Rereading the OP I think limiting this to standing jumps is too restrictive. My feeling is that the limitations must be muscle power alone (no springs or powered armor!) and you’ve got to land on the same level as you take off - jumping off high buildings dosen’t count.
If a long jumper, basketball player, or ballet dancer can stay in the air for more than a second after a running jump I would say the original premise “that a human cannot jump up and stay in the air as long as a second” has been proved false.
Amusingly, under levdrakon’s idea, there is no such thing as natural flight. All flying creatures essentially jump and glide. Airplanes, of course, don’t exactly do that, but they do absically strap a rocket on their tail and push.
It is irrelevant whether the jump is standing going straight up and down, standing going forward, or running going forward. The physics dictates that time spent in the air will be the same, regardless (with the sole exception being whether or not you can achieve a higher altitude from a running start as opposed to a standing start). The point being that, in projectile motion, horizontal flight is irrelevant in determining the time it takes to get from altitude 0 back to altitude 0.
The measurement that the OP is dealing with would be feet leaving the floor, legs stretched out, toes tippy, to the return of the toes to the floor. Since no one ever jumps that way, it’s a very difficult thing to measure. Often, we bend the legs before recontacting the floor, increasing the time in the air. Thus, the long jump, for example, is not a good measure because you get all crouched down to land, meaning you are actually falling further than you rose.
This web site discusses vertical jump and hang time. It asserts that Michael Jordan’s hang time is .98 seconds, but that he has the ability to increase that through swinging his arms up with the ball, and through bending his legs upon return to earth.
Ignoring the curvature of the Earth, you’re right.
But the extra energy available by taking a running start does look like it might be what makes the critical difference between aloft times of less and more than one second here.
It did not look slowed down to me, but I could be wrong.
So how about long jumps?
On this video starting at 48 seconds there a shot of a long jumper taken from the end of the pit. Her approach, take off and landing are all clearly shown. Her flight time seems to exceed 1 second both by time stamp on the video (:52-:54) and my playing the video with a stopwatch in hand.
This seems to satisfy all the criteria set forth so far. Flat ground, landing on feet, does not appear to be trick camera work.
This is manifestly untrue. While many birds do use a gliding flight regime in much of their locomotion–particularly larger species of birds for which sustained hovering or lift from flapping alone is insufficient to sustain lift–all flighted birds, as well as flighted bats and most flighted insects gain at least some or most of their lift from direct lift due to articulation of the wings. In birds, only the hummingbirds as a class fly exclusively by direct lift, but this is common in insects. Most birds, bats, and many insects also use induced lift from thermal currents, wind, or other external forces, but this shouldn’t be construed as being equivilent to a “jump and glide” motion like that of flying squirrels or hang gliders.
And strictly speaking, an aircraft jet engine is not considered a rocket; rather, a rocket is a special subclass of jet. In the narrow technical sense, i.e. that described in the Tsiolkovsky rocket equation a rocket is a self-contained, closed chamber in which the propellant is part of the mass of the rocket itself. One can readily see this by comparing the specific impulse and specific energy of a typical turbojet engine compared to a large rocket engine; the difference is around an order of magnitude in favor of the jet, owing to the fact that it gets the bulk of its reaction mass from the surrounding medium.
Despite levdrakon’s pedantry, flight is not narrowly defined as resulting just from aerodynamic lift; again, any propelled object can be considered in flight. A rocket will get motion primarily from reaction thrust, an aircraft from lift on its wing surfaces, and a cannonball on a purely ballistic path obtains its motion from the initial pressure of the confined powder charge, but all are in flight. Trying to narrowly define “flight” as resulting only from lift is not only pedantic; it’s wrong.
Is it possible to compare the two on any type of level playing field without using specific values, or somehow modifying them (i.e. incorporating the mass of the fuel and air combusted in a jet engine over the same amount of time a rocket of equal weight burns for).
What you are pushing on is irrelevant, in my eye. Gaseous bodies and liquid ones and solid earth are important relative to the weight/density, and “flight” characteristics of the creature. Thus, birds are jumping by flapping their wings - what are wings but funny-shaped arms or legs? Sure, the wings generate lift and only flap every few seconds, but the creature does have to flap to generate the lift. It’s jumping using an air scoop rather than a piston.
It was just pointing out that his definition was rather limited. Strictly speaking, it says that nothing flies or everything flies, unless he was differentiating air from any other medium, which some but not all of his posts did. In fact, one example of his used water.
For example:
To my knowledge, no creature actually does this over a time period all that longer than a second. Barring the larger birds using thermals, I understand that all birds must flap their wings and push off every 3-4 seconds or fall a bit. And they do fall, then climb slightly to get back, then glide a bit while falling, then
Up until 48 seconds or so, the footage looks like it’s normal, the segment from 48 to 55 seconds or so is very obviously slowed down. How can you not see this? Look at the guy behind her on the right - does he look like he’s moving normally?
Well, using specific values–that is, impulse or energy divided by reaction mass, so that your answers are per unit mass–is leveling the playing field, allowing you to compare engines of different of configuration or thrust in terms of a bulk or intensive quality. Turbojets are vastly more efficient than rockets specifically because they don’t have to carry all that propellant/oxydizer around with them, even though it is all spread out and uncompressed. If an aircraft did have to carry all of its working fluid it would turn into a terribly inefficient rocket engine compared to one using liquid or solid propellants.
Rockets are horribly inefficient engines for flight, but they also have the advantage of being (relatively) simple (at least in concept) and providing fairly consistant propulsion performance regardless of speed or ambient conditions. (This isn’t strictly true, as the ambient pressure does have a significant effect on nozzle efficiency, which is why nozzles need to be designed specifically for the range of altitudes they’re going to be flown at, but in this case “significant” means a few percent.) Air-breathing jet engines, on the other hand, have dramatically different performance depending on what speed they’re going, especially once you get to the transsonic range and above. It’s pretty easy to make a rocket that can go Mach 3+, but making an aicraft engine function at the same range is an elusive goal only obtained intermittently by the most extreme designs and with great compromise in efficiency and function at lower speeds.
And of course, if you want to actually put something in space, or even above 80k feet of altitude, your air-breathing engine isn’t going to have any air to breath; rockets become a necessity at that point, regardless of their relative inefficiency relative to an air-breathing jet engine.
To be fair, a golf ball does have a significant amount of aerodynamic lift.
Back to humans jumping, I highly doubt that the record will come from a long jump. While the hang time depends only on the vertical motion, and not at all on the horizontal (assuming no lift), the long jump still costs you, in that you have to put some of your motion into the horizontal in the first place. If we assume that there’s some maximum initial speed which can be generated by a human, we’re better served to put all of that initial speed vertical.
This guy (John Wendling) is pretty close. I counted 26-27 frames of airtime in the full-speed segment (29.97fps, I think), and if he crouched on landing he could get a couple more. Rick’s long-jumpers all appear to have about 24 frames of airtime.
How about a ramp that let you transfer some of your horizontal momentum into vertical momentum? I’d bet that if it hasn’t been done already, and we created a platform like this:
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(except of course with a lot less of an angle,) that you could have the longest hang time record over a level course. In fact, I wonder if you could have a graduating ramp that lets you increase your angle of attack gradually while keeping your same absolute momentum.
I would tend to agree if we were talking about the standing long jump, but I believe when doing the **running ** long jump, all of the forward momentum comes from the run, and the jump is strictly up. It’s possible there is even some advantage to running to add a bit of ‘spring’ effect. If you were to ask me to try to touch a basketball rim, for example, my natural instinct would not be to stand directly under it and jump, but to back up and take a little run at it.
Edit: as I think about it though, I would guess there is some disadvantage to jumping with one leg rather than two.
OK, so I was thinking about how one never really hovers at the top of a jump, because of the parabola curve of increasingly slower deceleration until a reversal into acceleration punctuated by an infinitely small point in time at the top. But, there is there ever a moment where there is a hover, or is more like a mathematical concept? Could one apply Zeno’s Paradox to this problem and make the claim that I can jump up without falling, because there will never be a moment when I make my way down. My head hurts.
It’s correct that the horizontal component doesn’t help the hang time, but what changes with a running start is the takeoff velocity, which is substantially faster with a running start, enabling a higher jump. That’s why high jumpers take a running start. To meet the criteria of the OP, wouldnt have to be a formal long jump; just not one with a standing start.
can stay in the air for more than a second after a running jump I would say the original premise “that a human cannot jump up and stay in the air as long as a second” has been proved false.