PATH DEPENDENT Energy Storage
About
A mechanical system utilizes leveraged gravity for performing work. The system comprises an effort mass configured to descend rotationally via a lever arm of effective radius r.
This rotational descent under gravity generates a variable torque (τ=mgrsin(θ)) at the lever's pivot, the magnitude of which depends on the lever's instantaneous angle (θ) relative to the gravitational vector, providing significant mechanical advantage compared to linear descent.
A transmission mechanism is configured to harness this variable rotational torque and convert it into a useful output, such as hoisting an opposing mass or driving a common axle coupled to a load or generator.
The system enables the controlled application of amplified gravitational force, offering high torque capabilities particularly advantageous for initiating motion against resistance.
The principles are applicable to experimental apparatus, mechanical energy storage and generation systems, and other devices benefiting from controlled, gravity-derived torque.
Repeatable Lab
While the instantaneous torque varies, the theoretical average torque over a significant portion of the operational cycle provides a useful metric for the system's potential.
For an idealized, frictionless system undergoing a 180° rotation (π radians) from the top vertical position (θ=0) to the bottom vertical position (θ=π), the average torque (τavg) can be calculated by integrating the instantaneous torque over the interval and dividing by the interval length (π):
τavg=π1∫0πmgrsin(θ)dθ=πmgr[−cos(θ)]0π=πmgr[(−(−1))−(−1)]=π2mgr
Thus, the theoretical average torque over this 180° cycle is τavg=(2/π)mgr. This value, approximately 63.7% of the peak torque (mgr at θ=90∘), serves as a benchmark for the average leverage generated during the primary power stroke in an ideal system.
Actual system performance will be influenced by factors including friction, inertia, and the specific dynamics implemented by the control mechanism and components