Why Do Wet Dogs Shake Their Bodies?
― The Smaller the Animal, the Faster It Must Shake to Fling Water Off
A dog fresh from the bath shakes for just a few seconds and sends most of the water flying out of its fur. This is no whim. Shaking off water is far "cheaper" than letting it dry, and dogs are known to shake at just the right speed for their body size.
A dog has been caught in the rain on its walk. You wait at the front door with a towel. But before you can wipe it, the dog plants its feet and shakes its whole body. Water sprays all over the entrance.
Look closely and the shake has an order. First the head, then the shoulders, then the rump, as a wave travels toward the back. The skin swings loosely from side to side, moving even more than the body does.
Cats, mice and bears do the same thing. But how fast they shake differs completely from one animal to the next. A small mouse shakes so fast that the eye can't follow it.
There are just two reasons for the shake
When water evaporates, it carries away a lot of heat. If an animal dries the water in its fur with its own body heat, it can use up a good fraction of the energy it eats in a day. Shaking the water off avoids losing almost all of that heat.
Droplets stick to fur through surface tension. To pull them off, the animal must swing its body hard enough to make the outward force big enough. The smaller the body, the faster it must shake.
The first reason answers "why shake?" and the second answers "how fast?" Let's take them in turn.
Drying costs more than you'd think
When we get wet, we can wipe off with a towel. But a furry animal has no towel. Left alone, the water slowly evaporates using body heat.
Here is the catch. When water evaporates, it takes a large amount of heat from its surroundings. That is more than five times the heat needed to warm the same amount of water up to 100°C. An animal with wet fur has to pay this heat bill from its own body warmth.
According to research, when a dog of about 27 kilograms is soaked, about 0.5 litres of water collects in its fur. Drying all of that with body heat would take heat equal to about 20% of the energy the dog eats in a day (the calculation is in the fold-out at the end). On a cold day, the body could chill, which can even be life-threatening.
On the other hand, the energy used to shake for a few seconds is tiny. A dog is reported to fling off about 70% of the water in its fur in roughly 4 seconds. Shaking is cheaper than drying by a huge margin.
Why do smaller animals shake faster?
Water droplets cling to the fur through a force called surface tension. If the animal stays still, the droplets don't fall even though gravity pulls on them. To knock them off, the animal has to throw them outward with about ten times the force of gravity.
When the body twists and shakes, the tips of the fur sweep out arcs. The droplets then feel a force trying to fling them outward (centrifugal force). This force becomes four times as strong when the shaking speed doubles. It also gets stronger the larger the radius of the swing.
This is where body size matters. An animal with a thick trunk, like a bear, can sweep a big arc even when shaking slowly. A mouse has a slim trunk, so its arc is small. It can only make up the difference by shaking faster.
Look at Figure 1. It is a curve calculated for the number of shakes per second needed to fling water off, for each trunk radius. When the radius becomes one quarter, the needed number of shakes doubles. Move the slider to check different body sizes.
The calculation gives about 4 shakes per second for a medium-sized dog and about 14 for a mouse. Measurements agree well: dogs are reported to shake 4 to 5 times per second. Small animals like mice shake even faster, at more than 20 times per second.
Loose skin matters too. Even if the bones rotate only a little, the slack skin whips around like a lash. This adds radius and speed, and is thought to help fling the water off.
Human bodies have little hair, and water spreads in a thin film over the skin. It doesn't gather into droplets at the tips of hairs, so shaking rarely throws it off. We have a tool instead: the towel. A salad spinner (the basket you crank round) turns the same "spin it off" mechanism a dog uses into a tool.
Summary
Wet animals shake because drying water with body heat would drain a great deal of warmth. To fling the water off, the centrifugal force must be stronger than the grip of the droplets on the fur. Centrifugal force also grows with the radius of the swing, so small animals with slim bodies must shake faster. From mice to bears, each animal flings off its water within seconds at a speed that suits its own body.
The speed of the shake is set by body size.
A small body shakes fast to beat the water.
How dogs cool themselves is covered in "Why Do Dogs Stick Out Their Tongues and Pant?", and the curious relationship between small bodies and water droplets is covered in "Why Aren't Mosquitoes Hurt When a Raindrop Heavier Than Them Hits?".
- Wet a toothbrush with water and shake it in small movements using only your wrist. Check that little water flies off.
- Wet it again, and this time shake it with the same rhythm but swinging your whole arm widely (in a place with no people or objects around).
- Compare the amount of spray from the two tries. Even at the same rhythm, the larger radius should fling more water.
If you have a dog, try filming a wet dog shaking in slow motion on your smartphone. You can see the shake travel from head to tail and the skin swinging widely.
For those who want to know more ― terms, formulas and links to textbooksIt shows clearly what level each part is, from junior high science to university courses
- Junior highCovered in junior high school science
- High schoolCovered in high school "Basic Physics / Physics"
- High school+Advanced high school material, or a textbook sidebar
- UniversityUniversity specialist courses (fluid mechanics, biomechanics) not taught in high school
- ResearchNot yet taught as settled fact even at university; being studied by researchers now
Junior highTerms: this phenomenon has names
- Surface tension: the force by which water tries to make its surface as small as possible. It makes water droplets round and makes them cling to fur.
- Centrifugal force: the force that seems to push you outward when you ride on something that turns in a circle. It is proportional to the square of the turning speed and to the radius.
- Heat of vaporization (heat of evaporation): the heat a liquid takes from its surroundings when it turns into gas. For 1 kilogram of water it is given as about 2260 kilojoules.
Junior highHigh schoolChecking with formulas: how many times per second must a dog shake?
We find the acceleration needed to pull off a water droplet from the surface tension, then calculate from the trunk radius how many shakes per second produce it.
| In symbols | a ＝ (2πf)² × R Condition for coming off: a ≧ 3γ ÷ (2ρr²) |
| In words | Outward acceleration = (2π × shakes per second) squared × swing radius. When this exceeds the value set by "surface tension ÷ droplet weight", the droplet comes off |
| Where it comes from | The formula for centripetal acceleration in circular motion, and the balance between the surface tension force holding the droplet on the fur (length around the droplet × γ) and droplet mass × acceleration |
| a | Outward acceleration on the water droplet (unit: m/s²) |
| f | Shakes per second (unit: times/s) |
| R | Swing radius = trunk radius (unit: m) |
| γ | Surface tension of water (unit: N/m) |
| ρ | Density of water (unit: kg/m³) |
| r | Radius of the water droplet (unit: m) |
| Surface tension of water γ | about 0.072 N/m |
| Density of water ρ | 1000 kg/m³ |
| Radius r of a droplet on a hair tip | about 1 mm (0.001 m) |
| Trunk radius R of a medium-sized dog | about 0.15 m |
| Gravitational acceleration | 9.8 m/s² |
| Numerator: 3 × γ | 3 × 0.072 ＝ 0.216 |
| Droplet radius squared | 0.001 × 0.001 ＝ 0.000001 |
| Denominator: 2 × ρ | 2 × 1000 ＝ 2000 |
| Denominator: 2ρ × r² | 2000 × 0.000001 ＝ 0.002 |
| Required acceleration a | 0.216 ÷ 0.002 ＝ 108 m/s² |
| How many times gravity | 108 ÷ 9.8 ≒ 11 times |
| Dog: a ÷ R | 108 ÷ 0.15 ＝ 720 |
| Dog: its square root (＝2πf) | The square root of 720 is about 26.8 |
| Dog: shakes per second f | 26.8 ÷ 6.28 ≒ 4.3 times |
| Mouse (R＝0.015 m): a ÷ R | 108 ÷ 0.015 ＝ 7200 |
| Mouse: its square root | The square root of 7200 is about 84.9 |
| Mouse: shakes per second f | 84.9 ÷ 6.28 ≒ 13.5 times |
About 4 times for the dog, about 14 for the mouse. When the radius becomes one tenth, the needed number of shakes rises about 3.2 times (the square root of 10). This agrees well with the 4 to 5 measured for dogs.
| Water in the fur (27 kg dog) | about 0.5 kg |
| Heat needed to evaporate it | 0.5 × 2260 ＝ 1130 kilojoules |
| Converted to kilocalories | 1130 ÷ 4.18 ≒ 270 kilocalories |
| Energy needed per day (rough guide) | about 1300 kilocalories |
| Share of a day's energy | 270 ÷ 1300 ≒ 0.21 |
A single soaking costs about 20% of a day's energy. By this calculation, the dog would lose about one meal's worth of food just by drying off.
High schoolHigh school+Speed squared, and radius to the first power
High schoolThe centripetal acceleration in circular motion is a ＝ ω²R, where ω is the angular velocity. Angular velocity is 2π times the number of turns per second, so doubling the shakes per second makes the acceleration four times larger. If the needed acceleration is fixed, ω²R is constant, so ω is inversely proportional to the square root of the radius.
High school+In real animals, the loose skin is said to swing more than the twisting trunk does. The skin lags a little behind the trunk, so speed is added on top, as if pendulums were chained together. It is similar to how the tip of a whip moves faster than the hand.
UniversityScaling laws and the Bond number
The idea of expressing the relationship between body size and motion as a power of body mass is called a scaling law (allometry). Trunk radius is proportional to body mass to the power one third, so the formula above predicts that the number of shakes is proportional to body mass to about the power minus one sixth. In 2012 measurements by Dickerson and colleagues, across mammals of many sizes, the shaking frequency was reported to be proportional to body mass to about the power minus 0.22. The ratio of centrifugal force to surface tension can be expressed by a dimensionless quantity in fluid mechanics, a kind of Bond number.
📖 Derivations and further reading: Dickerson et al. (2012), the paper measuring how wet mammals shake ／ Wikipedia, "Centrifugal force" (Japanese)
ResearchWhat is still not well understood
- Why do measurements come out a little faster than the calculation? Smaller animals tend to shake faster than the simple formula predicts. Differences in how loose the skin is and how dense the fur is are thought to play a part, but the details are not known.
- What triggers the shake? A study in mice reported that touch nerves at the base of the hairs trigger this movement. Whether the same holds for other animals is a task for the future.
- Why don't they get dizzy from shaking so hard? The head should be swung with many times the force of gravity, but how the effect on the brain and eyes is kept in check has not been well studied.
In other words, this article too is "an explanation within what is known now." The broad trend that smaller animals shake faster has been confirmed by both measurement and calculation.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Junior high | Science Field 1: "Action of forces", "Changes of state" | Forces on a water droplet; heat taken away by evaporation |
| High school | Physics: "Circular motion"; Basic Physics: "Quantity of heat" | Centripetal acceleration a ＝ ω²R; heat of vaporization calculation |
| High school+ | Physics (advanced): "Surface tension" | The force holding a droplet to the fur, and the condition for it to come off |
| University | Fluid mechanics, biomechanics (scaling laws) | Bond number; power law in body mass |
| Research | Animal behaviour, neuroscience | The nerves that trigger shaking; the role of the skin |
| ― | Connection to daily life | Wipe a wet dog right away, or let it shake first and then wipe. Salad spinners |
- Dickerson, A. K., Mills, Z. G., Hu, D. L. (2012) Wet mammals shake at tuned frequencies to dry. Journal of the Royal Society Interface 9
- Wikipedia, "Centrifugal force" (Japanese edition, ウィキペディア「遠心力」)
- Wikipedia, "Surface tension" (Japanese edition, ウィキペディア「表面張力」)
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (理科年表, Chronological Scientific Tables), Maruzen Publishing (values for the surface tension and heat of evaporation of water)
※This article is a general-audience science explainer. The numbers given are rough guides to help you understand the mechanism. Values vary greatly with an animal's build and the state of its coat. On cold days, please wipe a wet animal promptly so it does not get chilled.