# Could a hybrid system of mechanical levers and hydrostatic/hydraulic cylinders be able to lift 200+ kg with the force of an arm?

I don't know much about levers and hydrostatic/hydraulics myself, so I hope I don't make too many misconceptions.

## The idea:

Hypothetically, if you had a 40km+ long indestructible lever on a indestructible fulcrum, you could lift the Eiffel Tower with only your body weight.

With this in mind, the idea is to use these same principles (hydraulics/hydrostatics and levers) in order to increase the distribution of force without needing a 40km lever so an average human being could power this system with the strength of their arms and/or legs.

Yes, I would be "increasing" the "length" where the load is, but I would also increase the "length" where the force is being applied, increasing the distance in which the first moves. It makes me wonder if it would make sense at all, because even though you increase the length of the lever, it still has the same forces in the "same" proportions.

## The simplified system would be like this:

• First, a class-1 lever where the load would be a hydraulic/hydrostatic cylinder, and the force would be the hand/legs of a person.
• Second, I don't know much about these subjects myself: Option 1 would to make a larger and shorter piston at the end of the lever that would impel a longer but thinner cylinder.
• At the end of this thinner cylinder would be the final load, which, if wasn't a simple system laying on the ground, would be the weight of the load, which I would put at worst at 300 kg in total.

## How much bigger this system and/or the parts of the system would be required to be in order to lift something from 200-300 kg in weight with only the human force of a arm/leg?

• Hypothetically you position a big structure above the Eiffel Tower and use lots of pulleys and 40km+ long cable to connect tower to structure. Jun 10 at 15:13
• The real world has things like hydraulic jacks where one person can easily lift a car (thousands of kgs). Is that what you're looking for? Hydraulics are good for this, as long as they don't leak. Jun 10 at 15:34
• "... even though you increase the length of the lever, it still has the same forces in the "same" proportions." No, when you increase the length of the lever you reduce the force required but increase the distance that force has to travel to achieve the same work. Jun 10 at 15:40
• @Fulano You could make one that used a single really long pump. In fact this is what happens if you simply connect two hydraulic pistons together, with different sizes. Jun 10 at 16:24
• well if you can lift let's say 20kg then getting 200kg is a 1:10 ratio, so the distance will be multiplied by 10. That seems perfectly reasonable, you won't need a 40km distance unless the thing you are trying to lift is 4km away Jun 10 at 17:30

Levers and hydraulic cylinders are not typically used for the distribution of force, but are more frequently used to transmit and otherwise modify applied force.

Per your reference to class one levers, the fulcrum is located between the load and the force. This also (and obviously) results in a change in direction of the force with respect to the movement of the load. What cannot be overlooked is the mechanical advantage of a level with the fulcrum not located precisely in the center of the distance between the load and the applied force. Image from linked site. If the load is located one-third of the total way from the fulcrum, the applied force will be doubled at the load, but the travel of the load will be one-half of the applied force travel. This aspect doesn't appear to be a consideration in your question.

In the world of hydraulics, a similar ratio exists, but is applied to the surface area of the piston to which the force is applied in relation to the piston surface area of the loaded piston.

The math is a bit more complex than the simple class one lever, however and is left as an exercise to the reader. The image is from the linked site. In simplistic terms, a small diameter force cylinder can create a "force multiplier" on the load cylinder if the load cylinder is a larger diameter. As before, there is a compensation applied in that the travel of the smaller cylinder is much greater than that of the larger cylinder. As it can be impractical, for example, to have a 30 meter long small diameter force cylinder, a series of valves allows repeated / multiple strokes of a class one lever (!) to apply hydraulic fluid to the system, moving the load cylinder appropriately.

In the question, the suggestion to use a larger (diameter) cylinder at the force end is the reverse of the desired objective.

Consider a hydraulic bottle jack. Image from linked site. In the above image, the handle is not a class one lever, but it could be if desired or required. For practical purposes, the displayed handle accomplishes the necessary movement of the force cylinder, regardless of lever class.

The load cylinder is the piston of the jack and presents a cross section of greater diameter than the force cylinder. Missing from the image is the necessary return oil flow valve and passages for the jack to function in the real world.

Hydraulic floor jacks can be rated to lift as much as 10,000 pounds / 4500 kilograms using a reasonable length lever as shown in the above image operated by an ordinary human being. The key factor in this consideration is that many pumps of the lever is required to move that weight an appreciable distance.

If a specific and restricted objective is created (distance of travel, mass of load) the parameters of the lever length, force piston diameter and travel can be adjusted appropriately.

In relation to the comment added to my post, a hydraulic pump in an excavator or piece of similar heavy equipment is effectively a quantity of cylinders or means of imparting force to hydraulic fluid. I have seen swashplate pumps with sixteen very small cylinders. One rotation pumps quite a bit of fluid to the destination cylinder/s but also requires substantial energy, typically from an electric motor or petrol engine.

• I don't know if i should edit the question to fit this, but what if there was various pumps through the lever, which each would pump a different amount of liquid? Do you think this could work? Jun 10 at 17:20
• Regardless of the number of pumping devices, which in the case of the diagram, is a single cylinder, there's a mathematical relationship between input and output. More cylinders on the input means some form of compromise in that respect. Jun 10 at 18:28