1. Dec 3, 2015

Hi. First Post. I'm a DIYer with no physics education, so I apologize in advance.

I have a ladder 100 inches long that weighs 72 lbs. The top of the rails of the ladder are attached to hinges on a ceiling beam/loft floor joist 90 inches above the first floor. The run is 45 inches. I believe that lifting the end of the ladder from the first floor to the ceiling, it will weight approx 36lbs when horizontal. I believe the weight will change depending on the angle and I would like to know how to calculate the weight at the ladder's various angles during the lift. I would also like to calculate how much lift will be required at the midpoint of the ladder's 100 inch length (50 inches). Finally I would appreciate the equation for calculating the lift required at various points along the ladder's span.

Thanks You. JimK.

2. Dec 3, 2015

### Staff: Mentor

Welcome to the PF.

So it sounds like you want to figure out what it takes to swing the ladder from the vertical hanging position up to the horizontal storage position. The weight of the ladder does not change as you swing it up, but the effort required does change.

Are you going to be pushing it all the way up by hand, or can you use a pulley and rope to pull the ladder up into position?

3. Dec 3, 2015

Thanks for the welcome and reply Berkeman... You got my project... currently there is a folding attic ladder to the loft in my cabin that is not durable enough for the traffic. When the ladder is down it will be approx 60 degree slope. When up it will fit horizontally between two 4x6 wooden beams. And i want it to be a non-folding ladder for strength and stability. I'm thinking a line from each side rail at the midpoint to a pulley attached to the roof beam with weights at the end of the lines to assist. I also have some springs in my shop I could use, but I haven't figured out how that would work yet.

4. Dec 4, 2015

### CWatters

I don't have my calculator with me but ... You mention it is 90 inches from floor to ceiling and the ladder is 100 inches long. Is the ladder long enough to reach the ground at a 60 degree angle?

5. Dec 4, 2015

I think it's actually 63.43 degrees, but my measurements are pretty rough. I used this logic, my height is 90", my run is 45", a**2 + b**2 = C**2= 2025+7975=10,000. Then I used a calculator, although I wish I could remember how to calculate it with paper and pen.

6. Dec 4, 2015

### Staff: Mentor

So as a first cut, I'd put the pulley in line with the lowest rung on the ladder when it's in the horizontal stowed position. That will minimize the force required to finish torquing it up into the stowed position. This assumes that you will be using your hand to also lift the ladder up initially off the ground, while pulling on the rope over the pulley. So you will be adding your lifting force to the downward tension on the rope over the pulley.

If you cannot lift at the same time you pull down on the rope, then there is probably a better compromise position for the pulley, not at the end of the stowed position...

7. Dec 4, 2015

### tech99

The ladder weighs 72 pounds and at all times half of this is supported by the top hinge and half by the bottom end, irrespective of the angle.
If you try to lift it by using a rope that is not at right angles to the ladder, for instance by a vertical rope, the force required is magnified by the geometry.

8. Dec 4, 2015

### CWatters

I'm back home now and I agree it's about 64 degrees. For some reason it sounded like it would be a lot steeper.

9. Dec 4, 2015

### Staff: Mentor

So @Jackofalltrades -- That's why I asked if you can lift the ladder by hand part-way up as you also pull on the rope. Once you get the ladder up to about shoulder height, you can finish it off with the rope pulling very near the bottom of the ladder for the best mechanical advantage. Does that make sense?

10. Dec 4, 2015

### insightful

Here's an idea that should work, using one 36 lb weight on a rope over a pulley on each side of the ladder as shown.

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11. Dec 5, 2015

Thanks to all so far. The drawing by Insightful represents what I am planning. I reasoned that lifting one the end of the ladder 72 lb (100") would require 36lbs. This seemed to be supported by an answer elsewhere on the forum https://www.physicsforums.com/threads/lifting-one-end-of-a-beam.151526/#post-1214130. What I'd like to know is how to calculate the lbs of lift required when I attach at the midpoint (50") as drawn by Insightful rather than at 100".

12. Dec 5, 2015

### Staff: Mentor

As you move the tie point closer to the hinge, the load on the rope increases. Is there a reason that you don't want to attach the rope to the lowest point on the ladder?

13. Dec 5, 2015

Yeah, the size of the hole in the ceiling... about 54"

14. Dec 5, 2015

### insightful

Well, you calculate it by what's called a "free-body diagram" of the ladder, with x-y forces at the top pin and middle ropes, and just a vertical (y) force at the bottom. Since the ladder as shown in the diagram is almost totally supported by the ropes, the force to lift the bottom off the floor is less than 5 lb.

15. Dec 5, 2015

Thank you... how much downward force is on the ropes supporting the ladder?

16. Dec 5, 2015

### Staff: Mentor

Ah, now that makes more sense.

17. Dec 5, 2015

### Staff: Mentor

The tension in the rope (and hence the force pulling on it) is the weight of the ladder being lifted, plus a component related to the sideways angle off of 90 degrees that the rope is angled to the pull. If you have a long rope pulling it up from a ways away, the total tension/force is very high. There is a large horizontal force needed to generate the small vertical force.

If the rope is at a 90 degree andle to the ladder while pulling, then there is no extra force needed. Hence my initial comment about finding a compromise position for the pulley. Can you post a sketch of the setup? That would help us to show you the FBD that is needed to calculate the best compromise pulley location.

18. Dec 6, 2015

### insightful

The tension in each rope is simply the weight added to the end hanging down. In my diagram, that would be 36 lb tension in each rope.

19. Dec 8, 2015

### votingmachine

I did something similar to that with an actual staircase. I put the stairs onto garage door tracks and as the door swung shut the stairs simultaneously were sliding up the rails. When fully down, the stairs rested on the ground and an extra anchor at the top. I used counter weights to make the whole thing fairly easy to move.

The main reason to make it both swing and ride the rails up was to allow me to use a smaller opening length than the stair/ladder length.