# Bow wave

Bow wave of a ship
Kelvin waves

The bow wave is the wave that a floating object moving in the water pushes in front of it. It is created by the displacement of water and moves at the speed of the object. In addition to the bow wave, circular waves form within the bow wedge and a stern wave forms in the wake .

In contrast to the Mach cone , bow and stern waves arise from the superposition of waves of different wavelength and speed. Half the opening angle is constant at low speeds and is

${\ displaystyle \ alpha = \ arctan (1 / {\ sqrt {8}}) ​​\ approx 19 {,} 47 ^ {\ circ}}$.

At higher speeds, i.e. H. from a Froude number of

${\ displaystyle {\ text {Fr}} = {\ frac {U} {\ sqrt {g \ cdot L}}} \ geq (\ approx) 0 {,} 49}$

With

• ${\ displaystyle U}$ the speed of the ship
• ${\ displaystyle g}$the acceleration of gravity
• ${\ displaystyle L}$ the length of the ship,

half the opening angle merges into that of a Mach cone

${\ displaystyle \ alpha = \ arctan \ left ({\ frac {\ sqrt {2 \ cdot \ pi \ cdot {\ text {Fr}} ^ {2} -1}} {4 \ cdot \ pi \ cdot {\ text {Fr}} ^ {2} -1}} \ right) \ approx {\ frac {1} {2 \ cdot {\ sqrt {2 \ cdot \ pi}} \ cdot {\ text {Fr}}}} }$

and thus decreases.

The sketch illustrates the structure of a bow wave system that a ship creates at A. The wave crests between A and B or A and D are only pronounced near the wedge lines. The arcs marked at C dominate the interior. The waves, the superposition of which leads to the V-shaped design of the wake, are called Kelvin waves .

The wave length of the bow wave increases with speed. It determines the hull speed of a ship.

The bow wave of large ships is a source of danger. If a small vehicle comes too close to a large ship, it can run off course or overturn due to its bow wave . Bow waves can also cause damage to natural or man-made bank reinforcements. This is why there are speed limits for shipping at hazardous locations .

A bulbous bow lifts the bow wave forward, which enables early breakage and thus reduced friction . The reduced drag has positive effects on driving behavior and fuel consumption .

## history

In the late 19th century, Charles Algernon Parsons investigated the flow resistance with experiments in a water channel and studied the effect of the bow and stern waves, which were higher than previously known in boats of this size due to their speed.

## Individual evidence

1. ^ Marc Rabaud, Frédéric Moisy: ShipWakes: Kelvin or Mach Angle? In: Physical Review Letters. No. 110, 2013, 214503, doi : 10.1103 / PhysRevLett.110.214503