Re: "Peak Efficiency" Control Mode?
Posted: 30 Oct 2017, 16:51
rew wrote:If you keep talking about kinetic energy in electrons, one day I'll calculate that kinetic energy for you. It's going to be less than you expect. For all practical purposes the kinetic energy in the electrons is zero. You should also stop talking about 100% duty at stall.
The hobbyking motor I linked simply allows 1.5V of effective voltage above the BEMF. So if the rotor is stalled, you're allowed 1.5V or 3% duty cylce (at 50V battery voltage). If the rotor is doing 150RPM, (1V BEMF) you're allowed to do 2.5V or 5% dutycycle.
devin wrote:@rew If we take the number of copper free electrons in a typical motor winding, and send them on a straight line trajectory relative to the earth at their fermi velocity (1570km/s), how much kinetic energy is this?
@rew In theory, the stored kinetic energy in the free electrons of 10 cubic centimeters of copper is equivalent to the kinetic energy at the muzzle of about 63 x .50 caliber rifle bullets or about 1688 x .45 caliber handgun bullets. This same amount of kinetic energy is also equivalent to about 264 watt hours, or about 5AH from a 50V battery pack.
0.0000007725 kgs free electrons in 10 cubic centimeters copper (nearly a milligram or 1/1000th of a gram or roughly equivalent to a single grain of sugar)
1570000 meters per second = V = fermi velocity of copper free electrons
KE = 952067.625 joules
10 cubic centimeters copper
1,000,000 cubic centimeters per cubic meter
10 cubic centimeters is 1/100,000th of a cubic meter
8.49x10^28 free electrons per m^3 copper
(1/100000)*(8.49x10^28)=8.49x10^23 free electrons in 10 cubic centimeters copper
8.49x10^23 free electrons * 9.10*10^-31 kg mass per electron
(8.49*10^23)*(9.10*10^-31) = 7.725*10^(-7) kgs free electrons in 10cc’s copper
7.725*10^(-7)= 0.0000007725 kgs free electrons in 10cc’s copper
fermi velocity of copper free electrons = 1570000 meters per second = V
M = 0.0000007725 kgs
KE = 1/2 (M * (V * V))
KE = 952067.625 joules
952067 joules / 15037 joules per .50 cal rifle bullet = 63.31 x .50 cal rifle bullets equivalent Kinetic Energy
952067 joules / 564 joules per .45 handgun bullet = 1688 x .45 bullets equivalent Kinetic Energy
Image Source: https://www.survivalmonkey.com/threads/short-range-media-penetration-by-50-bmg-ap-rounds.49556/
*Also, the kinetic energy which is in theory stored in the roughly single-sugar-grain-sized mass of free electrons in 10 cubic centimeters of copper, 952067 joules, is the same amount of energy transferred by a human-sized 80kg object striking a brick wall at 345.10 miles per hour, 144.277 meters per second, or 555.39 kilometers per hour.