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## Can a Mouse Survive a Fall From a High-Rise?

by | May 10, 2019

Can a mouse survive a fall from a high-rise?

Probably.

In a fantastic essay from 1928 the biologist J.B.S. Haldane famously explained:

You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes.

Why is that? The answer relates to the terminal velocity.

Gravity acts on all objects with equal force. In a vacuum both cannonballs and feathers fall at 32 feet per second squared. However, for objects falling through the atmosphere, there is a force opposing gravity: air resistance, also known as drag.

In air, drag increases with the square of speed, thus an object pretty quickly reaches the point where drag and weight are equal and acceleration stops. At that point where gravity and drag are equal the falling object has reached terminal velocity, meaning that it is falling at a constant speed. The primary factors affecting terminal velocity are an object’s weight and surface area.* If you stop and think, you can picture this in your head – the force of gravity is pulling the object towards the earth and a pillow of air is providing resistance as the object falls. The faster the object falls the bigger the pillow until equilibrium is reached.

Two objects with the same weight, but with different surface areas will have different terminal velocities. For example:

• Assume Object A is 100 pounds and has a surface area of 5 square feet and is dropped from an altitude of 1,000 feet. It’s terminal velocity is about 157 ft/sec.
• Object B, also 100 pounds has a surface area of 10 square feet. It’s terminal velocity from the same altitude is 111 ft/sec.*

Two objects with the same surface area, but with different weights will also have different terminal velocities. For example:

• Assume Object C has a surface area of 10 square feet, just like Object B, but at 150 pounds Object C weighs 50 pounds more than Object B.
• The terminal velocity of Object C if dropped from an altitude of 1,000 feet is 136 ft/sec or about 25 ft/sec more than Object B which is lighter.*

An average mouse weighs a mere 25 grams (0.05lbs) and has a surface area of 78 sq cm. That results in a mouse’s terminal velocity being about 25 ft/sec which is about the speed a skydiver falls with an open parachute. Compare that to a human skydiver whose terminal velocity is about 170 ft/sec prior to the parachute opening.

Like all objects, when comparing the falling speeds of animals, the weight and surface area of the animals primarily determine the terminal velocity.* But, there are scale effects. As an animal increases in size its volume (which is highly correlated with its weight) increases by a factor of three but its surface area only increases by a factor of two. Thus, a larger animal will have greater weight per surface area than a smaller one (assuming similar shapes/drag coefficients).

From Haldane’s essay: “Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.” This is why the terminal velocity of a mouse is so much less than that of a horse. Thus, the mouse likely survives a high fall and a horse splats. Similarly, insects can fall from great heights and not be injured at all.

How about cats? Interestingly, it is so common for cats to fall out of high-rise apartments that the phenomenon has its own name: High-Rise Syndrome. For cats, falls between 5 and 9 stories are the most deadly. Below five stories they don’t gain enough speed for the fall to be deadly. Between five and nine stories they are unable to react fast enough to slow themselves and thus have a higher terminal velocity. Above nine stories they are able to spread themselves into a posture to obtain the greatest surface area to achieve a slower terminal velocity and slow their fall. Cats “parachute” when falling. Shockingly, cats have a survival rate of about 90% from falls out of high-rise apartment buildings. Read more about high-rise syndrome here.

Related IFOD on the cat superpower of being able to flip around to paws down in mid-fall: Cat Righting Reflex

*Note that the drag coefficient of the object also affects its terminal velocity, which primarily depends on the shape of the object. In the examples of Objects A, B and C, a drag coefficient of 0.7 was used.

1. Yay a physics IFOD that kept my attention all the way through.

2. John I enjoy your ifods but I love the way your family trolls you even more. Best – Jack

3. Ben and Jerry seem more evenly matched than I thought

4. Guess dropping you on your head as a baby makes more sense now. Excuse me while I go figure out if you reached terminal velocity…..,
Mom

5. this is the most practical IFOD yet, especially for a Physics Friday. Why do I say that? Well, I often think about this when I prepare for a nap. My eyes close when I reach terminal velocity–it is so relaxing to be in this state. I often think about things like mice, cats and cows falling from high places as I go into a deep, refreshing mid day slumber. Luv2Nap

6. Great teaser. You had me until “Assume object A….”

1. half-girl, half-robot - […] From: https://www.theifod.com/can-a-mouse-survive-a-fall-from-a-high-rise/ […]

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