Hull speed

From Boat Design Wiki

The "hull speed" of a displacement boat is, approximately, the speed of a free surface wave whose wavelength is equal to the boat's waterline length. For a vessel to exceed this speed, it must go faster than its wake naturally wants to go; thus, a marked change in power requirements and/or running attitude occurs. "Hull speed" is not an absolute limit, and there are many misconceptions surrounding it. The concept is of limited practical use, apart from a general rule of thumb that a displacement boat will typically cruise at somewhere between 70 to 90 percent of hull speed.

Definition

Hull speed is frequently defined as:

Hull speed (knots) = 1.34 times the square root of the waterline length (in feet), or 2.43 times the square root of the waterline length (in metres)

This corresponds, roughly, to the speed of a (non-breaking) surface wave whose wavelength is equal to the boat's waterline, in infinitely deep water.

Interpretations

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

Quote: Maximum hull speed of any non-planing boat

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. This is consistent with JB's comment below. 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.

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.

Origin of the term "Hull Speed"

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 judgment 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 equaled 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 traveling 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 judgment 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!

--MikeD

Links

Hull Speed Forum Thread

Disp Semi-displ lboatpowercat Hull speed Excel Spreadsheet