# Moving mass of lift exponentially

#### Tygra

(Edit: title should be 'Moving mass of lift increases exponentially)

Hi all,

I need some help understanding something, but to give you some quick background I am doing a final project on my access course at college on how tall can you build a skyscraper.

A problem engineers face is the issue of the elevator where the steel cable becomes too heavy as you get to 500 metres. I have read the moving mass increases exponentially, but how does it not increase proportionally? Double the distance/length of cable should surely mean the mass be twice as much.

The website here talks about it

Could some help me with the mathematics please?. I have an A-level in maths so I understand exponential functions and equations.

Thanks

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#### Woody

The problem is that as the length of the cable increases, its thickness also has to increase to give it enough strength to support its own weight.
But as the thickness increases, the weight increases, so it needs to be thicker to support the extra weight.
But as the thickness increases...

#### Tygra

Ah thanks for clearing that up for me. Could you give me any hints on constructing an equation, so that I could substitute a given height and perhaps determine the limit for a steel cable?

#### Tygra

I guess find out the density of steel would be one thing to do

#### Woody

And the tensile strength.
How much weight (per square centimeter cross-section) will the steel wire support?
What length of 1 square centimeter cross-section wire weighs that much?
Try again with 2 square centimeter wire, then 3 and 4...
The pattern should start to emerge, and then you should be able to encapsulate it into a single equation.

1 person

#### Tygra

For the tensile strength if steel has a strength of 181.8 kg/m2 that means if the cross section of the wire is 1cm2 it can hold 181.8 kg before it possible snaps?

#### Tygra

Sorry, Woody, 181.8 kg/cm2

#### Woody

Yes, but...

Steel does not just simply hold the weight, up to the limit, and then break.
It stretches elastically at first, up to what is called the yield point.
If a load greater than this is applied, it will stretch but remain stretched after the load is removed.
The actual breaking point is actually slightly higher than the yield point.

So an engineer would be looking to keep the loads below the yield point of the material (and they would also include a sensible safety factor).

However, the exponential nature of the weight to height relationship will remain, regardless of the actual limit point chosen.

1 person

#### Tygra

Actually could I have some further guidance, as I am bit stuck where to start? Could someone start me off. I need some more explantion of how cable thickness increases with length/height with formulas etc.

#### YellowPeril

You can google elevator and read the article on wiki for a start. Elevators are quite complex mechanisms. You will need to decided the service and payload requirements. Normally design considerations are static, i.e. the payload weight and the weight off the cable. Typically you will start by looking at a number of suitable cables and selecting the right one for your application, this you will do by trial and error to get as close as you can. You will need to incorporate a counter weight system with pulleys, there will be a few different ways of accomplishing this as you will see on the wiki article.

Hope this helps.

PS. One way of getting around the limit is to have two sets of elevators operating and a transfer floor inbetween. Although it will cause dissatisfaction to the users.

1 person