Silicon Productions

The MGB Electric Sports Car

__Analysis by Warren Winovich__Page 7

__Appendix__

__Definition of Terms__a | acceleration of the vehicle, ft/sec^{2} |

a_{0} | initial rate of acceleration, ft/sec^{2} |

A | cross section area, ft^{2} |

c | time constant of an accelerating vehicle, seconds |

C_{D} | drag coefficient |

D | distance traveled during an acceleration, feet or miles |

e | economy of energy usage, W-hrs/mi |

E | voltage, Volts |

f | frequency of applied stator voltage, Hz |

g_{c} | a constant for use with English System of Units: 32.174 lb_{m}-ft/#-sec^{2} |

G_{o} | initial value of the acceleratinq G-force, #/lb_{m} |

I | current, Amperes |

n | motor efficiency |

n_{c} | controller efficiency |

n_{m} | mechanical drivetrain efficiency |

N | synchronous rotational speed of magnetic field, rpm |

p | Peukert's constant for the battery system |

p_{n} | number of magnetic poles of the stator of an induction motor |

P_{d} | power component ascribed to aerodynamic drag, Watts |

P_{i} | power input to the induction motor, Watts |

P_{o} | power output of the motor, Watts |

P_{r} | rated power of the electric motor, Watts or kW |

r | rolling force, #/lb_{m} |

r_{0} | initial value of the rolling force ( V = 0), #/lb_{m} |

R | radius of the tire/wheel combination, ft or inches |

R_{b} | resistance of the battery pack, Ohms |

S | motor speed under load, rpm |

t | time, seconds or hours |

V | velocity, ft/sec or mph |

V_{f} | final velocity or top speed, ft/sec or mph |

W | weight of the vehicle, pounds (lb_{m}) |

&rho (rho) | air density @ standard pressure and temperature: 0.0745 lbm/ft^{3} |

The analysis uses the English System of Units. In this system an ambiguity exists in that the word “pounds” is used to designate both force and mass. To distinguish between force and mass, force is labeled “#”; mass is labeled “lb

_{m}”. The relation between force and mass is embodied in Newton's Law:

force = mass x acceleration

To satisfy the requirement of consistency of units in the English Units System, weight in pounds must be converted to mass units by introducing a conversion constant: “g

_{c}”. Then, Newton's Law becomes (ESU)

force, # = [(W, lb

_{m})/g

_{c}] x (a, ft/sec

^{2})

The value of the constant is determined by considering a pound mass is placed on a spring scale.

By Newton’s Law, the value of “g

_{c}” is found as

g

_{c}= 32.174 lb

_{m}-ft/#-sec

^{2}

( The numerical value is identical to the acceleration induced by Earth's gravity.)

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