Silicon Productions

The MGB Electric Sports Car

__Analysis by Warren Winovich__Page 3

The procedure for calculating the performance of electric cars has been applied to that for the MGB electric sports car. The basic steps are out-lined below. (Symbols used below are defined in an Appendix, p. 7)

First, the motor output is found by applying efficiency corrections for the mechanical drivetrain and controller/inverter to the power demand 'at the wheels’ The power demand at the wheels is the sum of the aerodynamic drag component and the rolling force component. Drag power component is the product of the dynamic pressure of the flow, the drag coefficient of the vehicle, the cross section area, and the velocity. This component is expressed as:

P

_{d}= (dynamic pressure) x (C

_{D}) x A x V

The dynamic pressure of the on-coming flow is simply the kinetic energy of the air mass that impacts the vehicle. Fluid dynamics derivations define it as:

dynamic pressure = ½ x (air density) x (velocity)

^{2}

dynamic pressure = ½ x &rho x V

^{2}

On combining expressions, the power component ascribed to aerodynamic drag is:

P

_{d}= ½ x &rho x CD x A x V

^{3}

The component of power at the wheels from rolling resistance is the product of the rolling force factor, the vehicle driving weight, and the velocity.

P

_{r}= [r

_{o}x (1 + (V,mph/90)

^{2}] x W x V

Note that the rolling force component includes a centrifugal pumping part of air entrained by the rotatinq tire/wheel combination. The "pumping" effect causes the rollinq force to double at a velocity of 90 mph. At a highway cruise speed of 50 mph, the rolling force increases by 31%.

The total power at the wheels is the sum of the two components.

P = P

_{d}+ P

_{r}= ½ &rho C

_{D}A V

^{3}+ r

_{o}[1 + (V,mph/90)

^{2}]WV

The drag component varies as the cube of the velocity; and this places an emphasis on the values of the dray coefficient and cross section area of the car's shape.

Motor output is obtained by applying efficiency factors for the drivetrain and the inverter/controller, That is.

P

_{o}= P/( n

_{m}x n

_{c})

Motor input is required to specify the current draw from the battery pack at the particular velocity value. Motor input is found from motor output value and motor efficiency,

P

_{i}= P

_{0}/n

Motor efficiency varies with motor output as determined by the inherent losses. It increases from zero at the no-load operation up to a maximum at the rated load and, for loads above rated load, it decreases. A representative model for the efficiency of the 15-kW induction motor is based on observations of the loss mechanisms. Typical no-load power is about 10 percent of rated power and represents total losses. For motors with service factors between 1.1 and 1.2 (the typical range), the motor efficiency remains relatively constant. At power ratios below 80% and above 120 %, losses vary with power output raised to the 5/2 power exponent. This efficiency model gives power input.

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