DougC, if you jump slower, you won’t go as high. Even though that’ll leave less slack for the balloons to take up, it’ll also leave them less time to do it in, and because the balloons are accelerating, they’ll be able to take up less slack on a low jump.
Balloons will certainly give you a longer “hang time”, but unless the slack is taken up before you get to the peak of your jump, they won’t let you get any higher. If you can jump high enough, there will eventually come a point where the balloons will take up all the slack before what would be your unassisted peak. I haven’t yet done the calculations for how high your unassisted jump would have to be for this, but it very much seems like it would be outside the range of human possibility.
You are not even beginning to understand the question. That site has balloons with enough bouyancy to lift a person off the ground and it is in an enclosed dome so you don’t just float away all the way to Germany.
Chronos has the right idea. The upwards acceleration of a balloon is very small due to the inertia of the gas in the balloon and the air above it plus the friction. You can have a Zeppelin pulling up with a force of tons and yet when you let it completely loose it will go up relatively slowly. Now look at a human jump which accelerates up for a fraction of a second and achieves the hisghest point in another fraction. All the balloon will do is slow your descent but it will not help you on your way up.
You are ignoring empirical evidence from my cite that proves you wrong, just because it doesn’t fit what you think should happen. Watch the videos of people equipped with balloons, they clearly jump higher than they possible could without them. These balloons are not large enough to just carry you away without some vertical force from your legs, but they compensate for a large part of your weigh, allowing you to jump higher.
From the FAQ on the Parabounce site:
Watch the videos and read the FAQ; it’s really indisputible.
OK, since no one is doing it, I guess I’ll have to do it. Here are the figures for a simple jump using SI units: let us consider S=0 for the CG at rest. It is lowered 0.3 m to prepare for the jump. An upwards acceleration of 29.4 m/s2 during 0.142852 seconds provides an upward speed of 4.2 m/s at “takeoff” after traveling .3 m up. After takeoff we have a negative acceleration of 9.8 m/s2. The CG takes 0.4286 sec to travel upwards another 0.9 m and comes to a standstill. In summary, since the beginning of the jump the CG has taken 0.5714 sec to travel up a total of 1.2 m (4’).
Now, who is willing to do the calculations showing a balloon let go will travel upwards more than 1.2 m in the first .57 sec since it is let go?
Sailor…some of us have done this. Get a little kid and a big old Mickey Mouse balloon. He’ll go hopping along with great big ol’ “7 League Steps.”
You’re trying to shoehorn us into one physical model…
Here’s another example: take a long inclined plane, like a loading ramp, and (with your balloons) run swiftly up it, at such a speed that the balloon strings always remain taut. When you come to the end of the ramp, you will continue to rise because of the upward component of your velocity…and you will rise farther than you would if you did exactly the same thing without the balloons.
Again, don’t take our word for it: do the actual experiment yourself.
(Checking back: even if you were completely right…you’re still wrong! If you jump upward, and the balloon lifts, then, at some point along your ordinary trajectory – the path you would take sans balloon – the string will tauten, and you will receive an upward impetus, which will alter your trajectory.)
No I am not ignoring anything. Those balloons are not on a free string as we are discussing. Those balloons are on a harness rigidly fixed to your body and when you jump up you are also pushing the balloon up which you cannot do if you have the ballon at the end of a string as we are discussing here. Different scenario.
Now I have already provided data for a jump without help. Can you calculate the upward acceleration a balloon would need to be helpful in a jump? Can you then show a free balloon whould have that acceleration?
I am afraid Chronos is the only one here who can understand this but what the heck. So we have our standard jump
t V S a
0.0000 0.0 0.0 29.4
0.1429 4.2 0.3 -9.8
0.5714 0.0 1.2
where we have an upward acceleration a = 29.4 m between t=0 and t= 0.1429 at which time we have takeoff. Do I have to explain to anybody here why it is impossible for a balloon to accelerate upwards at that rate? Does anybody want to calculate at what rate a balloon will go up and when the string will be taut again?
I don’t believe the acceleration of a balloon will be as small as you think. If I weigh 70 kg, and you have a balloon that can just equal my weight, it will be exerting a force of 687 kg-m/s^2 on me. If that balloon and the air in it weigh 5 kg(I could figure out what it would need to weigh, but it can’t be that far off), it will accelerate (ignoring air resistance for the moment - which will be LOWEST in the beginning and increasing with speed) at (F=ma) 687=5*a, a = 137.4 m/s^2. Right? Now, if you can jump 1 meter by yourself, then with an acceleration of 16.4 m/s^2 it will take you .27s (trust me, I figured this all out…) to go from zero to the 4.4m/s velocity you need to reach 1 meter with your legs that can stretch from zero to .6 meters (again, trust me, or figure it out yourself, I’m not about to put it all in here). In that same .27s, the balloon should go from zero (v=vo + at) to v=137.4 x .27 = 37 m/s. Note that the balloon is accelerating faster than your jump = no slack (again, ignoring air resistance).
Now, it will probably take you awhile to figure out if I screwed up some logic there, but I don’t think I did. I can’t figure out the air resistance of a fictional balloon yet, but I’m working on it. A better solution would be to go to a party store, get a mylar balloon, an army man, a rock and a small see-saw and do a test…
But, I don’t think the air resistance is so great that it will slow that balloon down that quickly.
I’m still thinking about it, but it seems to me that the lower your jump (not higher, as Chronos said) the easier it will be for the balloon to keep up, because the faster the balloon goes, the less is its acceleration due to air resistance…
We are not restricted to balloons on a string but mangetout and Trinopus assert a balloon on a string will help and I am saying it will not and I am willing to prove it will not. I never said you cannot push up a balloon faster than it would go by itself.
Certainly. This is why your hang time will increase, as I mentioned. But for a human jumping straight up off the ground, the “taut time” will be after the peak of the jump, and you’re already on your way down again. You’ll be going down more slowly, but you won’t be going up.
And with a rigid frame, slack won’t be an issue, but since the OP did mention “slack in the lines”, we’ve been assuming that you’re attached by strings. If you make assumptions different than those implicit in the OP, you’ll get different answers.
Geez, I hadn’t looked at the intervening posts since I last posted, getting pretty hot in here fellas! By the way **sailor[B/], you’re wrong. :eek: Ha, ha, just trying to stoke the fire!
I have to commend you for at least trying to calculate something which is the way to go. But you are wrong, it did not take me a split second to realize your estimate for the acceleration of the balloon is way off and impossible for obvious reasons. Plus, just think of it: did you ever see a baloon shoot up into the sky at a rate 15 times faster than a rock would fall from the sky? I don’t think so. Hint: the upwards acceleration cause by bouyancy can only be a fraction of that caused by gravity. Think about it.
As I say, I commend you for taking up the math because I find it frustrating in threads like this that the minute we go into the math everybody disappears. Nobody seems to have any interest in doing any serious study of the problem.
Why can’t we just jump slowly as someone suggested earlier to keep the string tight?
If we start with enough balloons so that the force of the balloons equals our weight, then any force we add will cause our velocity to be upwards until some downward force is applied. There isn’t any new force added except air resistance, so I would guess we could go pretty high, even though the original force we add by jumping isn’t very much. If you ignore air resistence (and a few other real world concerns) we would go up forever at exactly the same rate as we started because of the conservation of energy.
I knew there was an easier way… Conservation of Momentum! Let’s say there IS slack in the line! Let’s say I weigh 70 kg, and the balloon weighs 5 kg. Let’s say by the time the slack is taken up that I am heading DOWN at 0.3 m/s. At the same time, suppose the air resistance has kept the balloon acceleration way down (from what I calculated above), and it is going UP at 5 m/s.
We have m1v1 + m2v2 = (m1 + m2)v3.
70 x -.3 + 5 x 5 = (70 + 5)v3
v3 = .05 m/s UP!!! It ain’t fast, but it’s UP. Now, there is a time when you’re momentum going down will cause the system to go down (and I was just about there), but it CAN be done.
I can’t believe we’re seriously discussing this. (I hope I am not being whooshed here but this is getting surreal) “jumping slowly” is not “jumping”, it’s “getting up from your chair” and does not get you airborn. Jumping implies “fast”, the faster you jump, the higher up you go. Try it yourself. Try jumping very slowly and let us know how far up you reach.
By the way, WHAT obvious reasons, besides what your mind is imagining happens?
This is PeeWee, checking out for the night, can’t wait to see what happens while I’m gone… :dubious:
Hint: I do not need a calculator to know your result of an upwards acceleration of a = 137.4 m/s^2 is dead wrong by a factor of more than 15. the reason I do not need a calculator is I have common sense which tells me the upwards acceleration of the balloon can only be a fraction of g. which happens to be in my town 9.8 m/s2. Is gravity especially strong where you happen to be?