Elastic Energy and The Kangaroo

JP Cannistraro
May 11, 2017

Submitted as coursework for PH240, Stanford University, Fall 2016


Fig. 1: Eastern Grey Kangaroo hopping. (Source: Wikimedia Commons)

Kangaroos are well-known marsupials that are easily identified by their tendency to hop around on hind legs, as opposed to walking or running like most mammals. Fig. 1 displays a kangaroo jumping over a puddle. Their distinct movement pattern has led to serious curiosity and intrigue amongst different academic groups. While most people might associate any information about these animals with biology or zoology, we can learn a lot about the physics of energy through looking at how a kangaroo hops. Kangaroos utilize elastic energy every time they hop, allowing them to decrease demand on their muscles, and burn oxygen more efficiently than other mammals that are similarly sized. [1] A closer look at their biological mechanisms can help us understand how this is possible.

Elastic Energy

In physics, elastic energy refers to the energy released when a spring elongates. When a spring is compressed it stores energy that can be used later, at this point the spring contains elastic potential energy. [2] Releasing the spring, or elongating it, releases the elastic energy, allowing the spring to move. Releasing the spring does not require any work, as the elastic energy utilized is the same as the elastic potential energy that is stored when the spring is compressed. [2] In this example, the work done onto the spring happens when someone compresses it. Alternatively, if someone pulled apart a spring and held it, the spring would contain elastic energy until it was released. When releasing the spring, it snaps back together, utilizing the elastic energy that was stored previously. [2] Kangaroo's hind legs work like springs, compressing and elongating, storing and releasing elastic energy in the process. [1] In the kangaroo example, however, the kangaroo does not need to do work in order to elongate the springs that are their hind legs - gravity takes care of that.

Kangaroos have long hind legs that make them easy to spot in the wild. When taking a closer look at the muscular-skeletal make-up of these hind legs, one will notice unique characteristics of both the tendons and muscles. A kangaroo has extremely long tendons in its back legs that undergo drastic length changes when the kangaroo is hoping. Acting like springs, the tendons stretch under the weight of the kangaroo, and, while elongated, contain elastic energy. [1] The muscles in a kangaroo's legs are impressively strong and stiff, allowing them to handle the stretching of the tendons. One study conducted on the animals revealed that their tendons can store up to ten times as much energy as their muscles. [1] All of this stored energy is released when the kangaroo pushes up and the tendon contracts again. While the muscles in a kangaroos legs still work to help them hop, so much of the energy they use comes from the tendons. [1] Unlike muscles, tendons do not fatigue and they do not require oxygen to work.

Red Kangaroo Dogs
Average Weight 19.33 kg 22.60 kg
Maximum Measured Velocity 6.43 m/sec 1.56 m/sec
Maximum Oxygen Consumption Rate 3.00 mL kg-1 sec-1 3.05 mL kg-1 sec-1
Table 1: Comparing the Red Kangaroo with Dogs. [3,4]

A Comparison

Since kangaroos garner so much of their hopping energy from the tendons in their legs, they consume oxygen at a significantly slower rate than other mammals of similar size. [3] When studying the movement patterns of red kangaroos, one team of scientists determined that as the kangaroos increased speed over flat ground their rate of oxygen consumption stayed nearly constant. In fact, the maximum measured rate of oxygen consumption of 3.0 mL kg-1 s-1 tops all animals with exception of a few vertebrate species. [3] A study done by the University of Wisconsin - Madison looked at oxygen consumption rate in three dogs that were trained to run on the treadmill. [4] When looking at movement statics obtained from the two studies above, and comparing red kangaroos and dogs, it is clear kangaroos hold the advantage in efficiency statistics. Table 1 outlines the differences between the two mammals.

While the oxygen consumption rates of the two animals are similar, the Kangaroo is moving at over four times the pace of the dogs. Achieving the same oxygen consumption rate while moving at such a faster pace is truly an impressive feat for the kangaroo.


Kangaroos are impressive animals whose unique usage of elastic energy allows them to move at high speeds for long distances, and makes them models of efficiency in the animal kingdom.

© J. P. Cannistraro. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] D. L. Morgan, U. Proska, and D. Warren, "Measurements of Muscle Stiffness and the Mechanism of Elastic Storage of Energy in Hopping Kangaroos,", J. Physiol. 282, 253 (1978).

[2] R. D. Knight. Physics for Scientists and Engineers: A Strategic Approach (Pearson, 2012).

[3] R. Kram and T. J. Dawson, "Energetics and Biomechanics of Locomotion by Red Kangaroos", Comp. Biochem. Physiol. B 120, 41 (1998).

[4] K. Steudel, "The Work and Energetic Costs of Locomotion," J. Exp. Biol. 154, 273 (1999).