Optimizing Generator Efficiency with Metal Spheres: A Calculation Study

[mailhiot]

I need to do some calculations to know if a metal sphere (iron, steel, whatever) that is 0.25kg is dropped from 2 meters, will it produce enough torque (kenetic energy?) to start a generator with the specifications below? Furthermore, if a metal sphere was dropped every second, continuously, would the generator generate the 3500 W? If not, what size would the metal sphere have to be to make the generator work?

Rated rotation speed: 250 RPM
Rated output: 3500 W
Weight: 75 kg
Rotor inertia: 0.066 Kg.m2
Starting torque: <2.0 NM
Phase resistance: 2.7 ohms
Recified DC Current at Rated output: 11A
Required torque at rated output: 150 NM

Thanks!

 

[rcgldr]

force = .25 kg x 9.81 m/s^2 = 2.4525 Newtons
energy from dropped sphere = 2.4525 Newtons x 2 meters = 4.905 joules

If a sphere is dropped every second, you'd have 4.905 watts of input power, less than 1/700 of the output power you're trying to achived.

 

[mailhiot]

Thanks! Your answer shows that the energy from the dropped sphere is 2.45 NM. The generator requires a starting torque of 2 NM, so it looks to me that it would be enough to start the generator. The generator needs to get to 150 NM to get to the rated output of 3500 Watts. Wouldn't dropping a metal sphere every second eventually get the generator to the 150 NM? In other words, if each metal sphere delivers 2.45 NM, then it would take about 61 metal speres to get to 150 NM? Thanks!

 

[rcgldr]

Thanks! Your answer shows that the energy from the dropped sphere is 2.45 NM. The generator requires a starting torque of 2 NM.

Those are the same units, but the dropped object's NM is a quantiy of energy, not a torque. Also the energy is 4.9 NM, not 2.45 NM. Torque equals force times radius, and the force from the collision of the sphere would depend on how stiff the surfaces at the point of collision are. The torque generated would be related to the collision force times the distance from the axis of the generator to the point of impact. Depending on the inertia and loading of the generator, the impulse (average force x duration (time) of impact) of a single sphere may be too small to achieve initial startup.

Wouldn't dropping a metal sphere every second eventually get the generator to the 150 NM? In other words, if each metal sphere delivers 2.45 NM, then it would take about 61 metal speres to get to 150 NM? Thanks!

Each sphere has 4.9 NM of energy, but the goal is to generate 3500NM of energy every second. You'd have to drop at least 715 spheres every second to input 3500NM of energy to the generator.

 

[mailhiot]

Thanks for your reply. The metal spheres drop and pass through a turbine, which is connected to a generator, similar to hydro, or even wind. The specs say it only needs 250 rpm and the output that this particular generator is 3500 W, so I am trying to get it to teh 250 rpm using metal spheres. From experiments I have done, dropping 715 spheres every second would probably destroy the turbine/generator, especially after a few minutes or hours! It seems like an awful lot. Are you sure there isn't some other variable in the equaltion, because every generator is different, that is, if you look at 3500 W generators, the start up torque required, rpm, etc can range a lot. I chose this one because the rpm is low at 250. Thanks!