# Is there a pulley configuration that can both reduce distance and weight?

I'm trying to find some kind of clever workaround to engineer a solution to the fact that a typical pulley can't reduce both distance and weight.

I am designing a counterweight system for a hangar door (folds straight up to open, unlike typical residential garage doors). It needs to have a pulley system with counterweights that exactly equal the weight of the door so it can be opened to any height and stay there. Due to constraints in my wall between the studs, the counterweights (buckets full of sand or water) only have half the vertical distance as the door, and I don't have enough physical space to put twice the weight of the door.

I'm trying to come up with a configuration that will allow me to overcome one or the other of my two problems: e.g., either find some way to get more distance out of the distance I have available or get more weight into the space than I have available. I don't mean in a breaks-the-laws-of-physics sort of way. I'm looking for some clever engineering solution.

For the sake of thinking about this, imagine the door weighs 100lbs and each bucket of water weighs 10lbs. The door must raise 10' but there is only room for the bucket to go 5'. There is enough room in the wall for 10 buckets but since they have to stack, every bucket you add reduces the distance available to travel: 10 buckets wouldn't have room to move at all.

Edit: for those who think I'm just trying to cheat on homework, here's a photo of me actually building this (prototype):

• Sounds like a homework problem. – JACK Jan 3 at 21:06
• Lol, no, I'm actually building this. Let me upload a photo. – brentonstrine Jan 3 at 21:25

There are lots of ways to do this, but first and foremost, you should understand that counterweights on garage doors have gone out of fashion for safety as well as size/complexity reasons. Springs have almost entirely replaced them.

The classical approach to keeping the counterweights in stud bays is to divide and conquer. The counterweights do not need to be located in the space-restricted area right by the door - you can run cables all the way to back wall of the garage, or all along the side wall(s) and get multiple stud bays involved by using multiple cables to multiple counterweights.

When choosing components, especially cable, cable clamps and pulleys, consider what happens when a cable breaks, or becomes unclamped. This is not the place to choose the cheapest thing you can get. i.e. concrete-filled paint cans are perhaps a dubious choice for the counterweight itself, unless you embed a suitable anchor in the concrete - a paint can handle is not what you want to entrust with holding up a moving counterweight for some number of years.

• The paint can is really for the purpose of simplifying the explanation and the prototype (prototype is actually full of water). I will likely make a concrete form exactly to fit in the stud bay with a piece of rebar through for strength and to make the attachment point. I have several springs but it seems harder to get the spring to exactly balance the weight of the door. I don't understand the advantage of springs. If a cable breaks, the other counterbalance (I will have two or even three depending on what I figure out) will slow the fall of the door. – brentonstrine Jan 4 at 1:24
• I was planning on using the springs just as shock absorbers. I will look into how springs can be used for this but it seems unlikely to work for a hangar door counterbalance. I want to be able to let go of the door at any height and have it stay in that position. (This is how my prototype currently works.) – brentonstrine Jan 4 at 1:30
• In thinking about this more, I have realized that springs only make sense for doors that go horizontal because the force needs to decrease as the door is opened more and more, the way a spring's force decreases as it is unsprung. For a door that just goes straight up, like a hangar door, a counterweight is needed. See this answer to a great Stack Exchange question on the topic. – brentonstrine Jan 4 at 2:52

Basically you can't reduce both the travel distance of the weight and its mass at the same time. If you want the weight to have a shorter travel (say half) then you have to use a pulley like the second one from the left, which means the force on the string will be half the weight. In other words the counterweight will have to be double the weight of the door. No free lunch!

the space for the counterweights (buckets full of sand or water) is half the height that the door will actually open

I see on the photo that the ceiling is quite a bit higher than the door. If you put the pulley higher, then you can have more travel on the counterweight before it reaches the floor, and you can use the same weight as the door.

Note you should put the counterweight inside some sort of cage to prevent people from standing under it.

• The prototype has room, but the actual built door will have counterweights in the wall with less vertical room. Using space above is a good idea, I was trying to figure that out. Maybe horizontally having lots of weights that travel only a few inches. – brentonstrine Jan 3 at 22:08
• You could use a bucket of lead shot if sand takes too much space... – bobflux Jan 3 at 22:28
• According to this chart, concrete is only slightly less dense than pure iron, and I can get a 70 lbs bag for \$5, so that's probably the most cost-efficient weight I can make. About 20 lbs per paint can, if my calculations are right. – brentonstrine Jan 3 at 23:28
• If you need more than a couple of bags of "premix" you'll save money by getting a 94 lb bag of cement and a pile of gravel (depending what passes for gravel in your area, possibly also a pile of sand) and mixing your own. – Ecnerwal Jan 4 at 1:29
• I think you're on the right track here - you need something that's more dense than water. As you've found, water is a little over 60 lbs/ft3, and concrete is around 140. But iron is much more dense than either of these. The chart refers to "iron chips", not a solid chunk of iron. The density of solid iron is around 490 lb/ft3 - almost 10 times denser than water. You might want to look for some scrap iron - maybe old barbell weights or steel plate from a scrapyard. My grandfather had a heavy wooden door over his cellar steps and he used a chunk of railroad rail as a counterweight. – Mark Jan 4 at 5:03

Any door which goes straight up/down is a significant injury risk. What would you do if a cable snapped while the door was in the open (up) position? This whole setup is a bad idea.
Even if you insist on a solid (no hinged sections) door, please consider rotating it up and horizontal (such systems do exist) so there is no danger when in the full-open position. You have the additional advantage that you need raise the center of mass of the door only half the door height, rather than 100% of the door height as in your current design.

• Yes, please research what a hangar door is as I described. – brentonstrine Jan 6 at 23:44