# Hull speed

Discussion in 'Boat Design' started by Mike D, Jan 7, 2003.

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### Mike DSenior Member

Hull speed

Notes on hull speed and the gross misconceptions surrounding it. These notes concern displacement craft.

I did a fast search in Google for boat “hull speed” max and got 528 hits. I did not open them all because I was laughing too much but here is a gem

Although this one is merely repetition of some family legend there are some sites that give the impression of reputability but still put forward the same nonsense even though they may cloak it in more pseudo scientific bafflegab.

Reference is often made to Froude’s Law and he must be turning in his grave. Froude was a scientist who worked in the second half of the 19th Century doing much research work for the British Admiralty. The work was for warships so any references to sailing and Froude are probably distortions even though he did like yachting.

He did his basic research on models of 3 ft, 6 ft and 12 ft for two different hull forms. He observed that when models were run at speeds in proportion to the square of their length they created similar wave patterns. In 1876 he gave his famous Law of Comparison which states that the resistances of similar ships are in the ratio of the cubes of their linear dimensions when their speeds are in the ratio of the square roots of those dimensions. This is equivalent to saying that the resistances vary as the cube of the scale when the speeds vary as the square root of the scale (Note; this is for the wavemaking resistance not the frictional.)y

Nowhere did Froude make reference to a maximum speed or an unattainable speed based on the waterline length.

When a vessel proceeds through the water it creates a wave train at the bow and another at the stern depending on the speed and the length on the waterline. If there is an interaction the resistance is higher than the smooth line ignoring all the interferences. If there is no interaction the resistance is less than the smooth “average” line so there is a series of humps and hollows. Although the LWL is the usual length used in resistance calculations the length actually depends on the pressure variation at the ends and it varies so that LWL is a kind of average used to simplify the problems.

The shape of the wave is assumed to be a trochoid which gives a good relationship between calculations and observations. Some years ago the children’s toy Spirograph allowed the construction of beautiful wave patterns among them the true trochoid. Imagine a straightedge, a large coin, a sheet of paper and a pencil.

Put the straightedge on the paper lengthways and the coin on the paper near one end resting against it. Make a mark on the coin where it touches the straightedge and then roll the coin along one complete revolution. This represents the length of the wave and the line the point makes would be the wave form where the wave height is the coin diameter. This would be a huge wave and real waves are much lower.

Now imagine a spoke in the coin from the point on the edge to the coin centre. As the coin rolls a point on the spoke also traces a curve in the form of a trochoid. Near the coin edge it would be a big wave and near the coin centre it would be a small wave.

There are mathematical expressions giving the results of energy transformations of collapsing waves and the result is that all waves travel at a speed determined by the wave length independent of wave height. It is given by the expression v^2=L*g/(2*Pi) where v is the speed in feet per second, L is the length in feet, g is the acceleration due to gravity in feet/second/second and Pi is the circumference of a circle divided by the diameter.

When the expression was developed, a U.K. nautical mile was 6080 feet so the speed in knots was multiplied by 6080/3600 to give feet/second. The term g is approx 32.2 feet/sec/sec and Pi is 355/113 approximately. Using a speed V knots then the formula becomes V^2 = L*g/(2*Pi)/(6080/3600)^2 and V = (L*g/(2*Pi))^0.5/(6080/3600) which simplifies to V = 1.340 x L^0.5, using the modern knot of 1852 metres/hr gives a coefficient of 1.341

Because Froude’s Law used his number or V/L^0.5, model testing results were initially plotted on such comparative speeds because the calculations were easier to perform, manipulate and compare. The final full size vessel speed used knots but comparisons with other vessels also used V/L^0.5

The early experimenters pointed out that the resistance was exponential and it was increasingly difficult to achieve higher speeds (so what else is new!). What we all tend to forget is that they were thinking of coal fired boilers and steam engines. The very earliest steam plants weighed in at around one ton per shp, by around 1900 this fell to about 400 pounds per shp then dropped again when steam turbines appeared. Today with gas-turbines and fast, high bmep diesels the weight has tumbled. The last US battleship with reciprocating steam engines, USS Texas, had 28,000 shp, the machinery and boilers weighed 2,350 tons. A large ferry my yard built a few years ago also had 28,000 shp. Four diesel engines each 40 tons, two gearboxes about 15 tons each, two shafts and propellers just under 200 tons and say add 30% for miscellaneous auxiliaries etc giving a grand total of about 500 tons. The same happened on small ships and boats and now an outboard hanging over the stern replaces the old huge engine and boiler as well as coal or wood bunkers.

The only limit to a boat’s speed is power and does the system fit, it is physically impossible to install sufficient hp to drive it at any imaginable speed. A practical limit is reached when the boat speed is high enough to travel fast enough to get there yet is slow enough so it is not too thirsty. It is a judgement call not a mathematical law. The so-called hull speed is a reasonable compromise and is often exceeded especially by small boats as the power needed is still relatively low and fuel is relatively cheap. It is rarely exceeded by ships except mainly by fast warships that top 1.5 or more at flank speed or Government large patrol boats around 200 feet that often exceed 20 knots.

This is not a law on the maximum attainable speed but only the formula giving the hull speed at which the created wave length equals the hull length on the waterline. If it is a sailing vessel then the boat speed is quite obvious but if the boat is powered then a propeller travels through the water at the speed of advance. The speed of advance is the hull speed times (1 – Taylor’s wake) so it is nearly always less than the hull speed. Naval architects and designers of motor vessels take care to differentiate between the hull speed and the speed of advance when calculating propellers and making power calculations. I am not aware of any other meaning of the term hull speed used by professional naval architects.

In the quote at the beginning of these notes is the notion that a boat can climb up and over its bow wave. Agreed that a planing boat may rise and may travel very fast but the wave is still there at the position where the point of contact is. On a displacement boat the idea of climbing up and over is foolish to put it kindly. It’s like asking somebody to run instead of walk so the chin can pass the nose.

The hull speed is only a guide to a speed that should not be exceeded in the interest of fuel economy but then it might as well be 1.3 or maybe 1.4 or 1.2 perhaps. But what is just as important is the power setting of the engine and sufficient power in reserve to overcome bad weather. A gas engine has the characteristic of efficient operation at almost full power whereas a diesel should not run at more than about 70% output. It is unfortunate but it means a gas engine is inefficient at lower, cruising speeds whereas a diesel is more suited.

The first two charts below show the case of a 32 foot LWL trawler type, displacement 26,000 lb with a fuel tank of 100 US gallons of diesel fuel. The power has an allowance for small waves and a slight wind. What is rather noticeable is that at top speed the range reduces by 190 n.miles per knot whereas at about half speed it changes by about 760 n.m./knot. At the S/L ratio of 1.35 the boat speed is 7.64 knots.

There should be enough power installed to overcome a high wind and yet maintain a reasonable speed ensuring you reach your destination. It is risky to simply double the power or triple it because very small boats need a higher proportion add-on than larger boats.

A quick, simple way to get a handle on the effect of wind is to use a formula based on a combination of Adm. D.W. Taylor’s experimental version and the results of the Lucy Ashton. The worst effect is at about 30 degrees off the bow depending on the boat speed and the true wind speed and angle. Instead of trying to calculate the effect just increase the effect somewhat when the wind is ahead and use the formula hp = A*V^3/50,000 where A is the projected area in square feet and V the combined boat and wind speed in knots. Strictly speaking, the power should be reduced by the effect of the boat moving at its own speed without any wind but this will be very small in proportion and can be ignored unless the boat speed is high compared to the wind.

In the latter case reduce the added power by (boat speed/combined speed)^3. If the boat made 7 knots against a wind of 20 knots then (7/27)^3 means that a reduction of 1.74% could be made, if the boat speed equalled the wind speed a reduction of 12.5% could be made.

A quick example; the transverse projected area of the example boat is about 100 square feet. That is, the average hull width above the LWL times the freeboard amidships plus the house width times the height. The chart shows the power needed to overcome a headwind with the boat travelling at various speeds.

Suppose a boat speed of 7.5 knots is chosen and the wind is neglected then 40 hp is needed. Against a wind of 20 knots the boat would make about 6.5 knots – slide left along the 40 hp line until you hit the 20 knots wind speed then read down to the boat speed. Suppose you included the effect of 20 knots wind speed then you would need about 65 hp and you would do only 6.5 knots against a 30 knot wind.

It seems a helluva waste of money to include power that may not be used so a great deal depends on the where you are sailing and the general, prevalent weather conditions. If there is always a strong wind you must make allowance but if this occurs only a few hours a week then it would be costly to allow for it. Like I mentioned earlier it is a judgement call.

If you make long trips in inclement weather it is also advisable to derate the engine generally so that it cannot operate at more than say 90% output, ie a maximum continuous rating (MCR) of 90%. In the example above 65 MCR = 65/0.9 installed ie 72.2 say 75 hp. Because of the wide range in power the propeller selection is critical and it explains the increasing interest in controllable pitch and, to some degree, electric propulsion motors. Ah well, he who calls the Piper and all that!

Michael

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### PolaritySenior Member

Michael

Excellent post, really informative with just the right number of equations to get my head around - thanks!

Paul

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### Mike DSenior Member

Paul

Thanks Paul. Only problem is that my head is now three sizes larger than before I read your posting

Michael

PS Sorry the image is so wide making the message awkward to read. I tried to delete the posting intending to reduce the image size and re-post but I kept getting a message to the effect that I wasn't logged in or that it wasn't my posting.

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Hi .
Lots of tecko info ..
but i have been in a displacement hull doing 33Kts..
all be it 300' long and with approx 50,000 HP!!!!!!!!
bow wave and stern wave awsome!!!!!!!!
don

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### JeffModerator

I really enjoy your posts too Michael.

I can't thank you enough for being a part of our forums.

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### JeffModerator

That's strange - sorry about that. Once someone else posts, only the admin can delete the first post of the thread (which deletes the thread as well). The only other reason I can think of would be if under your user cp -> edit options, "browse board with cookies" was set to no - it should be left 'yes' (default) in order for the forum software to properly remember you, but I don't think it is this in your case.

I took the liberty of resizing your image down to 550 and inserted a link to the original. If you ever encounter any problems with the forum software and want me to look into them, just let me know.

Thanks again for so many excellent posts,

Jeff.

--now I promise I'll get back on topic

7. ### GuestGuest

Thanks for the excellent explanation Mike.

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### fishboatJunior Member

Mike,

Great reading and very helpful. You covered a similar speed/power topic for planing boats in another recent post. Above you've given a great discussion of displacement boats/hulls. I'm sure you see it coming...how about semi-displacement hulls?

At the risk of imposing on your good nature here, could you post similar thoughts as above( or just the plots would be plenty... power requirements vs fuel usage vs wind) on a 30 foot/11000 pound & 35 foot/16000 pound Cape Island or lobsterboat?

Thanks,
kevin

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### Mike DSenior Member

Kevin

It had to happen I suppose but how can I refuse such a request?

There is very little difference, if any at all, in the hydrodynamics of displacement hulls compared to semi-displacement hulls. The basic rules are just the same and the only difference is that s-d hulls operate at higher S/L ratios (speed in knots divided by the square root of the LWL) causing form changes.

Generally this means that faster hulls tend to be longer and narrower which reduces the wave-making resistance and the total resistance. At high S/L ratios wave-making resistance is much greater than frictional resistance whereas at low S/L ratios the opposite is true. Once again this raises the long-standing issue of the operational speed compared to the flat-out maximum and a suitable hull form.

Warships are a good example, particularly fast destroyers. Destroyers were originally quite small and were termed Torpedo Boat Destroyers with the purpose only of destroying fast torpedo boats in the late 19th Century. These TBDs had a displacement of only around two to three hundred tons on a length of around 200 feet and a speed of 27 or 28 knots, an S/L ratio almost 2. They were extraordinarily long and narrow and designed for high speed. The Whitehead torpedo was recent and could sink a battleship, so the tiny Torpedo Boat suddenly turned naval tactics on its head with this new-fangled weapon.

The TBD then got bigger, guns were added and voila – the Destroyer. The typical modern destroyer is around 400 feet long with a top speed of about 34 or 35 knots. Probably the propulsion system is CODOG meaning Combined Diesel Or Gas Turbine.

This system gives the best of both worlds; a pair of high power gas turbines for very high speed operation and a medium speed diesel of around 15,000 hp for cruising up to about 17 knots or so. One turbine is used at intermediate speeds. This is the extreme case solution as it gives economical diesel ops up to cruising speed, so-so economy in the mid range but high speed when it is called for in emergency situations. The use of CP propellers also helps as do contra-rotating props etc.

Other small ships may have a system with the same principles. Possibly the most common is the Father-Son arrangement on deep sea fishing trawlers. This is a large engine and a small one into one gearbox with one shaft/propeller drive. High speed is required from the port to the fishing grounds to save time and both engines are in operation. On the grounds the boat will slowly search for fish using the small engine and will switch to the bigger engine when trawling.

These two ship types also illustrate another consideration in design – how do you take best advantage of the internal space? As ships get smaller they also tend to become proportionately wider for two main reasons. More beam is necessary as a 10 foot wave could be a killer to a narrow, small ship. Long, narrow spaces in the hull are not economical use of space and the ship cost rises with length anyway.

The net result is that small, single-hull boats, whatever their type, all tend to break the fast but long ship notion. The old TBDs had an L/B ratio of about 12, Destroyers are usually around 10, deep sea trawlers about 4 but modern small trawlers are often around 3 or even less.

Although it would take less power if the small trawler was a bit longer it may not necessarily be more economical overall. Keeping the displacement constant and increasing the length will increase the hull surface area and the deck area. This will add cost and as there will be some kind of insulation on the skin or thickness of framing then the internal area and volume will shrink. This will be improved by making the boat a bit bigger and so will add more cost.

Because boats are rather small anyway an unacceptable power increase on a large ship is normal on a boat. But the basic question still remains – how fast is it and what operating conditions are the norm.

As vessels get shorter it becomes relatively more important to evaluate the speed as the S/L ratio increases dramatically. From 20 knots to 15 knots on a ship about 750 feet long is only S/L 0.75 to 0.55 approximately whereas on a 30 foot boat it is 3.65 to 2.74 or from a planing boat to a semi-displacement hull.

The planing speed depends on the form and weight and occurs usually at an S/L of about 2.75 or 3. Because of the potential reduction in power it can be economical to opt for a planing boat rather than a semi-displacent PROVIDED you repeatedly operate at such high speeds. The only way to find out is to conduct a series of cost benefit studies making use of an operational profile which is a table of duration at various speeds. If you run at planing speeds 99% of the time the decision is obvious but what if you run at that for only 60% or even only 40% then what? Somewhere along the line a compromise will be necessary.

Any compromise will result in a distinct change in the hull form to suit both the speed and function of the boat. It will also be tailored to where the boat will operate as ocean goers are heavier than river goers and require more stability as well as more power for the worse weather.

In a nutshell it all reduces to a general consensus that displacement hulls should not operate over an S/L of 1.34 and semi-displacement hulls are up to about 2.75. As I said at the beginning the hydrodynamics are the same, only the form changes to suit.

I modified the spreadsheet I posted for planing boats to make it for displacement hulls and semis.
• The image appended to this posting shows the output.
I hope it answers your questions, Kevin. At least you can doodle yourself and let me off the hook

Michael

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### Mike DSenior Member

Here are the notes

Michael

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### Mike DSenior Member

Michael

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### fishboatJunior Member

hooray!

Michael,

THANK YOU! You are a fountain of terrific information. The base case in the spreadsheet are the numbers on a boat I'm considering up your way. Your spreadsheet results look better than my not-quite-so-elegant estimates on economy & needed power. I think you've mentioned previously that your experience is primarily with large ships....I must say that your thoughts & tools geared to the smaller types is extremely helpful.

thanks again,
Kevin

13. ### GuestGuest

Years ago the AYRS came up with a simple method of figuring "hull" speed for a variety of boats.

The old formula was created by looking at fat boats of the time , and doesn't work well for skinny fast boats.

S = L/3b X SQRT (L)

When run for some theoretical hulls it may be a bit fast , but seems to work.

I have found that boats are priced more by the pound than the overall leignth..

A 35 ft 3 story "wedding cake" will cost more to build than a 65 X 10 single deck fast boat .

With a D/L of about 50 to 100 she should be able co cruise at 12 K on 2 gal an hour or 14K on 3. Top speed of about 18 would get the usual 1 mpg tho.

FAST FRED

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### Mike DSenior Member

Hi FRED

I wish I could answer your question but unfortunately, I don’t know the definition of hull speed used by AYRS to come up with their formula.

Since my first posting, I have now skimmed through over 800 sites or forum threads that use the term “hull speed.” Only one site used it correctly and it was a US Coast Guard paper on yacht safety where it was discussing the speed of a yacht compared to the water without any reference to LWL.

One other site came close by stating
referring to the S/L ratio but then blew it by adding
There are always practical limits to the speed but the limits are only a case of power and the means of application. Maybe someone will develop an ultra-lightweight engine of incredible power but how could you use it in a small boat? Even if the propulsion system problem were to be solved, where do you put the fuel?

As far as displacement hulls and semi-displacement hulls are concerned using a factor of 1.34 is merely coincidental to the boat length equally wave length. It most certainly is not a limit and if it were then there would be no such things as planing boats.

The attached image below is taken from Basic Naval Architecture by Barnaby and it was used to demonstrate how resistance increases disproportionately with speed and the number of waves in the vessel length.

The numbers in the top left of the chart are the number of waves occurring in the vessel length, which is invariably taken as the length of the waterline with the vessel static in still water. The plotted curves are the Residual Resistance (upper pair) and the Frictional Resistance (lower pair) on the base of the S/L coefficient.

At low speeds the Frictional Resistance dominates but above S/L = 1 (will vary with hull form) Residuary Resistance quickly takes over and round about 1.2 it begins to rise very quickly. This S/L ratio is about where economy begins to drop off rapidly and is about the upper limit for any reasonable operator. It is easy to see that there is nothing special about 1.34 except that it is about half way up the steepest stretch of the curve.

In the formula you quote
S = L/3b X SQRT (L)
I assume that b is the breadth on the waterline so it would give a coefficient of 1.34 when the beam is about L/4. For sure when applied to modern trawlers and passagemakers where the width is often L/3 it gives a coefficient of 1 that is much more economical in fuel but gives rather slow speeds of operation.

Similarly, it gives a very high coefficient for a fast, slender hull so that in both cases it points in the right direction for speed but is not an absolute canon.

Agreed, provided the quality and source is similar. However, the boat weight will increase if the design uses a long length but displacement is constant. It is very rare to see a designer quote the wetted surface area for his designs but SNAME’s Principles of Naval Architecture has many references to boats of all types. The researchers all seem to use a small variation to Taylor’s formula and WSA = 2.75*(Vol of displacement*LWL) – note that 2.75 is an overall average and it varies from around 2.5 to 2.9 depending on the form.

So as you see the WSA varies with the square root of the length, it is easy to verify that the total area will increase and so the weight increases and you’ll pay more. Naturally, if you add icing you’ll pay more again but a long icing boat will cost more than a short one for the reasons cited above.

The D/L values you mention seem low for displacement or semi-displacement hulls.

Michael

In the image below, Residuary Resistance means Total Resistance less Frictional Resistance.

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### aquafiend65Junior Member

huh?,
i hope that wasn't laymans terms! how would all that pertain to a 45' outrigger canoe?
-gary

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