greendoor wrote:OK - first build a see-saw with a low friction bearing. Bolt 20 kg dumbell weights on each end, and allow the end radii to sweep out a height of at least 4 meters. This is quite large for a reason - we want an extreme example to allow room for experimental errors, and we want it really slow and heavy so we can see what is happening in slow motion.
What length do we make the see-saw? Also what is the see-saw's expected weight?
greendoor wrote:When this is perfectly balanced, the see-saw will find it's own horizontal level.
If it is perfectly balanced then it will stay in any particular position that it happens to be in. It will not move to a horizontal level. If it is balanced but the pivot point is slightly above center then it will balance horizontal. If on the other hand the pivot point is slightly below center then the see-saw will tilt fully to one side or the other side.
Fletcher wrote:Point of order before I get to far into it - a perfectly balanced beam [with dumbbell weights each end ?] will only be perfectly balanced if it is entirely symmetrical i.e. the pivot is centered in the beam - pivot it from above or below & then it has a bias to find its lowest Pe - e.g. pivot at bottom of beam will see one end drop [unless so well balanced that the low bearing friction is enough to hold it in preset horizontal position] - pivot on top of the beam & the beam has a self righting bias & will find & maintain horizontal position.
N.B. when the pivot is centered then there is absolutely NO bias & it won't find horizontal - it will stay wherever it is put.
greendoor wrote:If we place a small mass of 100g on one end, we can see that this whole system slowly accelerates and builds up speed over time. Obviously it reaches maximum velocity when the heavy end hits the ground, but we aren't going to let it do that.
In order to calculate the velocity of the swing we need to know the exact shape and position of the all of the weight masses involved. Or alternately we need to know the radius of gyration. There are two reasons why we need this information. One is that as the see-saw tilts then the weight masses must not only rise and fall but they also rotate around the see-saw pivot point. The second is that the exact center of each mass must be known in order to do the calculations accurately.
greendoor wrote:Build a flywheel with a mass of 1 kg and flanges that allow strong packing ribbon to be wound around this flywheel (like a lawnmower coil starter). Mount this on a solid base in the ground, on a low friction bearing.
What diameter do we make this flywheel? Since it is the radius of gyration that determines the inertia of the flywheel we need to know the shape of the flywheel in order to calculate the radius of gyration.
greendoor wrote:The object of this machine is to allow the beam with the 100g passenger to fall 1 meter unrestrained. The total mass of the system will be the mass of the beam, plus 2 x 20kg, plus the 100g passenger. After falling for 1 meter, it will have accumulated a specific amount of Momentum over a long period of time that calculates to be signficantly greater than the Momentum that the 100g passenger alone could gain in 1 meter of freefall.
I must assume that one end of the lever starts at 2 meters above the pivot point?
greendoor wrote:Arrange the coiled up rope to be attached to the opposite end of the beam, with sufficient slack so that it does not restrain the beam until it has fallen 1 meter, at which point it because taut and starts to accelerate the 1kg flywheel over the next meter or so.
The end of the see-saw will now be about level with the pivot.
greendoor wrote:The object of this design is to transfer all the momentum from the moving beam to the lighter flywheel. We can allow the 100g passenger to fall off after the 1m drop - the beam has sufficient mass to keep moving.
Tune this so that the beam comes to a dead stop, and the small flywheel takes all the momentum. The flywheel, being much lower mass, will end up with a much higher velocity than the beam had.
Transferring
all of the momentum of the masses of the beam, the two weights and the drop-off weight in the space of 1 meter swing of the see-saw will require some real extensive leveraging, but it can be done. Because you selected such large weights (two 20kg dumbbells) on the see-saw and drive it with a 100g falling weight and then transfer this momentum to a single 1kg flywheel the leveraging you will need to be in the range of slightly over 200:1. Also with a simple arrangement as you describe you will not be able to transfer all of the momentum. There are two problems. When the rope first becomes tight there will be an initial shock tension as the flywheel tries to come up to the speed of the see-saw. Then once up to speed the see-saw still has speed left over that has not yet passed to the flywheel.
greendoor wrote:Now all we have to do is use the energy in the small spinning flywheel to winch up a 100g mass as high as it can go. A length of nylon string with a hook that can fall onto the flywheel and catch a nail or something should be able to prove the point initially. A centrifugal clutch might be a long term solution. Hydraulic motors or electrical alternators that can be switched on at the right moment might be other options if there is any overunity effect to be achieved.
First you must overcome the problems of transferring all of the momentum of the slow moving 200kg see-saw to the 1kg flywheel. Your basic design using a starter-rope will not work. Back to the drawing board! The correct design must use some type of variable transfer mechanism whereby the heavy weight slows down to a stop while the light weight flywheel speeds up from a stop. This requires some type of special mechanism other than a simple rope around a flywheel pulled by the see-saw.
greendoor wrote:If we can't winch 100g higher than 1 meter, then we have proved this whole principle to be wrong.
If we can winch 100g significantly higher than 1 meter, then the rest is history.
Converting this into a balanced self-resetting reciprocating model should be fairly obvious - if we can lift the falling mass higher than it falls.
Don't forget that the 200kg see-saw must be accelerated/moved/tilted back up to its start position.
Fletcher wrote:N.B. I realize that the beam is a flywheel analogue but if you want it to start from horizontal either it has to have pivot point bias to self right itself & that has back-torque issues or you have to supply energy to reposition it to horizontal & overcome the inertia apparent.
Engineering something requires an accounting of all the little bothersome details. Ralph uses gut instinct from years of experience and then rebuilds things when they don't fit or work as expected. A good engineer builds things on paper using calculations so as to know what the expected results will be.
Fletcher wrote:Not sure if this can be modeled in this form but I will probably have a play - I may have some more questions as I/we work thru it with you - they are not pedantic or inane but necessary detail - I may have to change things [but not conceptually] to fit with WM2D & my own abilities with the program - some, like broli, will apply their imagination differently & come up with different work-arounds that maintains the integrity of your idea to test - I'll see how far I can get.
Details! Details! Details! It is all in the details!
