• Wakewing physics mug, rotating view
  • Wakewing physics mug, close-up
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 1
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 3
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 4
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 5
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 6
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 7
  • Wakewing – Kelvin Wake pixel-art physics mug, black ceramic, view 8
1 9

WakewingKelvin WakeMug

Wakewing – Kelvin Wake Physics Mug

$21.99 USD
$21.99 USD
Sale Sold out
Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Size
11oz · 15oz
Made
To order · shipping times

Why do a duck and a ship leave the same V? Wakewing rides deep water. The dispersion of gravity waves fixes a Kelvin wake half-angle of arcsin(1/3), about 19.47°, independent of speed. Lord Kelvin derived it in 1887. Very fast hulls can show narrower apparent wakes. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Size

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Wakewing flies low over deep water, and the V behind her never changes.

A duck and a cargo ship leave the same wedge. In deep water the wake behind a small moving source has a half-angle of arcsin(1/3), about 19.47°, whatever its speed. Lord Kelvin derived it in 1887.

The reason is in the second line. For deep-water waves, wave energy travels at half the speed of the crests. Add up the waves a moving source keeps making, and that factor of one half confines them to a wedge of fixed angle.

ANY SPEED. SAME ANGLE. holds for Kelvin's case: deep water and a small, point-like source. Measurements published in 2013 by Marc Rabaud and Frédéric Moisy found that fast hulls, which are not points, show narrower wakes, and shallow water changes the angle too.

Wakewing keeps it simple: deep water, small source, 19.47° since 1887.

Equations

\[\sin\theta_K = \frac{1}{3}\]
\[\theta_K = \arcsin\frac{1}{3} \approx 19.47^\circ\]
\[\omega^{2} = g\,k\]
\[c_g = \frac{d\omega}{dk} = \frac{1}{2}\,c_p\]
SymbolMeaningUnit
\(\theta_K\) half-angle of the Kelvin wake (deep water) \(\mathrm{°}\)
\(\omega\) angular frequency of a surface wave \(\mathrm{rad/s}\)
\(g\) gravitational acceleration \(\mathrm{m/s^2}\)
\(k\) wavenumber \(\mathrm{rad/m}\)
\(c_g\) group velocity (speed of wave energy) \(\mathrm{m/s}\)
\(c_p\) phase velocity (speed of wave crests) \(\mathrm{m/s}\)

Sources

  1. Thomson (Lord Kelvin) (1887) On Ship Waves, Proc. Inst. Mech. Eng. 38, 409
  2. Rabaud & Moisy (2013) Ship Wakes: Kelvin or Mach Angle?, Phys. Rev. Lett. 110, 214503
View full details

Field notes

View all
1 3
View all