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* / 2*rBI* -> 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*