I used to perform a lot of physics calcs in my youth, but not of these types; itÃ¢â‚¬â„¢s all new to me. Thanks for spot-checking meÃ¢â‚¬Â¦ IÃ¢â‚¬â„¢ve been at this for days with spreadsheets and no one to talk to.

OK, I edited/corrected the formula notation above. On we goÃ¢â‚¬Â¦

Calculate Steady State:Previously stated:

Given

P =

I *

V, solve for

V:

V = P / I -> 1491.4 / 44 = 33.9

This is amusing. From the relationship of

P =

I *

V we can play around and manipulate the factors until we arrive at suitable products for the system.

The part that bugs me is that the

Motor Torque Constant (

Kt) is relative and not constant at all unless we choose it to be so for control. In other words, if I am going 30 mph (

er, sorry 48.3 kph) for hours on level ground and my battery drops voltage then

Kt must change. Similarly, if I have a current limit set and along my journey I encounter wind or an incline,

Kt must change. Perhaps itÃ¢â‚¬â„¢s a moot point but it has had me twisted up Ã¢â‚¬â€œ at least until I could explain it:

K is an ideal theoretical value only. Do you agree?

Meat & Potatoes:The whole point of this exercise is to mathematically anticipate the requirements for a steady-state wheel in motion given three values:

diameter,

velocity, and

power consumed. I think weÃ¢â‚¬â„¢ve flogged the observed system enough, therefore I wish to analyze the internal workings and construct a model of the electromotive forces to complete the energy balance equation.

A single straight wire passing through a uniform magnetic field produces a force, (formula derived from the

Lorentz force equation

F =

qv x

B):

F = IL x B, where

F = Force in Newtons (N)

I = Current in Amps (A)

L = Length of wire in Meters (m)

B = Flux density in Telsa (T) or Gauss (g x 10,000)

Given as Torque:

In a single electric circuit (

one loop, turn, or winding), we have two sides pulling in opposite directions along a common axis, therefore:

For the sake of discussion let us assume that

r = Â½

d of the original wheel. The value for Flux density (

B) is picked arbitrarily (we can discuss calcs a bit later).

r = 12 inches / 0.3048 meters

B = 0.5 T

I = 44 A

Ãâ€ž = 33.9 Nm

Solve for

L:

L = Ãâ€ž / 2rBI -> 33.9 / (2 * 0.3048 * 0.5 * 44) = 2.53 m

Observations:- This is a single-phase solution.
- The frequency would be 420.2 rpm or 7 Hz.
- The conductor would have to be 11 AWG to carry 44 A safely.

The heat generated by the system would be as follows:

R = 4.1328 ohms/km for 11 AWG -> (4.1328 * 2.53) / 1000 = 0.01046 ohms

R = V / I

P = I^2 * R = V^2 / R

P = 44^2 * 0.01046 = 20.2 watts

Calculate the Efficiency:

Pe = (Pi Ã¢â‚¬â€œ Pr) / Pi -> (1491.4 Ã¢â‚¬â€œ 20.2) / 1491.4 = 98.6%, where

Pe = Power, Efficiency

Pi = Power, inital or imperical

Pr = Power, resistance

This is probably the best this theoretical system will ever see. To overcome the loss of efficiency the system would need to provide > 1.4% more power.

Summation:In the first post of the thread I calculated the Angular Velocity (

Ãâ€°) and Torque (

Ãâ€ž) given wheel diameter (

d), velocity (

v), and power (

P) used. The second half of this thread develops a model which predicts the electromotive forces for a single circuit. Thus we can represent the elementary

Energy Balance Equation as:

Efinal = Ein - Eout, where

Ein = (1512w @ 44A x 34.4V) Ã¢â‚¬â€œ (20.5w required to overcome electrical resistance**); Work on the system, constant current

Eout = 1491.4w; Work by the system

Efinal = 0; balanced

**Calculation: 1491.4w / 98.6% = 1512w; 1512 - 1491.4 = 20.5. If current (

I) is constant then

V must rise to 34.4V.

EDIT: Corrected

EBE arithmetic.

Are you still with me?

Are my calculations correct? hehe

Thanks for checking,

KF