What if your legs were as long as a giraffe’s?

Stand on one leg and let the other one swing. Back and forth, back and forth!

A giraffe's legs are very long. What if your legs were that long?

Stand on one leg, hold onto something, and let your other leg hang loose. Give it a small push and it swings back and forth, like a swing in the park. When you walk, each leg does something similar: it swings forward from your hip, then plants on the ground.

A giraffe's legs are about 6 feet (1.8 meters) long, roughly twice the length of the model leg in this lab. So what if your legs were as long as a giraffe's? Would they swing faster or slower? Would you walk faster? Let's test it with a pendulum model.

During walking, each leg alternates between stance, supporting the body, and swing, moving forward beneath the hip. Biomechanics courses model the swinging leg as a pendulum pivoted at the hip, because gravity alone can carry it forward with little muscular effort.

This lab asks what happens to that swing if the leg is twice as long: from the lab's 0.9-meter model leg to 1.8 meters, the leg length the San Diego Zoo gives for a giraffe. The pendulum model gives the period; Rod Lakes's University of Wisconsin notes connect period and leg length to walking speed.

A pendulum is a weight that swings back and forth.

A long one swings slowly. A short one swings quickly. Your leg is like a pendulum!

A pendulum is a weight hanging from a pivot that swings back and forth. Gravity always pulls it back toward the bottom, so it keeps swinging. For small swings, how long one swing takes depends on just two things: the pendulum's length and the strength of gravity.

In Olly's model, a 0.9-meter pendulum stands in for a leg. Pulled back 20 degrees and let go, it swings over and back in about 1.918 seconds, about 31.3 swings a minute. Rod Lakes, an engineering professor, uses this kind of pendulum to estimate how fast people walk.

For small amplitudes a simple pendulum's period is T = 2π√(L/g), independent of mass and nearly independent of amplitude (OpenStax). The model integrates the full equation, so a 0.9 m pendulum released at 20° has T = 1.918 s (the small-angle formula gives 1.903 s), or 31.3 swings per minute.

Rod Lakes's University of Wisconsin biomechanics notes model the leg swinging under gravity with the muscles adding minimal effort. Treating a 1 m leg as a simple pendulum gives a stepping frequency of 0.5 Hz; as a uniform rod, 0.61 Hz. With two paces of 1.14 m per cycle, he estimates about 1.4 m/s, a comfortable adult walking speed.

Now Olly makes the model leg twice as long, like a giraffe's leg.

It swings more slowly! But not twice as slowly.

Now double the model leg to 1.8 meters, the length of a giraffe's leg. The swing slows down: over and back now takes about 2.712 seconds, about 22.1 swings a minute.

But look closely. The leg is twice as long, yet each swing takes only about 1.4 times as long, not twice as long. That's because a pendulum's swing time depends on the square root of its length. To make a swing take twice as long, you'd need a leg four times as long: 3.6 meters takes about 3.835 seconds.

Doubling L from 0.9 m to 1.8 m raises the model period from 1.918 s to 2.712 s and lowers the rate from 31.3 to 22.1 swings per minute: a factor of 1.414, which is √2. Since T ∝ √L, quadrupling the length to 3.6 m doubles the period (3.835 s).

The bottom speed also rises, from 1.03 to 1.46 m/s, because v = √(2gL(1 − cos θ₀)) also scales as √L. A longer leg swings more slowly in time, but its foot travels a longer arc faster. Mass does not appear: changing the bob's mass leaves the period unchanged.

Long legs swing slowly. But each step is much bigger!

So long legs can still cover lots of ground.

A longer leg swings more slowly, so you'd take fewer steps each minute. But each step would be much longer. Which wins?

Rod Lakes works it out: if an animal's shape stays the same as it gets bigger, its walking speed grows with the square root of its size. By that reasoning, if your whole body were scaled up so your legs were twice as long, your steps would be twice as long but only about 1.4 times as slow, so you might walk about 1.4 times as fast. That's an idea from a simple model, not a measurement.

Lakes's scaling argument: stepping frequency scales as L^(−1/2), while stride length scales as L if body shape is preserved, so walking speed v = (stride) × (frequency) scales as L^(1/2). Doubling leg length would then multiply comfortable walking speed by √2, about 1.41.

This is a geometric-similarity argument and carries assumptions: the whole body scales together, the swing is driven by gravity with minimal muscle effort, and the same walking style is used. A human with only longer legs is not geometrically similar, so the 1.41 factor is an idea about tendency, not a prediction.

Giraffes are the tallest land animals. Their legs are about 6 feet long!

When a giraffe walks, both legs on one side move together.

The San Diego Zoo says giraffes are the tallest land animals, and their legs alone are about 6 feet (1.8 meters) long. A giraffe calf is already about 6 feet tall when it's born!

Giraffes also walk in an unusual way called pacing: both legs on one side of the body move forward together, then both legs on the other side. Our model is much simpler. It treats a leg as a single weight on a light rod. Real legs have their weight spread along them, and muscles can speed a leg up or slow it down, so real swings differ from the model's.

The San Diego Zoo Wildlife Alliance gives giraffe legs as about 6 feet (1.8 m), with back legs about the same length as front legs, and describes their pacing gait, in which both legs on one side move together; giraffes can run about 35 mph (56 km/h) over short distances.

Model limits: the pendulum model is a point mass on a weightless rod, while a leg is a physical pendulum with distributed mass; Lakes shows a uniform rod swings faster than a simple pendulum of the same length (0.61 versus 0.5 Hz for 1 m). Real walking uses muscles to drive and brake the swing, and stance mechanics differ by gait. The model isolates one idea: longer pendulums swing more slowly, as √L.