Location: AUSTRALIA I will try to give an intuitive answer so that I might stand to be corrected later.
Froude's Law also states that a displacement hulled boat will go no faster than the wave length created by the hull as it moves through the water. The prediction of hull speed before planing is most simply the square root of hull waterline length in feet x 1.34.
Remember the 20 footer needs to achieve about 3.5 times it's theoretical hull speed now to catch the planing 60 footer. Then instability issues become a major factor for the 20 footer trying to go at 3.5 times it's sub-planing hull speed. So all you have to do (in competition with every young and old designer in France) is to find a way of increasing the power (more sail, more righting moment, less weight) and reducing the drag (less WS, thinner foils, less displacement, etc) while staying within the class rules. Ironically, the optimum solution of these trade offs seems to come at differing size points, the windsurfer being a classic example. Once you break away from class rules, you are able to explore other solutions, and splitting the hull into two and dumping the lead ballast does great things for increasing your righting moment (sail carrying ability) and losing weight. I should have narrowed my question more concisely to planning ocean going mono hulls in planning mode. From what I have read there seems to be a point where even when planning there is a rapid(non linear?)increase in resistance; and I guess the bigger boat 'sees' the water as thinner than the littler one?
Note that all high performance dinghys capable of reaching sppeds equal to or higher than larger keelboats all use devices which either (or both) increase available righting moment (wings, trapezes etc) or reduce drag (foils, planing hulls).
Location: Scotland Does the width of the boat have any significance in its top speed before it needs to plane to reach a higher speed.
Is there any way of working out how much extra force is required to go from top hullspeed to planning. When a boat planes does its stern dip into the water creating a trough which increases the effective hull length which in turn increases max attainable speed.
Lots of questions need answering fast as we are making our hull as we speak for our school rc boat race. On a side line do flares at the bow of the boat help dissipate bow waves from swamping the deck as i had noticed on some of the v70s that they appear to have quite a large flare.
At the moment our hull design is very narrow as i thought that narrower would be faster i think off the top of my head that the ratio is about 5. Location: Australia At the weights and lengths I think you are talkling about the boat won't plane. Location: Scotland Why are the competition all building boats which are clinically obese. In RC boats where keel depth is unlimited or nearly so narrow has almost always been faster. When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. When I was a lad, I was taught that no boat could go faster than about 1.4 times the square root of its waterline length, in knots.
What stops a boat which is not 'planing' from going faster than its max hull speed, regardless of whether its motive power is wind or engine and regardless of 'horsepower', is the boat's inability to ride up and over its own bow wave. 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. 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. The shape of the wave is assumed to be a trochoid which gives a good relationship between calculations and observations. Put the straightedge on the paper lengthways and the coin on the paper near one end resting against it.
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. The early experimenters pointed out that the resistance was exponential and it was increasingly difficult to achieve higher speeds (so what else is new!).
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. 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. In the quote at the beginning of these notes is the notion that a boat can climb up and over its bow wave. 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. There should be enough power installed to overcome a high wind and yet maintain a reasonable speed ensuring you reach your destination.
A quick, simple way to get a handle on the effect of wind is to use a formula based on a combination of Adm.
A quick example; the transverse projected area of the example boat is about 100 square feet.
Suppose a boat speed of 7.5 knots is chosen and the wind is neglected then 40 hp is needed. 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 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%. Excellent post, really informative with just the right number of equations to get my head around - thanks!
There is very little difference, if any at all, in the hydrodynamics of displacement hulls compared to semi-displacement hulls.
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.
These two ship types also illustrate another consideration in design ? how do you take best advantage of the internal space? The net result is that small, single-hull boats, whatever their type, all tend to break the fast but long ship notion. Although it would take less power if the small trawler was a bit longer it may not necessarily be more economical overall.
Because boats are rather small anyway an unacceptable power increase on a large ship is normal on a boat. Any compromise will result in a distinct change in the hull form to suit both the speed and function of the boat. 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.
The old formula was created by looking at fat boats of the time , and doesn't work well for skinny fast boats. 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.
This ratio allows you to determine hydrodynamically similar speeds for yachts with different waterline lengths. There are always practical limits to the speed but the limits are only a case of power and the means of application. 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.
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.
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. 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. In the image below, Residuary Resistance means Total Resistance less Frictional Resistance.

She is a center console fishing boat that is 50 feet long and goes 60 MPH with twin engines. Most OPC classes use the water-skimming tunnel boat design, with an air space under the boat between the sponsons. Gaining popularity across the country, the Formula 150 class was originally developed to keep older equipment viable on the race course. Sport C is an entry-level tunnel boat class that is very popular on the West Coast and in the Midwest. SST 120s are one of the largest and most competitive powerboat racing classes internationally.
The SST 45 Class, sometimes known as Formula Lights,  is a highly competitive class for drivers of all varieties. This V bottom production boat class started out small in the Midwest and is now a National class.
Froude's Law indicates that at sub-planing speeds hull velocity is directly proportional to the square root of waterline length. Unfortunately I think their concept would prove even more uncomfortable than a mini for sailing the Atlantic. Have to brush up on relativity and similtude-an identical hull form doubled in size has 16 times more stability! THe little boat struggles in that when the wind is string enough to go really fast the waves are too big.
They are not designed for use in salt water!It is not intended for persons under 14 years of age, unless closely supervised by an adult. Froude was a scientist who worked in the second half of the 19th Century doing much research work for the British Admiralty.
He observed that when models were run at speeds in proportion to the square of their length they created similar wave patterns. If there is an interaction the resistance is higher than the smooth line ignoring all the interferences. Some years ago the children?s toy Spirograph allowed the construction of beautiful wave patterns among them the true trochoid. Make a mark on the coin where it touches the straightedge and then roll the coin along one complete revolution. What we all tend to forget is that they were thinking of coal fired boilers and steam engines.
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. 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.
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.
But what is just as important is the power setting of the engine and sufficient power in reserve to overcome bad weather.
It is risky to simply double the power or triple it because very small boats need a higher proportion add-on than larger boats.
That is, the average hull width above the LWL times the freeboard amidships plus the house width times the height. 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. 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.
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. 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. Once someone else posts, only the admin can delete the first post of the thread (which deletes the thread as well). 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.
The typical modern destroyer is around 400 feet long with a top speed of about 34 or 35 knots. Keeping the displacement constant and increasing the length will increase the hull surface area and the deck area.
But the basic question still remains ? how fast is it and what operating conditions are the norm. 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. 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. My next post will be notes about the spreadsheet Then the spreadsheet itself I hope it answers your questions, Kevin.
Maybe someone will develop an ultra-lightweight engine of incredible power but how could you use it in a small boat? It most certainly is not a limit and if it were then there would be no such things as planing boats. However, the boat weight will increase if the design uses a long length but displacement is constant. 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. A variety of engines can be raced in the Formula 150 class, ranging from 100 to 158 cubic inches .
The GT Pro class allows for V-bottom, Modified Vee or Tunnel Hull boats, built of any material. These affordable 12-foot boats average 50-55 MPH and are powered by 35 cubic inch engines mounted on true tunnel race hulls.
Spectacular when they take off from the dock together; amazing in the turns, and lightning-fast (80-100+ MPH) on the straightaway. The SST 200 (Super Sport Tunnel) outboard is the next generation of  Formula 2 powerboat racing.
Many drivers step up to OPC racing from the outboard kneeldown categories through the SST 45 Class. Super Sport uses off-the-shelf EPA compliant 150 production engines that can be purchased from any marine dealer across the country.
It is an excellent entry-level class for OPC and powerboat racing in general, with a little extra horsepower and great potential.
I find it helps if you sometimes imagine things at extremes: So strip the mast, keel, rigging and excess interior weight away and fit a jet engine to it.
The top speed of a 49er in faster is the water is smoother than if it is rougher for the same wind strength.
Do you reckon it would be even possible for a 2kg boat which has a waterline length of 70cm to even plane. In the IOM class(semi-development) where keel depth is restricted and ballast limited I believe a relatively wide boat did well for a while.
Any comments on this would be usefull we are also planning to add some flares to the front which we think will help it ride over the waves as that is often a major concern with rc models. A 45 footer with a 36 foot waterline length has a max hull speed of about 9 knots, which it cannot exceed unless it can 'plane', or is actually falling as noted below. The work was for warships so any references to sailing and Froude are probably distortions even though he did like yachting. 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.
If there is no interaction the resistance is less than the smooth ?average? line so there is a series of humps and hollows. 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. Near the coin edge it would be a big wave and near the coin centre it would be a small wave. 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.

The speed of advance is the hull speed times (1 ? Taylor?s wake) so it is nearly always less than the hull speed. 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. The chart shows the power needed to overcome a headwind with the boat travelling at various speeds. 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.
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.
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. 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. 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.
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.
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.
That kind of performance in a full fifty foot boat that weights in at seven and a half tons and in a fully found luxury boat is amazing! TechCapable of speeds over 140mph, the Outboard Performance Craft has come a long way since its beginnings as the “Outboard Pleasure Craft” class.
If you own an older Suzuki, Yamaha, OMC, or Mercury, this class may be able to get you out on the race course.
Powered by two-cylinder OMC motors with hydraulic trim and stainless steel propellers, GT Pro is for serious mini-boat racers, and is a natural progression from the Mini GT class.
A variety of legal hulls (vee, flatbottom, modified vee, or tunnel design), the boat must be at least 48.0 inches wide.
In fact, drivers can race identical equipment in both Stock Outboard's 45SS and OPC's SST 45. See picture below…When these small open-cockpit boats with their supersized engines speed into a turn, it's total chaos—and that's what the drivers and fans love about this exciting class. Since we're not talking about being stuck in a wave through- what say keeps a minitransat 6.5 proto from going as fast as a volvo70? Then to achieve double the theoretical hull speed in each case may entail a relatively small further increase in power, say 20% for arguments sake. 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 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. 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. It is unfortunate but it means a gas engine is inefficient at lower, cruising speeds whereas a diesel is more suited.
The worst effect is at about 30 degrees off the bow depending on the boat speed and the true wind speed and angle. High speed is required from the port to the fishing grounds to save time and both engines are in operation. Long, narrow spaces in the hull are not economical use of space and the ship cost rises with length anyway.
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? Yes, the beam is narrow (9’) for good offshore rough water performance at speed, but the speed numbers verses the size and weight numbers speak for themselves.
This category of racing features some of the biggest, most powerful outboard engines in Powerboat Racing.
You can start with a class that uses off-the-shelf production engines and pleasure boats and move up to highly modified racing engines and built-for-speed composite hulls. It uses a maintenance free "green" engine that does not require mixing gas and oil—truly the non-mechanic's friend.
The engine units used in these boats utilize the production full shift gear case with a nose cone. The last US battleship with reciprocating steam engines, USS Texas, had 28,000 shp, the machinery and boilers weighed 2,350 tons.
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. I am not aware of any other meaning of the term hull speed used by professional naval architects.
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. On the grounds the boat will slowly search for fish using the small engine and will switch to the bigger engine when trawling. The final component of this performance center console fish boat is the high tech hand laid fiberglass construction using tri directional and bi directional fiberglass materials. OPC engines can range from off-the-shelf production engines to heavily modified, high tech engines built for world record speed.
Whether Many racers move from Stock, Modified or PRO racing to the Sport C or SST 45 class. The OptiMax is one of only two engines that can be bought and raced as-is direct from the manufacturer.
Full fields of competitors challenge you to learn fast how to make the start and negotiate the turns at incredible speeds. If it's not rough when they start racing, don-t worry - it will be by the time they're done. For the 20 footer to catch up to the longer boat is going to require a very large increase in power as drag forces, particularly wavemaking turbulence of the hull and appendages, and drag forces produced by the rig then increase rapidly, and are difficult to overcome.
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. Today’s most high tech OPC race boats can start from a dead engine start, go 0 to 100mph in 6 seconds and turn 180 degrees with forces of up to 5 G’s. Boats must be original Tri-Hull design, with walk-through windshield and bow rider configuration.
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. Sportsman classes like Tri-Hulls (in the Texas-Louisiana area), Mini GT and GT Pro get the whole family out on the water, racing together.
The same sleek tunnel hull raced in SST 120 is matched with the OptiMax engine for a powerful racing package. Tri-Hulls are an APBA-approved Sportsman (Local) class and are very popular in Texas and Louisiana. 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.
Name it and they can do it, and will do it with a routine that will startle you on how easy it is during the boat build with them.
For planing hulls, friction is the predominant resistance factor, which scales proportional to the square of the waterline length. For similar boats, the available righting moment is proportional to the displacement, which scales according to the cube of the waterline length. The proper coring and reinforcement is an important part of the culture of their Hi-Performance boat building.

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