One thing that fascinates me are tapered bands. I use to uses coil springs on the design of some of my machines so fairly familiar with them. So.... "logically", I can see why and how tapered spring's work, but so far, I found no confirmation.

In my mind, from what I know about springs, two things are happening.

1....the narrower part stretches more then the wider part so it stores an equal amount of energy. In other words, if we hung a given weight (or pull), the band will have to stretch more where the band is narrower.

This would be easily proven by marking out the band in equal segments at rest and measuring the segments after stretching. The narrower segments should be longer.

I don't have a tapered band so can someone confirm my "theory"?

2....if the above is true, then the wider segments contract first because they have a higher tension rate, meaning they will return to their normal state faster, then followed down the line. This has the effect of giving the ball a higher and higher velocity as the spring, meaning band retracts faster......thus transferring more energy, thus more velocity.

Thinking it another way.....as the wider band retracts faster, the band right behind it is still trying to catch up because it has the weight of the ball it's trying to accelerate AND close to it's normal state (legnth) because it's stretched further. And so on behind it.

This is straight up "logic" theory and I haven't found any article with the "science" behind it.

Also if this is true, then someone smarter then me can do a mathematical formula that can predict the acceleration of the mass through the the variable tension rate of the spring (band).

So....

Do tapered bands stretch unevenly?

Are there articles out there with empirical testing on straight versus tapered bands?

Is the above "theory" already fact and I'm just another newbie that needs to shut up and learn more?

Or am I so far out into nutty land that I should chuck my theory into the trash heap and have another beer?