Hull speed is a hydrodynamic concept that deals with the complex physics of a vessel's interplay with the surrounding water. It is the speed at which the wavelength of a vessel's bow wave is equal to the waterline length of the vessel. As a boat's speed increases, the wavelength of the bow wave also increases, and usually, its crest-to-trough dimension (height) increases as well. When hull speed is exceeded, a vessel will appear to be climbing up its own bow wave, a process called planing, which wastes a lot of energy.

## What You'll Learn

**Hull speed is the speed at which a vessel's bow wave wavelength equals the waterline length**

The hull speed of a boat is the speed at which the wavelength of its bow wave is equal to the waterline length of the vessel. In other words, it is the speed at which the boat's waterline is equal to its bow wave's wavelength.

As a boat moves through the water, it creates waves that oppose its movement. The wavelength of these waves increases as the boat's speed increases. At hull speed, the boat's bow wave and stern wave are synchronized, and the boat moves very efficiently.

**The formula for calculating hull speed is:**

> V_hull = 1.34 * square root of L_waterline

Where V_hull is the hull speed in knots, and L_waterline is the length of the waterline in feet.

For example, a boat with a waterline length of 28 feet will have a hull speed of a little over 7 knots (1.34 x square root of 28 = 7.09).

It's important to note that hull speed is not a perfect concept and is dependent on the shape of the hull. Modern ship design considers speed-to-length ratios, such as the Froude number, rather than hull speed. Additionally, the effective waterline length of a boat can increase as it goes faster, affecting its speed potential.

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**The speed at which a boat sails uphill**

Hull speed is the velocity at which a boat's waterline length matches the wavelength of its bow wave. In simpler terms, it is the speed at which a boat starts to sail "uphill," requiring a significant increase in power to maintain forward momentum. This speed can be calculated using the formula:

> Hull speed (in knots) = 1.34 * square root of waterline length (in feet)

For example, a 28-foot boat with a waterline length of 28 feet has a hull speed of approximately 7 knots.

However, it's important to note that hull speed is not solely dependent on the boat's length. The shape of the hull, the vessel's displacement, and other design factors also play a role in determining its hull speed. For instance, long and thin hulls with piercing designs can surpass their hull speed without planing. Additionally, the load carried by the boat can influence its waterline length and, consequently, its hull speed.

The concept of hull speed is particularly relevant when discussing the performance of displacement hulls, which move through the water rather than on top of it. As a boat with a displacement hull sails faster, it creates larger bow waves. Eventually, the wavelength of these waves matches the length of the boat, and it becomes increasingly challenging to maintain speed without a significant increase in power.

While hull speed is an important consideration, it is not the only factor influencing a boat's maximum speed. Modern naval architecture considers speed/length ratio or the Froude number to be more useful metrics. These factors take into account the complex hydrodynamics and wave mechanics that come into play as a vessel moves through the water.

In summary, the speed at which a boat sails uphill, or its hull speed, is influenced by a combination of the vessel's design, the laws of physics, and the surrounding water conditions. While hull speed provides insight into a boat's performance, it does not define its absolute maximum speed, and modern design considerations have led to vessels that can exceed their hull speed.

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**Hull speed depends on the length of the boat and the hull shape**

Hull speed, or displacement speed, is the speed at which the wavelength of a vessel's bow wave is equal to the waterline length of the vessel. As a boat's speed increases, the wavelength of the bow wave increases, and so does its crest-to-trough dimension (height). When hull speed is exceeded, the vessel will appear to be climbing up the back of its bow wave. At hull speed, the bow and stern waves interfere constructively, creating relatively large waves and a large amount of wave drag.

The hull speed of a boat is dependent on the length of the boat and the shape of the hull. The load waterline length (LWL) is the most relevant measurement when evaluating a boat's performance potential. This refers to the horizontal length of a hull at the water's surface when the boat is carrying a normal load. The formula for calculating hull speed is:

> Hull speed in knots = 1.34 x square root of the waterline length in feet (HS = 1.34 x √LWL)

For example, a 35-foot boat with a waterline length of 28 feet will have a hull speed of around 7 knots (1.34 x √28 = 7.09). The multiplier of 1.34 comes from the law of natural physics, which states that the speed of a series of waves in knots is equal to 1.34 times the square root of their wavelength.

The shape of the hull also plays a significant role in hull speed. Long and thin hulls with piercing designs can easily exceed their hull speed without planing. Such hull designs are commonly found in canoes, competitive rowing boats, catamarans, and fast ferries. On the other hand, heavy boats with hulls designed for planing generally cannot exceed hull speed without planing.

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**The concept of hull speed is not used in modern naval architecture**

The concept of hull speed is an important one in marine engineering and naval architecture. Hull speed, or displacement speed, is the speed at which the wavelength of a vessel's bow wave is equal to the waterline length of the vessel. As a boat's speed increases, the wavelength of the bow wave also increases, and usually, its crest-to-trough dimension (height) increases as well. When hull speed is exceeded, a vessel will appear to be climbing up the back of its bow wave, a process known as planing, which wastes a lot of energy.

Despite its importance, the concept of hull speed is not used in modern naval architecture. Instead, naval institutions favour more modern measurements of speed-to-length ratio, such as the Froude number. This is because hull speed is heavily dependent on the hull's shape, and many boats can easily exceed their nominal hull speeds. For example, hulls with very fine ends, long hulls with relatively narrow beams, and wave-piercing designs can exceed hull speed without planing. These hull forms are commonly used by canoes, competitive rowing boats, catamarans, and fast ferries.

The Froude number, introduced by English engineer and naval architect William Froude, is a dimensionless ratio of speed and length. It is used to estimate resistance effects and hull-water interaction. As a ship moves in the water, it creates standing waves that oppose its movement. This effect increases dramatically in full-formed hulls at a Froude number of about 0.35, which corresponds to a speed/length ratio of slightly less than 1.20 knot·ft−½. As the Froude number increases, so does the wave-making resistance, which peaks at a Froude number of ~0.50 (speed/length ratio ~1.70).

In conclusion, while hull speed is a crucial concept in marine engineering, it is not used in modern naval architecture due to its limitations and the availability of more advanced measurements.

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**Hull speed is a hydrodynamic concept**

A moving vessel is inevitably associated with a system of wave patterns, specifically transverse and longitudinal waves. Transverse waves move in a direction perpendicular to the vessel's direction of motion, while longitudinal waves traverse from the bow to the stern or from front to back. These longitudinal wave systems are mostly triggered by the kinetic energy of the moving vessel and thus increase quadratically with the vessel's speed. As the vessel transfers its kinetic energy to the water, the vessel loses energy, and the waves gain energy, hindering the vessel's forward motion.

The speed at which the wavelength of a vessel's bow wave is equal to the waterline length of the vessel is known as hull speed or displacement speed. As boat speed increases from rest, the wavelength of the bow wave increases, and usually, its crest-to-trough dimension (height) increases as well. When hull speed is exceeded, a vessel in displacement mode will appear to be climbing up the back of its bow wave. At hull speed, the bow and stern waves interfere constructively, creating relatively large waves and, thus, a relatively large value of wave drag.

**Hull speed can be calculated using the formula:**

> {\displaystyle v_{hull}\approx 1.34\times {\sqrt {L_{WL}}}}

Where {\displaystyle L_{WL}} is the length of the waterline in feet, and {\displaystyle v_{hull}} is the hull speed of the vessel in knots.

It is important to note that hull speed is not used in modern naval architecture, where considerations of speed/length ratio or Froude number are considered more helpful. Additionally, hull speed is dependent on the hull's shape, and long and thin hulls with piercing designs can easily exceed their hull speed without planing.

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**Frequently asked questions**

Hull speed is the speed at which a vessel with a displacement hull must travel for its waterline to be equal to its bow wave's wavelength.

Hull speed can be calculated using the formula: Hull speed in knots = 1.34 x square root of the waterline length in feet.

The number 1.34 in the formula does not account for hull shape. A more accurate formula would include a coefficient ranging from 1.18 for barges to 1.5 for very sleek vessels.