Why can some animals jump much higher than us?

[chipotleaway]

Compared to humans, why can some animals jump many more times their size? I'm thinking of cats here which apparently can jump up to seven times their length.

From a physics standpoint, what would be an approximate answer to this, and how would determine it using scaling arguments?

 

[Andy Resnick]

Using simple dimensional reasoning, you will find that similarly constructed animals all jump to the *same* actual height. Similarly, one can show that if animals jump to heights proportional to their size, the crushing strains (the amount of strain that results in structural damage) scales as l^1.5, where l is the linear dimension of the animal. Thus the elephant is in more danger due to accidental falls than a mouse.

To get you started, realize the muscular power available for work is proportional to the mass of muscle, and the maximum force is proportional to the cross-sectional area of the muscle.

Similar scaling arguments can be used to show that small animals cannot live in cold climates.

 

[Danger]

The key here, as Andy mentioned, is "similarly constructed". Not all animals are created equal. A kangaroo and a black bear are not all that far apart as to size, but they have vastly different talents.
If you want to investigate the extremes of almost any ability, look at insects. A flea, for instance, pulls something like 120 g's when it jumps. That would kill a human.

 

[pumila]

Muscle gearing is an issue too. Humans for example have their leg muscles distributed along the greatest length of the leg; horses on the other hand have their musculature packed high on the leg structure. In the latter case the foot structure is extended to increase the packing, and horses run on their toes.

The power of the muscles is delivered to where it is needed by tendons. Having the muscles high on a horse lightens the weight of the leg and increases its speed and allows it to move back and forth faster for the same rates of contraction, allowing higher speeds.

 

[Danger]

Having the muscles high on a horse lightens the weight of the leg and increases its speed and allows it to move back and forth faster for the same rates of contraction, allowing higher speeds.

You have put me to shame. During four decades of messing about with artificial limbs for various projects, and even coming up with an idea or two for actual medical prostheses, that weight distribution issue never occurred to me. Thanks!

 

[chipotleaway]

Thanks everyone, some interesting points.

The key here, as Andy mentioned, is "similarly constructed". Not all animals are created equal. A kangaroo and a black bear are not all that far apart as to size, but they have vastly different talents.
If you want to investigate the extremes of almost any ability, look at insects. A flea, for instance, pulls something like 120 g's when it jumps. That would kill a human.

This might have more to do with biology but what is it about a flea that allows it to survive such a huge a acceleration?

 

[Danger]

This might have more to do with biology but what is it about a flea that allows it to survive such a huge a acceleration?

I'm not sure. There is a scaling factor at work (bugs don't react to gravity the same way as larger animals), but I suspect that in this case it's more just because of having a dense internal structure as well as the ubiquitous exoskeleton that all adult insects have. How they achieve that sort of launch is more specialized. They are essentially spring-loaded; they "wind up" their leg muscles over a short period of time, and then unleash them in an even shorter period. It's like loading and then firing a crossbow.
It might be worth your while to post this particular question in the Biology section, where someone more knowledgeable about anatomy can assist you. Physics definitely applies to how things work, but not to how they're organized.

 

[A.T.]

Aside from the scaling issue mentioned by Andy, there are also differences in muscle propeties between very similar animals, like humans and apes:

http://rspb.royalsocietypublishing.org/content/273/1598/2177.short

Vertical jumping performance of bonobo (Pan paniscus) suggests superior muscle properties

This was twice the output expected on the basis of muscle mass specific work and power in other jumping animals but seems physiologically possible. We suggest that the difference is due to a higher specific force (force per unit of cross-sectional area) in the bonobo.

 

[A.T.]

This might have more to do with biology but what is it about a flea that allows it to survive such a huge a acceleration?

If you put a human into a water tank, he will also survive huge accelerations of the tank. Insects are a like a tank with the organs floating inside.

 

[pumila]

Kangaroos have a specialised jump - the Achilles tendon is long and springy, essentially being a mechanical energy storage system that reduces the need for high muscle output for each jump. They store energy when landing and release it at takeoff. http://wiki.answers.com/Q/Why_do_kangaroos_have_large_strong_hind_legs