Think again. Yes, you can use any upward force to jump higher.
>> If you use too much helium, you just float, use too little and you you come right back down without much benefit. I guess you’d have to use an amount of helium that slightly exceeds the the minimum amount to cause weightlesness.
No, there are other factors involved, as you will see, but any upward force will help you jump higher. There is a range between “too much” and “too little”. That’s why we have math: to calculate and measure things.
>> I ask this on behalf of a friend (seriously) who wants to make a sturdy vest of some sort that would allow him to “jump 20 feet in the air”. Any figures on how many cc’s of helium required to lift a 175lb man?
A “vest” will not do. You need a “harness” similar to what rock climbers and parachutes have.
>> My thinking says that if you could defeat the slack in the line caused by leaping, and get 20 feet off the ground, you’d just keep floating. The BB gun method of releasing gas could work to a point, but then you’d have to tie a new balloon on each time you ascended right?
The only thing you got right, in spite of wjat others have said, is the “slack in the line” thing but that can be dealt with, as you will see.
>> Any feasability and logistics input would be appreciated.
Ok, tighten your belt and get ready:
The Earth pulss you down with a force of, say, 180 lbs. If you have a harness pulling you up with exactly the same force then you just hover in place without moving. This is what happens when you hang from a beam. But imagine a constant upward force that exactly cancelled your weight, like if you had a rocket. Then if you jumped up you would just keep going up except slowed dow by air friction. But, if we neglect to consider air friction, if the rocket makes your apparent weight 1/2 then you can jump twice as high, if it makes it 1/3 then you can jump 3 times as high, if it makes it 1/4 then you can jump 4 times as high, and so on.
So, if you can normally jump up 3’ and want to jump up 12’ then you need to reduce your weight by 3/4. In other words, if you weigh 180 lbs then you need a rocket pushing you up with a force of 125 lbs.
Now, a rocket is not practical or easy but we can find simpler ways of exerting a constant or quasi-constant upward force. Bungee cord of sufficient length is one way. We have said the range is 12’ so if the total length of the bungee is 250’ the difference in force is not going to be much. (I am using a factor of 20 but you could use much less and still get good results) So all you have to do is:
1- Build bungee cord which will stretch by 1/20th with a weight of 125 lbs.
2- Build helium balloons which have a bouyancy of 125 lbs plus the weight of the bungee cord.
3- Tether the balloons to your harness using the bungee cord
4- Enjoy the jumping until the wind or something else spoils the fun.
Now, think about it, the bungee cord does not need the balloons at all, all it needs is an upward force. The bungee cord is more important than the balloons. You could hook the cord to an overhead beam in a room 240’ high or hang it from a bridge that high or hang it between two buildings. it does not matter. Also, if you hang from a ceiling 240’ high you have a good range of horizontal movement. If you hang from a bridge you could make a really long leap across the river below.
Now, I realize not many homes these days have 240’ high ceilings. You can use a factor of 1/10 stretch and it would still work but 120’ is still a lot. If you are going to jump 12’ you need some overhead space. Let us assume your college gym has ceilings 30’ high and your teachers are willing to play along with the experiment in the interest of science. This is what you can do: You take up the cord to a block (pulley) hanging from the ceiling, then down to another on the floor (or a far away wall) and make the cord go around as many times as needed to take up whatever length you are using. You could also use a rope from your harness, up to a block in the ceiling and out some window where you could have the shock cord made fast to some distant object like a tree.
Then again, if I had 240’ of thick elastic cord I could think of better things to do with it like, say, launching goats a great distance.