How much would a person weigh who would be unable to jump?

October 3, 2012 4:38 PM

How much would a human have to weigh to be unable to jump (lift both feet off the floor at once at least a couple of inches)?

Can folks with a better understanding of math and physics help me figure this out?

So I understand that volume and mass increase much faster than the dimensions of an animal as it grows larger and this leads to small animals being relatively stronger than larger ones (like how an ant can lift many times its body weight). That's the same thing as smaller animals surviving greater falls, right? And the same thing as them being able to jump proportinally higher?

I understand that jumping power also depends on body mechanics and that some individuals are much more athletically able than others, but I believe that really big animals can't jump at all. So roughly (allowing for varying strength) what is the point for a human where they would not be able to jump at all? Jump here is defined as propelling both feet off the ground together from standing.

(this has been bugging my wife and I for a while, scientific curiosity, no nefarious fatphobic purpose)

posted by crabintheocean to science & nature (12 answers total)

You don't need to jump in order to lift both of your feet. In as much as gravitational acceleration is a constant for all objects (less than a million tons), your size doesn't matter in that case. All that matters is how fast you can pull up your legs, and if you aren't paralyzed you'd be able to do that faster than you could start falling.
posted by Chocolate Pickle at 4:41 PM on October 3, 2012

Elephants, rhino and other large animals can jump just fine, as far as I know.

There are plenty of healthy, active people of Very Large Substance, and I think that the outliers who are bedridden and/or confined to wheelchairs may have disabilities that feed into their obesity and vice versa. People who are bedridden or confined to wheelchairs are often very large, but that's because of their confinement, not the other way around.
posted by jrochest at 4:44 PM on October 3, 2012

Do they have to survive the landing without harm? or merely make the leap?
posted by Jehan at 4:48 PM on October 3, 2012 [2 favorites]

I notice on the Wikipedia list of Olympic records in weightlifting that the current record in the +105kg (which I assume is the human's weight) is 263kg. I don't know how much upwards force that involves in the legs, but let's say that that person may be able to get a little loft north of 300kg total, maybe even 350kg, if some of that weight is in the arms.

I think, that as the other nitpickers are pointing out, there are too many variables and qualifications to give you a straight answer on this.
posted by straw at 4:53 PM on October 3, 2012

What you are describing is the square-cube law by the way, which determines why (in a simplistic way) an ant is built differently than an elephant.
posted by 2bucksplus at 4:54 PM on October 3, 2012 [1 favorite]

Elephants, rhino and other large animals can jump just fine, as far as I know.

It is generally accepted that an adult elephant cannot jump. It is similarly the case for rhinos, although they might have four feet off the ground for a moment when running.

Because of the square-cube law, the larger an animal is, the less ability it is going to have to jump (or move itself about in general). If an ant were to grow to the huge size in "Them!", it would not be able to lift many times its own weight. In fact, it would collapse under its own weight.
posted by Tanizaki at 4:56 PM on October 3, 2012 [1 favorite]

Actually, that link suggests that they can't jump a 6 foot trench -- that they can't jump like a horse -- not that they can't lift themselves a couple of inches off the ground.
posted by jrochest at 5:00 PM on October 3, 2012

That link isn't working for me, but both StraightDope and HowStuffWorks seem to say elephants really only lift one foot up at a time (they can do two but it's tough on them).
posted by crabintheocean at 5:05 PM on October 3, 2012

How much would a human have to weigh to be unable to jump (lift both feet off the floor at once at least a couple of inches)?

There's no one weight where you can draw a line. Shaquille O'Neal weighed around 325 pounds in his playing days; Andre the Giant was significantly heavier (though probably never his billed 525 pounds) but was surprisingly athletic in his younger days; Mark Henry (pro wrestler and powerlifter) weighs around 400 pounds and can dunk a basketball. Sumo wrestlers are often well over 500 pounds and capable of jumping, under your definition -- on the other hand, there are plenty of five-foot-tall people who weigh less than half that but couldn't get both feet off the ground.

I suspect no one over 650 pounds has ever been capable of jumping (the heaviest near-top-tier sumo wrestler was about 630), but I wouldn't say that's an upper limit, just because no one's ever really been in a position to get into the Guinness Book for World's Heaviest Jump.
posted by Etrigan at 5:57 PM on October 3, 2012

Maybe ask these guys - An optimal control model for maximum-height human jumping Journal of Biomechanics Vol.23(12) 1990, 1185–1198.

Sorry, paywalled article. Knowing grad students, if someone hasn't already written a calculator for this kind of thing, I'm sure it'd be trivial to do the experiments, if they haven't already been performed countless times, to write formulae that describes maximum leg press strength versus total mass. If you want to get fancy, you can even try to model the momentum and fluidity of the fat folds of which there will likely be (many?) different distribution patterns.
posted by porpoise at 8:01 PM on October 3, 2012

I diasgree with Tanizaki and 2bucksplus. Assuming that an organism is scaled isomorphically, the height it can jump is independent of its size. This is a very large assumption: in practice, things like the shape of the skeletal system change, which makes a difference.

The maximum force that a muscle can exert will be proportional to its cross sectional area (L^2). The distance by which it contracts will be proportional to its length (L). The kinetic energy produced will be their product, and hence proportional to the mass (L^3). At the highest point of the jump, kinetic energy will be zero as all of this energy will be converted into gravitational potential energy (G.P.E.=mgh). Hence the total size jumped is independent of size.
posted by James Scott-Brown at 4:02 AM on October 4, 2012 [1 favorite]

The ability to "survive falls" is different, and is a result of smaller animals having a lower terminal velocity. For sufficiently small animals, impacts at this terminal velocity are harmless, so they can survive a fall from an arbitrarily large height [however, they may be injured by very short falls, where they do not have time to orientate themselves before landing].

A falling object will continue to accelerate until it experiences a drag force equal to its weight. The drag force will be proportional to area (L^2) and dependent on velocity, whereas the weight is proportional to L^3. Hence larger objects will have a higher terminal velocity.

posted by James Scott-Brown at 4:12 AM on October 4, 2012 [1 favorite]