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 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. From a technical perspective, at hull speed the bow and stern waves interfere constructively, creating relatively large waves, and thus a relatively large value of wave drag. Ship drag for a displacement hull increases smoothly with speed as hull speed is approached and exceeded, often with no noticeable inflection at hull speed. The concept of hull speed is not used in modern naval architecture, where considerations of speed/length ratio or Froude number are considered more helpful. Background 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 (see below for definition) of slightly less than 1.20 knot·ft−½) because of the rapid increase of resistance from the transverse wave train. When the Froude number grows to ~0.40 (speed/length ratio ~1.35), the wave-making resistance increases further from the divergent wave train. This trend of increase in wave-making resistance continues up to a Froude number of ~0.45 (speed/length ratio ~1.50), and peaks at a Froude number of ~0.50 (speed/length ratio ~1.70). This very sharp rise in resistance at speed/length ratio around 1.3 to 1.5 probably seemed insurmountable in early sailing ships and so became an apparent barrier. This led to the concept of hull speed. Empirical calculation and speed/length ratio Hull speed can be calculated by the following formula: where is the length of the waterline in feet, and is the hull speed of the vessel in knots If the length of waterline is given in metres and desired hull speed in knots, the coefficient is 2.43 kn·m−½. The constant may be given as 1.34 to 1.51 knot·ft−½ in imperial units (depending on the source), or 4.50 to 5.07 km·h−1·m−½ in metric units, or 1.25 to 1.41 m·s−1·m−½ in SI units. The ratio of speed to is often called the "speed/length ratio", even though it is a ratio of speed to the square root of length. First principles