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I think perhaps viewing this image taken from the Wikipedia article on Hydraulic Machinery may be helpful. (Note that while gas is a fluid, most gases are compressible)
Larger Pic
Notice that we get a force amplification relative to the area of the piston by the following equation:
F2 = F1 * (A2 / A1)
Also notice that the two pistons are not connected to each other - this is an important factor here.
Like the lever, one side must move farther than the other side to get the mechanical advantage - it is a volumetric distribution - but from a static force perspective, if no movement occurs, a small force F1 can deliver a large force equal and opposite to F2. But if we wish to do work and push F2 upwards, then F1 will move downwards and the distance traveled by each will not be equal. The piston with A1 must travel considerably farther than A2 and this is where the payment is made for the mechanical advantage of moving against the greater force F2.
So now we turn our attention to your apparatus and we see that the two pistons of different area are in fact connected together, so they cannot move independently. In this case we have an interesting situation. If we used a hydraulic fluid, which could not expand or contract where volume changes occur,(as is the case with lowering your pistons), then a vacuum occurs in the upper cylinder when we try and force an increase in the volume there. This causes the pressure to drop to zero and dead lock stopping movement where the pressure reaches zero which must occur before the pistons reach the bottom. Now, if the weight on top exceeded the pressure in the lower chamber by a differential great enough to fully compress the pistons against the vacuum, then we would have an upper chamber containing the liquid from the lower chamber (minus the port volume) with a vacuum space above the fluid. This can be problematic, as negative pressure tends to cause hydraulic fluids to do strange things like vaporize. For example, This Article shows that particular fluid as having Vapor Pressure: <0.01 mmHg @ 37.8 °C (100 °F) which means in could turn to vapor below that pressure. It also causes a problem where we must have a tank with a lower vacuum pressure if we intend to evacuate the upper chamber on the upstroke.
Now if your system were to work with gas, such as air pressure. Then the expanding volume of the upper chamber would simply be filled with the gas from the lower chamber and the pressure would drop accordingly and this too will subtract from the mechanical advantage.
Eventually, we must put energy into the system from somewhere to increase pressure to raise the weights. So the pump is turned by a motor of some type that converts one form of energy to another.
Looking at the crankshaft in your drawing, we see opportunity for four weights to be used. Two push down, while the other two are raised up. So the system is balanced from a mass point of view. This would be similar to the Mouse Power diagram I show above. So in this case, the gas pressure is used to put the crankshaft in motion and overcome any frictional losses in the system. But energy must be expended and work still has to be done to move the weights from inertial rest to a state of momentum. So the gas must provide a force capable of accelerating that mass from that rest state to that state of momentum. The reciprocating pistons have two rest states at each end of travel and a maximum velocity at the center of travel. This means that an external force must be applied to go from rest to maximum after which the kinetic energy of the piston is given to the angular momentum of the crankshaft and the piston decelerates back to a rest state at the bottom of the stroke. Now we are faced with either converting some of the energy stored in the angular momentum of the crankshaft back to the piston, or we must add new energy from outside the system to raise the piston back to the midpoint velocity - after which the deceleration of the upstroke also can be added to the angular momentum of the crankshaft.
Now an interesting thing about gravity is that it will accelerate any mass to the same velocity. So if Force equals Mass times Acceleration, the larger the Mass the greater the Force for the same Acceleration. When we balance the mass, gravitational forces net to zero for that portion which is balanced. But for both the crankshaft and the lever, the upward movement of the mass adds to the net force the same as downward movement - they are both additive. This means, that as long as our mouse has enough mass to overcome the moment of inertia associated with the great weights - the system will move. The same is true of the gas pressure. If the inertia is overcome, then the weights will move according to the gravitational acceleration of the mouse. And if the weights are accelerated, then they must represent a Force equal to the mass of the weights times the acceleration that has moved them. In this case, we find a link between not distance, but time. It takes a much longer time for the small asymmetric force of gravity on a mouse to cause the rest inertia of our balanced weights to move. But given enough time, and barring frictional losses, they will move and they will strike with a force greater than that of the mouse.
The mouse uses gravity (and some food it eats) to move the weights. Your engine uses a pump. But I do see some similarities.
But of course, I must have made a mistake somewhere - if we could extract energy from the gravitational field with something as simple as a playground see-saw surely we would have done so by now . . .
Larger PicNotice that we get a force amplification relative to the area of the piston by the following equation:
F2 = F1 * (A2 / A1)
Also notice that the two pistons are not connected to each other - this is an important factor here.
Like the lever, one side must move farther than the other side to get the mechanical advantage - it is a volumetric distribution - but from a static force perspective, if no movement occurs, a small force F1 can deliver a large force equal and opposite to F2. But if we wish to do work and push F2 upwards, then F1 will move downwards and the distance traveled by each will not be equal. The piston with A1 must travel considerably farther than A2 and this is where the payment is made for the mechanical advantage of moving against the greater force F2.
So now we turn our attention to your apparatus and we see that the two pistons of different area are in fact connected together, so they cannot move independently. In this case we have an interesting situation. If we used a hydraulic fluid, which could not expand or contract where volume changes occur,(as is the case with lowering your pistons), then a vacuum occurs in the upper cylinder when we try and force an increase in the volume there. This causes the pressure to drop to zero and dead lock stopping movement where the pressure reaches zero which must occur before the pistons reach the bottom. Now, if the weight on top exceeded the pressure in the lower chamber by a differential great enough to fully compress the pistons against the vacuum, then we would have an upper chamber containing the liquid from the lower chamber (minus the port volume) with a vacuum space above the fluid. This can be problematic, as negative pressure tends to cause hydraulic fluids to do strange things like vaporize. For example, This Article shows that particular fluid as having Vapor Pressure: <0.01 mmHg @ 37.8 °C (100 °F) which means in could turn to vapor below that pressure. It also causes a problem where we must have a tank with a lower vacuum pressure if we intend to evacuate the upper chamber on the upstroke.
Now if your system were to work with gas, such as air pressure. Then the expanding volume of the upper chamber would simply be filled with the gas from the lower chamber and the pressure would drop accordingly and this too will subtract from the mechanical advantage.
Eventually, we must put energy into the system from somewhere to increase pressure to raise the weights. So the pump is turned by a motor of some type that converts one form of energy to another.
Looking at the crankshaft in your drawing, we see opportunity for four weights to be used. Two push down, while the other two are raised up. So the system is balanced from a mass point of view. This would be similar to the Mouse Power diagram I show above. So in this case, the gas pressure is used to put the crankshaft in motion and overcome any frictional losses in the system. But energy must be expended and work still has to be done to move the weights from inertial rest to a state of momentum. So the gas must provide a force capable of accelerating that mass from that rest state to that state of momentum. The reciprocating pistons have two rest states at each end of travel and a maximum velocity at the center of travel. This means that an external force must be applied to go from rest to maximum after which the kinetic energy of the piston is given to the angular momentum of the crankshaft and the piston decelerates back to a rest state at the bottom of the stroke. Now we are faced with either converting some of the energy stored in the angular momentum of the crankshaft back to the piston, or we must add new energy from outside the system to raise the piston back to the midpoint velocity - after which the deceleration of the upstroke also can be added to the angular momentum of the crankshaft.
Now an interesting thing about gravity is that it will accelerate any mass to the same velocity. So if Force equals Mass times Acceleration, the larger the Mass the greater the Force for the same Acceleration. When we balance the mass, gravitational forces net to zero for that portion which is balanced. But for both the crankshaft and the lever, the upward movement of the mass adds to the net force the same as downward movement - they are both additive. This means, that as long as our mouse has enough mass to overcome the moment of inertia associated with the great weights - the system will move. The same is true of the gas pressure. If the inertia is overcome, then the weights will move according to the gravitational acceleration of the mouse. And if the weights are accelerated, then they must represent a Force equal to the mass of the weights times the acceleration that has moved them. In this case, we find a link between not distance, but time. It takes a much longer time for the small asymmetric force of gravity on a mouse to cause the rest inertia of our balanced weights to move. But given enough time, and barring frictional losses, they will move and they will strike with a force greater than that of the mouse.
The mouse uses gravity (and some food it eats) to move the weights. Your engine uses a pump. But I do see some similarities.
But of course, I must have made a mistake somewhere - if we could extract energy from the gravitational field with something as simple as a playground see-saw surely we would have done so by now . . .
perhaps, I can draw the complete version so easy for everybody look closer and hope will come up with different idea.
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