As I watched a muskrat swimming a bit offshore, I wished I had a better grasp of naval architecture (watercraft design) for it looked as if the muskrat were travelling at approximately its hull speed. Its concave body seemed to be draped between two wave crests of its own making.
An object (boat, muskrat) travelling across the surface of water creates a bow wave that necessarily travels at the same speed as the object. However, a bow wave is a wave so its subsequent troughs and crests will extend back alongside the hull. The wavelength depends on the wave speed and thus the boat speed. A slowly moving boat will produce a slowly moving, and thus a short wave. If the boat is long, this leads to many distinct waves along the hull. With greater and greater boat speed, and thus wave speed, there comes a time when the wavelength of the water wave has grown to equal the length of the hull. That speed is called the hull speed and the boat now sits neatly between the wave crests it created, just as did the muskrat I was watching.
For an animal moving across the surface, its hull speed may well constitute a practical speed limit. If it attempts to swim faster, the wavelength increases and the animal must now struggle to continuously travel uphill between the trough and crest of its own bow wave. In a boat, when sufficient power is applied, the bow will first tip up as that hill is climbed, but soon, with even more power, the boat is up and planing. About the only animals that seem to be (temporarily) capable of planing are birds landing on water. Apparently a muskrat swims at a speed just below its hull speed. (Fish, 1993). But what is that speed?
The relationship between wave speed and wavelength in a deep–water wave is,
c = √(g λ/2π), where c is wave velocity, λ is wavelength, and g is gravity.
If we put metric (MKS) numbers in this we get c = 1.25√λ and if λ = 0.3m, the average length, ℓ, of a muskrat body, we get a velocity of 0.7 m/s or about 2.5 kph.
Of course, estimating the actual speed of an object moving in the distance is difficult, so I will play a trick. Again set λ = ℓ, the muskrat’s body length, but now divide through by ℓ so the velocity, V, is expressed as the number of hull lengths travelled per second. We now get,
V = √(g/2πℓ).
Numerically, this is V = 1.25/√ℓ, and with ℓ = 0.3 m, we get that the muskrat travels at about two body lengths each second.
Indeed, that is what the muskrat appeared to be doing; travelling at its hull speed of about two body lengths per second. Incidentally, when travelling underwater, an animal will not encounter this problem with waves and so can travel faster than it can on the surface. Now, if only it didn’t have to return to the surface to breath, it could move really quickly.
The concave body of a muskrat is suspended between the crest of two waves of its own making as it travels at about its hull speed of two body lengths each second.
Representation afar 2
This is the second posting where I represent the delights of Kootenay Lake to folks attending a meeting some nine time zones away. The first discussed my situation and my photography, this one presents features of the lake itself.
When I explore Kootenay Lake, I do it with a camera. The resulting pictures enable me to study discoveries at my leisure, and then report on them on my blog.
The pictures I show here are only a peek into the delights of the region.
The interaction of the water and shoreline is endlessly fascinating to me. Here is the beautiful, but uncommon pattern known as beach cusps.
Equally ephemeral delights are the many wild orchids found around the shores. The Giant Helleborine is only found in Western North America.
Kootenay Lake plays host to two species of swan, one of which, the Trumpeter is the world’s largest waterbird. It has a wing span of over two metres.
We also have two species of bear. The grizzly is our counterpart of Europe’s brown bear,
and the Black Bear, which despite its name, comes in a striking array of colours. Here is a cinnamon version,
and a blue one.
Seven species of ungulates (hoofed animals) wander our mountains, two of which I show. Our mountain goat, which is distantly related to Europe’s chamois, spends its time on the protective narrow ledges of mountain cliffs.
The bighorn sheep is unique to the mountains of western North America. They are noted for the enthusiasm with which they fight for their mates.
I am fascinated by the interactions of various species. Sometimes this takes the form of mating, such as these copulating Spotted Sandpipers.
Sometimes the interest is the nurturing of offspring by a parent: This Tree Swallow is bringing food to its chicks.
Often it is food gathering, such as this White-tailed buck taking apples from a tree.
And a grizzly sow eating black hawthorn berries.
Here a River Otter is eating a fish it captured.
For a long time, I tried to get a shot of an osprey lifting a fish from the lake. This picture marked success.
Another delight was watching an eagle eating a large rainbow trout at the edge of the water.
In the end, my favourite shot is of a vole facing death in the bill of a heron. As the vole stares into the eyes of the heron, does it know that in less than a second it will vanish down that heron’s gullet?
My penultimate offering is a curiosity. In the mountain lakes of British Columbia, there are legends of a large serpentine lake monster. It is our counterpart to the Loch Ness Monster. Known as the Ogopogo, stories of it predate European settlement and it has continued to be spotted perhaps in every decade since. I have seen it swimming across the lake from my home on two occasions. On this occasion it caught and crushed a fish as it undulated up the lake.
When it spotted me watching from a distant dock, it headed straight at me with the loops of its snake-like body rising and falling in the water.
When it neared me, it turned out to be a family of River Otters.
It seems that our lake monster is just a distantly seen family of travelling otters, but observed by someone who just does not not understand otter behaviour. Here is the ogopogo when it is not coursing down the lake, but resting on an ice shelf — not all that scary.
I end with a picture I tried to get for decades — and when I managed it, it was taken in front of my home. It is a low-sun rainbow with the circle completed by its reflection in the calm waters of the lake.
