Theoretical max speed - heeling

[Robert Wilson]

The waterline increases on heeling - does this increase the maximum theoretical speed?
Or does the shortening of the windward side compensate because of changed "foil" dimensions - or whatever??

Khamsin has noticeable tumble-home.
Upright waterline length is 7.7m, whereas the "fattest" part of tumble-home length is 8.9m.

Does that increase theoretical max from 6.7kts to 7.2kts?

The length stated on my purchase data states waterline is 22 feet which is presumably the straight-line distance from bow to stern at the waterline.
This would make theoretical max 6.4kts, which is what I have always reckoned to be the case; but the boat has sailed faster than this at times.

Speeds calculated using:-
"Sq.root of waterline length in feet, multiplied by 1.34"

 

[DJE]

The designer's dimensions for my boat state the LWL as 9.60m (Static) and 10.80m (Dynamic). I assume this is due to the bow and stern waves climbing up the hull overhangs and I would have thought that this would be a bigger effect than heeling. Either way I'm happy to believe that it will give me an extra 0.5 knots of boat speed.

 

[flaming]

The waterline increases on heeling - does this increase the maximum theoretical speed?
Or does the shortening of the windward side compensate because of changed "foil" dimensions - or whatever??

Khamsin has noticeable tumble-home.
Upright waterline length is 7.7m, whereas the "fattest" part of tumble-home length is 8.9m.

Does that increase theoretical max from 6.7kts to 7.2kts?

The length stated on my purchase data states waterline is 22 feet which is presumably the straight-line distance from bow to stern at the waterline.
This would make theoretical max 6.4kts, which is what I have always reckoned to be the case; but the boat has sailed faster than this at times.

Speeds calculated using:-
"Sq.root of waterline length in feet, multiplied by 1.34"

Basically, yes.

That was the whole point of designs that increased length once they heeled, in the era when the measurement rules only measured the static waterline length. With the side advantage that designs with long overhangs, especially at the stern, are generally very good looking boats! A rather extreme example being the J class yachts.

 

[johnalison]

Although I more or less understand the physics, it has always puzzled me why the water should care about touching a short section of hull, and why this should substantially lengthen the wave that has been induced. Modern designers seem to have learned to cheat by fooling the water into thinking the boat is longer than it is. My boat is a '90s design, but I am sometimes impressed by modern fast cruisers at near maximum speed, and how little wave and spray they are making.

 

[Robert Wilson]

Thank you.
It is what I always thought, but having watched on these fora over the last five years I have begun to realise my knowledge of the science of sailing is far outweighed by my aspirations:-
Hoist sails, drop mooring - sail !! :encouragement:
Not to be complicated by notions of aero-foil shape.

Khamsin has the advantage of fairly long overhangs and a reverse-counter (IMHO staggeringly beautiful, but I'm biased!)

So, if my purchase data stated LWL 22' (6.7m) that presumably referred to the straight line from bow to stern, at the waterline.

Beautiful boat above, thanks.

 

[bignick]

Although I more or less understand the physics, it has always puzzled me why the water should care about touching a short section of hull, and why this should substantially lengthen the wave that has been induced. Modern designers seem to have learned to cheat by fooling the water into thinking the boat is longer than it is.

Imagine a boat moving through the water at speed.
The bow is pushing water out of the way = high pressure = wave crest. This wave crest is dragged along by the vessel at the speed of the vessel, so the wave celerity is determined by the motion of the vessel. In deep water there will be a particular wavelength that corresponds to this celerity.
At the stern, another wave pattern is generated.
As boat moves faster, these two wave patterns are forced to move faster with it, so the associated wavelength becomes longer. At some speeds the wave patterns from the bow and stern superpose positively to form a larger wave. At other speeds the bow and stern wave patterns superpose negatively to reduce the size of the wave pattern formed by the hull.
At "max hull speed" ( though there's really no such thing...) the wavelength approaches the length of the waterline, so the 2nd crest of the bow wave pattern coincides with the stern wave. This forms the biggest wave pattern and larger waves require more energy to create. This creates a large hump in the resistance curve, which "displacement vessels" are unable to get over, so characterises the max speed of these vessels.

The above is pretty simplistic, but gives you a flavour of what is going on.
For more info try googling : Froude number, Froude scaling or Kelvin wave pattern.

 

[Birdseye]

The waterline increases on heeling - does this increase the maximum theoretical speed?
Or does the shortening of the windward side compensate because of changed "foil" dimensions - or whatever??

Khamsin has noticeable tumble-home.
Upright waterline length is 7.7m, whereas the "fattest" part of tumble-home length is 8.9m.

Does that increase theoretical max from 6.7kts to 7.2kts?

The length stated on my purchase data states waterline is 22 feet which is presumably the straight-line distance from bow to stern at the waterline.
This would make theoretical max 6.4kts, which is what I have always reckoned to be the case; but the boat has sailed faster than this at times.

Speeds calculated using:-
"Sq.root of waterline length in feet, multiplied by 1.34"

There is no maximum speed. Have a look at https://en.wikipedia.org/wiki/Hull_speed

The difference between 6.7 and 7.2 is small and I doubt your log is accurate to that degree anyway. But yes, the longer the hull the less water resistance at a given speed and so heeling might make the hull faster at the same time that heeling makes the sail power less.

 

[dom]

As others have said you need to to take this 1.34 x sqroot LWL formula with a pinch of salt. Firstly this is only an average number and will vary a lot depending on hull shape/dynamics; a snappy cat and an old tub will have very different coefficients.

Also bear in mind that the max hull speed does not represent a mathematical non-linearity where no speed gain accrues from increasing propulsion power. At max-theoretical some boats (generally fat heavy boats) will indeed get pretty much stuck, whilst others (generally thin multihull jobs) face a much slower increase in resistance. Boats that are designed to plane will face an increase in resistance around max-theoretical carefully calibrated to allow a smooth transition from displacement to planing.

 

[DJE]

At the stern, the water is being "sucked in" to fill the hole in the water left by the passing of the vessel = low pressure = wave trough.
At "max hull speed" ( though there's really no such thing...) the wavelength approaches twice the length of the waterline,

I always thought it was crest at the bow, crest and the stern and trough in the middle. Otherwise what use is that big stern overhang?

 

[Robert Wilson]

There is no maximum speed. Have a look at https://en.wikipedia.org/wiki/Hull_speed

The difference between 6.7 and 7.2 is small and I doubt your log is accurate to that degree anyway. But yes, the longer the hull the less water resistance at a given speed and so heeling might make the hull faster at the same time that heeling makes the sail power less.

Thanks to all.
I accept that heeling makes for less sail-power. I am gratified that by sailing heeled some way "off the vertical" does indeed make the speed a little greater, although as you say the difference is marginal. At least it means I'm not doing something drastically wrong by enjoying a zippy zip through the water with the ocean approaching the toe-rail!

As for the log being inaccurate - bloomin' thing does its own thing as and when it wants. Same for the echo-sounder!

Fascinating replies, always interesting to learn why the things that I do happen the way they do

 

[bignick]

I always thought it was crest at the bow, crest and the stern and trough in the middle. Otherwise what use is that big stern?

Oops. Should wake up before I post.

 

[Tranona]

Thanks to all.
I accept that heeling makes for less sail-power. I am gratified that by sailing heeled some way "off the vertical" does indeed make the speed a little greater, although as you say the difference is marginal. At least it means I'm not doing something drastically wrong by enjoying a zippy zip through the water with the ocean approaching the toe-rail!

As for the log being inaccurate - bloomin' thing does its own thing as and when it wants. Same for the echo-sounder!

Fascinating replies, always interesting to learn why the things that I do happen the way they do

The important point to remember with "hull speed" is that it is an estimate of the point at which any more speed requires a substantial increase in power to overcome wave resistance. On a sailing boat with low auxiliary power this is unlikely to be achieved under engine. You often see the consequence of overpowered yachts digging their stern in and creating a big stern wave when they hit this barrier - but going little faster. That is why engines and props are matched to achieve hull speed at maximum power. Programmes for calculating engine power and props tend to use a lower factor of 1.25 or so rather than the more common (optimistic?) 1.35 to predict maximum speed.

However a sailing boat can fairly easily exceed hull speed in 2 ways. The most obvious is simply increasing sail power - more sail, or more wind. So a big kite and a good broad reach will usually see speeds in excess of hull speed for short periods, particularly if assisted by sea state. Of course the danger here is of loss of control. The second and now common is having both enough power (in terms of power to weight) and an appropriate hull shape to get over the hump and plane.

Going back to your boat, the advantage of your hull shape is that once the boat is moving the sailing LWL increases as the ends are immersed, so moving the "hull speed" up, crucially cheating the rating which is based on static LWL. The difference of course is relatively small. Going from 24' to 26' LWL increases theoretical hull speed by just over 0.2 knot - but in racing terms this can lead to a big advantage, particularly on windward legs where the increase is more likely to be consistent. To access that increased potential you need to be able to generate the power from your sails, hence the need for efficient sails and trimming.

The current design trend is to increase waterline length and shorten overhangs which has a number of other benefits, particularly increasing the usable volume of the hull. My 33' has the same LWL as my old 37, so the same maximum speed potential, but potentially loses a bit because their is no increase in LWL when the boat heels.

 

[Robert Wilson]

Verrry interesting :encouragement:

I'm glad that being a fan of "lovely old boats" with graceful and exciting lines (IMHO) actually has a wee benefit - some of the time!

 

[snowleopard]

The basis of 'hull speed' is that the form of the hull creates a wave with crest at bow and stern which is difficult for the boat to climb out of. The relation of hull speed to LWL is that waves travel at a speed proportional to the square root of the wavelength. Think of the speed of a ripple on a pond - barely walking pace - compared to a tsunami travelling at 200+ knots. The art of hull design is to make the distance between crests of bow and stern waves as long as possible; increasing LWL is only one of the ways of doing that.

Another way of removing or reducing the hull speed limit is to increase the length:beam ratio. There is a widely accepted ratio of 8:1 above which hull speed no longer applies which is why most multihulls continue to go faster the more power is applied. Here is an extreme example - a long narrow boat travelling at around 12 knots. Not a lot of bow/stern wave!

 

[Robert Wilson]

The basis of 'hull speed' is that the form of the hull creates a wave with crest at bow and stern which is difficult for the boat to climb out of. The relation of hull speed to LWL is that waves travel at a speed proportional to the square root of the wavelength. Think of the speed of a ripple on a pond - barely walking pace - compared to a tsunami travelling at 200+ knots. The art of hull design is to make the distance between crests of bow and stern waves as long as possible; increasing LWL is only one of the ways of doing that.

Another way of removing or reducing the hull speed limit is to increase the length:beam ratio. There is a widely accepted ratio of 8:1 above which hull speed no longer applies which is why most multihulls continue to go faster the more power is applied. Here is an extreme example - a long narrow boat travelling at around 12 knots. Not a lot of bow/stern wave!

If I understand you correctly, then a long thin boat e.g. 45ft LWL: 2ft beam would go faster than a 40ft LWL: 6ft beam?
So, with a boat like mine with significant tumblehome, which increases the LWL and beam when heeling, the respective dimensions are increased disproportionately i.e LWL increases by perhaps 2ft whereas beam only increases by say 6 inches.
If my boat had straight sides, the beam would not increase but the LWL would?
Or am I still whoofing up the wrong oak tree?

 

[Aja]

There is also the concept of metracentricity. Robert Clark design most of his boats where the heeled hull shape was similar in curvature and displacement no matter the angle of heel. He drew some very pretty (and fast) boats. I'm no expert on this but a bit of googling will find more about it.

My parents owned a Robert a lark for over 40 years. One of the other benefits was a boat that was as light as a feather going up wind. One that you could really leave the helm and go for a wander round the deck and when you came back to the helm she was still in the groove. A lot to be said for that these days with modern fast hull shapes,

Donald

 

[Tranona]

There is also the concept of metracentricity. Robert Clark design most of his boats where the heeled hull shape was similar in curvature and displacement no matter the angle of heel. He drew some very pretty (and fast) boats. I'm no expert on this but a bit of googling will find more about it.

My parents owned a Robert a lark for over 40 years. One of the other benefits was a boat that was as light as a feather going up wind. One that you could really leave the helm and go for a wander round the deck and when you came back to the helm she was still in the groove. A lot to be said for that these days with modern fast hull shapes,

Donald

If you are interested in that theory it is worth reading Harrison Butler's book on yacht design. The metacentric shelf theory comes from a 19 century Admiral Turner. HB was the first person to use it extensively for small yachts with a view to balancing the fore and aft waterlines such that they remained constant as the boat heeled. As you described the desired outcome was neutral balance leading to light consistent helm. Remember this was in the days when even small boats often had to resort to tiller lines to cope with weather helm.

You can see in many modern boats that this property has been lost with fine bow sections and fat rear ends. However with modern keels and rudders which are far better foils than the long shallow keels of the past it is quite possible to achieve similar outcomes - at least as far as balance as the boat heels. Some twin rudder boats for example are particularly good at this.

 

[snowleopard]

If I understand you correctly, then a long thin boat e.g. 45ft LWL: 2ft beam would go faster than a 40ft LWL: 6ft beam?
So, with a boat like mine with significant tumblehome, which increases the LWL and beam when heeling, the respective dimensions are increased disproportionately i.e LWL increases by perhaps 2ft whereas beam only increases by say 6 inches.
If my boat had straight sides, the beam would not increase but the LWL would?
Or am I still whoofing up the wrong oak tree?

It all depends on hull shape. Some relatively narrow hulls kick up enough bow wave to create a hull speed effect, for example the Catalac. A fine-hulled mono could also have effects from the keel when heeled.

 

[Robert Wilson]

It all depends on hull shape. Some relatively narrow hulls kick up enough bow wave to create a hull speed effect, for example the Catalac. A fine-hulled mono could also have effects from the keel when heeled.

A helpful effect, or a hindering effect?

I don't know if my Javelin30's hull is fine or not, but it was her shape and lines (on the hard) which attracted me to her when I bought her. I instantly fell for her, and chose her over various other yachts' lines.:encouragement:

 

[doug748]

"...... However with modern keels and rudders which are far better foils than the long shallow keels of the past it is quite possible to achieve similar outcomes - at least as far as balance as the boat heels. Some twin rudder boats for example are particularly good at this. "


Or to put it another way, some hulls are so cranky when pressed, you need two rudders to keep them pointed in the desired direction.