baffling question

[Gunfleet]

My son has posed me a baffling question. We all know that boats with a longer waterline go faster. Why? I can't answer. A pub full of East Coasters couldn't answer, though like us they know it is true. So why?

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[westhinder]

It has something to do with the wavelength of the bow wave, I seem to remember. The boat accelerates until the bow wave equals the waterline length. To accelerate beyond that, the boat has to ride up its own bow wave, to start planing. Hence, the greater the LWL, the higher the potential speed before planing is required.
Someone else will certainly be able to provide the scientific explanation. Looking forward to it.



<hr width=100% size=1>Johan

 

[jeanne]

I hope this is both simple enough, and right! When a boat moves through the water, it makes a bow wave, which gets longer [crest to crest] the faster the boat goes. When the bow wave reaches the transom, and the boat is sitting in the trough, the boat is effectively trying to go up hill, to climb the bow wave. Without a great deal of power, it can go no faster. The usual rule of thumb to find this speed is this:the square root of the waterline length in feet x 1.3 [ a Fudge factor that changes slightly with hull form]= speed in knots. E.g., a 25 ft waterline boat will have trouble exceeding 6.5 knots. 5 [root 25]x1.3. At this speed a longer boat will not be trying to go uphill, so it can go faster. This rule does not apply to planing hulls, multihulls, or harbour pilots [ or so they seem to believe].

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[Sybarite]

Hi John

I saw a nice explanation on the site of an Atlantique 50 motor yacht. I think the following explanation comes from the architects, Sparkman & Stephens :

<< The Atlantique 50’ is in a displacement hull design due to our aim to achieve a sea kindly hull, long range, durability and low operating costs. Displacement boats are limited to hull speeds but this trades off against countless advantages, some of which we will demonstrate below.
The hull speed is primarily a function of the water line length; beam, weight and power, with the ultimate factor the hull shape. If these factors are not transgressed a round bilge hull design such as used in the Atlantique 50 will provide a natural flow of the bow and stern waves which offer the least resistance. Exceeding these parameters would leave the stern wave farther aft and the resulting gap will be filled with stalling turbulences. Increased power would also become necessary to climb above the bow wave, and the load factor, insignificant until now, will become effective to the necessary lift. As a result the gain for every knot over the hull speed will have an exponential cost in engine investment and lightweight construction. A 50 foot displacement boat will reach hull speed with just 60 hp; a semi displacement hull will need 900 hp to reach 18 knots and a planning hull 1500 hp to reach 25 knots. Beside tremendous consumption differences, the displacement hull will offer ranges at least 5 times bigger. Plus, a semi displacement or planning hull will not have an appropriate shape to be used efficiently at hull speed. Their chines and flat surfaces combined with propellers and struts and hanging rudders, offer too much resistance or drag. The Atlantique 50’ hull could be best described as being similar to a sail boat for being easily driven through the water, but with a wide beam to enhance stability.

To improve on hull speed we decided to include a bulbous bow version which although common nowadays to all freighters and tankers, remains the exception in yachting. Without a bulb, the speed/length ration of our hull should give an 8.84 knot hull speed when computed with the commonly agreed ration of 1.34. The addition of a bulb will move the bow wave further forward, and lead the water flow to think the boat is longer than it is. A ration of 1.6 is then achievable, which, combined with the engine size, will allow a speed of 10.56 knots.

Although calculations would show that 60 h.p. is enough to bring a 60,0000 pound 50 foot boat to hull speed, the Atlantique 50’ will be equipped with a 300 hp unit to provide plenty of safety margin >>

I am sending a copy of this to S & S with a commission request.

John

PS This would be on a Lottery win short-list provided there is a good sailing dinghy on the roof. It is really a lovely little ship.


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[franksingleton]

Take the question to the extreme. Consider a very narow boat, say as thick as a line and some arbritrary length, say 10 metres. Just think of how little resistance that will give. Will there be a bow wave? What is there to create resistance? Nothing apart from drag along the side which would be inifitesimal.

Now think of a vary broad boat, in the extreme, say a mile wide. and 10 m long. Think of how much resistance there would be to it moving at all.

In other words, it is not length, per se, it is length to beam ratio and shape that determines how fast a hull can go with a given driving force.

<hr width=100% size=1>Frank

 

[boatless]

Think of it this way. If you accept that the top speed of a displacement hull occurs when the second bow wave has travelled back to the stern. As has been said, the hull will now have to climb the bow wave. So, make the boat longer, and, importantly, give it more power, and it can go faster.

The reason that the relationship is connected to the square root of lwl in ft is actually quite simple. Given that both hulls will be lifting a similar sized pair of waves, the longer hull has more skin frction, and that's a problem that gets worse the bigger the boat. Wave drag + skin friction = total drag.

The next phase, from 2 x to 3 x the root of lwl is known as semi displacement, and this is what pilot boats and non-planing motor boats do. After 3 x you then get to planing, which is a whole 'nother ball game.

Not sure that Frank's thin boat would float

<hr width=100% size=1>my opinion is complete rubbish, probably.

 

[Twister_Ken]

Tugs forelock

Welcome Frank, honoured to be in your company.

<hr width=100% size=1><A target="_blank" HREF=http://www.writeforweb.com/twister1>Let's Twist Again</A>

 

[qsiv]

The reason the thin boat goes so much faster is more because it doesnt make a significant bow wave, and as such it doesnt have significant wave making resistance. The length/beam ratio at which wave making becomes significant is a function of the Froude number for the fluid you are operating in.

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[qsiv]

Total drag also needs to include appandage drag - which isnt just an extension of frictional resistance. It's a function of the hydrodynamic properties of all the appendages, and the angle of attack they are running at (Lift/drag ratios)

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[ParaHandy]

hmmm ... reasoned argument rarely works with offspring but could try this:
two swimmers, one long t'other short. the long one also has longer arms? so, each rotation of arm pulls him/her through water further ...


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[extravert]

Narrow hulls

Narrowness of the parts of the hulls that are in the water is the reason why performance multihulls are not limited to the the theoretical hull speed of equivalent length monohulls.

Monohulls in the size range we here sail generally have a LWL to BWL ratio of about 3:1. I have a LWL to BWL ratio of approximately 10:1, and make no noticeable bow waves.

<hr width=100% size=1>One day, I want to be a real sailor. In the mean time I'll just keep tri-ing.

 

[FullCircle]

We are all assuming an upwind performer like a Dragon or Squib being the thin line of Frank's theory, but downwind perf seems to require a greater beam aft, say like an SJ320 or similar sportsboat type.
Why is that?

<hr width=100% size=1>Second Chance - First Love. Still no wind instruments, c'mon peeps its for (my)charity

 

[Capt_Marlinspike]

Re: Narrow hulls

Is this right???
I thought that multihulls exceeded hull speed as they are not displacement hulls!

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[Chris_Robb]

The broad beam aft allows the yacht to plane - so it no longer conforms to the displacement boat rules.

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[Chris_Robb]

I have noticed on various boats I have sailed that the stern - or quarter wave seems to be the thing that seems to hold the boat back. I used to race an Oyster 41 - Steven Jones extreme IOR design - and this at about 7 -8 knots on a reach would built such a huge quarter wave it would not go any faster and became a pig to steer.

At the same time - a double decker (Victory 40) I had until recently seemed not to obey these laws and would run under spinnaker - at 10 knots (with 25 knots of wind). On looking astern I was always struck by the total absence of any quarter wave. By the way there is no way she would plane on flat water.

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[extravert]

Re: Narrow hulls

Multihulls have displacement hulls, long narrow ones, which have a U or V shaped cross section. They don't plane. Planing hulls need a flat bottom aft to sit on when on the plane.

Think of a rowing 8 hull (Oxford/Cambride boat race type). They take the LWL:BLW ratio to the extreme. They will never plane, and make barely a ripple as they pass through the water.

This is one of the hulls of the floats on my tri. The LWL:BWL ratio of the floats is 16:1.

<hr width=100% size=1>One day, I want to be a real sailor. In the mean time I'll just keep tri-ing.

 

[snowleopard]

at hull speed the boat sits in a trough between the bow wave and stern wave and doesn't have enough power to climb out of it, it can only follow at the wave's natural speed.

the speed a wave travels at is a function of the crest-to-crest length, the longer the wave the faster it goes, and the formula for that is 1.3 x sq root (wavelength in feet).

the finer the hull the smaller the waves it makes and beyond about 8:1 length:beam is too small to provide enough resistance to slow the boat.

i was amused to read in tracey edward's autobiography "all waves travel at 22 knots", you've only to toss a pebble in a pond to see how wrong that is.

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[Sybarite]

You see the same phenomenon in saloon car racing where two team members will actually touch nose to tail on the straight because the increased overall length facilates air penetration too.

John

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[cameronke]

Re: Narrow hulls; Wave piercing?

I have read with great interest the contributions regarding max speed for a displacement hull and feel I understand much better.

However I have spent some time contemplating how a wave piercing hull would work. If I am no longer trying to climb over my bow wave but rather just punch through it due to sufficient speed and insufficient local bouyancy am I in a new ball park?. Consider the work done in (say) a SWATH type hull (submerged wave piercing) All we are doing as we move through the water is parting it. OK then we have skin friction.

Am I ranting?

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[Aja]

Think example one would sink first. /forums/images/icons/smile.gif

Donald

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