally Posted by tunnels

ARE you talking about Chines or strakes ??
to get a hull to go it needs lift but where are you going to get that lift ? What sections of the hull are in the water when the hull is planning .
Strakes are usuall placed at the front and disapated as they go aft and most never get to the back. To me this is all the wrong way round .
Where does a hull slamb? in the bow, in the middle ,or at the aft end . Basicly from the chine at the bow end to the chine at the aft end it can be divided roughly in the 1/3s ,The front 1/3 is where the hull hits waves and needs to part the water !so why have strakes there ,the second third is in combination to the first third and gives lift and carries the hull and all its weight this is where starkes need to start , The very aft third of a hull is load carrying and strakes should be there to give the hull lift and get it up to reduce wetted surface area .
To get the hull up and have a less wetted surface Strakes should be used to give this lift ! . Small strakes like you see on just about every hull are not even worth a mentioning . They need to do what they are ment to do lift! !! so give them width and length . All the way from the transom to about the front third of the water entry section and graduually disapate into the hull shape . I have only seen this on one power boat and it completely makes sense , Fine water entry and a area to carry the boat and all its weight . The pad on some boats is to do just what i have written about .

Tunnels, I used to also think this same way about strakes, but some research showed the error in this concept.

The reason strakes are useless on the back part of boats, besides those boats that go VERY fast, is because they contribute a lot of drag and very little lift underwater. This is because a strake, underwater, holds a high pressure area that is long and narrow. Like a wing with a very, very low aspect ratio.

What is the shape of a glider wing, and why? The lift to drag ratio of a lifting surface (such as a wing or the bottom of a planing boat) is directly proportional to the aspect ratio. Therefore, the higher the aspect ratio (the wider per unit fore-and-aft length), the higher the lift to drag ratio. And vice versa. So the higher performance glider will have higher aspect ratio wings. The limit is purely structural: eventually its too heavy to make a wing that long and thin to carry the weight of the airplane.

So a strake underwater does create some lift, but it creates a lot of drag. So its better not to have them underwater.

Above the water, however, strakes do help, because then the flow of water (really, spray) is not not fore-and-aft along the line of the strake, instead the flow is up the sides of the bottom, ACROSS the strake. In this regime, the strake acts as a very high aspect ratio lifting surface, so high lift to drag: all good.

Chines remain a good thing because they release the flow of water. But actual studies show the size of the chine can be very small (like an inch in most applications) as long as the outer edge is sharp.

Many studies of planing craft with chines show that in steady state with wetted chines, the lift of a V with a chine is virtually identical (within measurement accuracy) of a V with less deadrise, the deadrise reduced by the size of the chine. In other words, a wetted chine is essentially identical to a chineless surface going straight from the keel to the outer edge of the chine. This has been shown to be true regardless of the width or the shape of the chine: flat, curved, negative slope.

Therefore, the well demonstrated optimum configuration of strakes is to have them END right about where the spray stops and the fully wetted bottom of the boat begins. Hence, your observation that most boats have the strakes start at the bow and run 1/3 to 2/3 of the way aft.

Its not intuitively obvious, but its well supported by nearly a century of well published research.

[tspeer]

Originally Posted by u4ea32

Tom, makes sense for a shape to achieve constant deceleration. The outer flare continues to impart the same deceleration even as the vertical motion almost stops.

Its an excellent analysis, thanks!

If you drive your car like that, you'll hate it: what one does to stop smoothly is to gradually increase the force, then decrease the force again, and not a constant force.
...
Today we only see this shape bottom by designers who don't study history and are therefore doomed to repeat it, and by those who are intentionally recreating specific historic boats.

I agree that jerk needs to be considered in a real design. (Actually, I do know people that drive the way you describe!)

The bell section may not be popular for powerboats, but you do see it used a lot today for sailing mulithulls, because of the emphasis on minimizing wetted area compared to a planing powerboat. And you're right about the abrupt initial onset being objectionable - I've noticed that from a lot of hours sitting out at the front beam going upwind in a chop! It's one of the things I like about my boat - the deeper, more rounded sections do provide a smoother ride going through waves compared to some of the boats I've crewed.

I think the real message of the bell-shaped bottoms is it's possible to design a section to have a specified force profile. That would allow trading off conflicting requirements, like minimizing wetted area vs the forces in a seaway.

For example, by using a power-function in the spreadsheet and varying the exponent, a family of bottom shapes are generated, ranging from the bell to something much like a deep V (attached). The flared V profile will build to a maximum force just as the boat comes to a stop, but the initial impact will be zero. That's not likely to be a practical approach, either. But it wouldn't take much effort to come up with a function that was tailored to have a smooth buildup and drop-off at the ends, with a constant force in the middle.

Aside from ease of design and construction, I think the deep V is popular because it is self-similar - a large V looks just like a small V. That means the force profile for a heavy slam is also similar to a small one in shape, just bigger. It's a good approach for handling waves of different sizes. The bell bottom has to be designed for a specific amount of kinetic energy, which is not a bad approximation for a seaplane that always lands with the same rate of descent, but perhaps not so good for a boat that has to negotiate a variety of sea states. A self-similar shape would be a good all-round design, but I think we can do better if the requirements are better defined.

[u4ea32]

Well put, Tom.