Silicon Productions

The MGB Electric Sports Car

__Analysis by Warren Winovich__Page 4

Power input allows for an intermediate step to determine the current draw from the battery pack. With an allowance for the resistance of the battery pack, the current is the quotient of the power input and the pack voltage.

I = P

_{i}/E

The discharge time for the battery pack is obtained from Peukert's discharge law. For the battery in the MGB electric car, discharge time (100 %, DOD) is:

t = (63/I)

^{1.183}, hours

The principle performance parameters for the electric car are found using the relations developed above.

economy, e = P

_{i}/V, W-hrs/mi

Range, R: = (V, mph) x (t, hrs). miles

Economy is shown in figure 5 for the MGB electric sports car as a function of velocity. ( Recall that the performance factors are for driving at steady speeds over level roads. ) Minimum (or “best” ) economy is found as 154 W-hrs/mi at 23 mph. Economy increases for speeds below 23 mph as motor efficiency falls to zero when power output decreases to the no-load condition. Above 23 mph, economy increases as aerodynamic drag becomes the dominant retarding force. The economy at a highway cruise velocity of 50 mph is 246 W-hrs/mi. This level of economy for highway driving is considerably higher than values measured for enclosed passenger cars. Typical economy values for electric cars are in the range of 170 - 190 W-hrs/mi for production and home-built electric cars. The high economy found here is attributable to the high drag coefficient of the open-roadster design. Economy can be lowered by including a hard top accessory for the MGB electric sports car.

Range between charging is usually the performance factor quoted by drivers of electric cars. Range between changing for the MGB electric sports car is shown in figure 6 as it varies with velocity. Maximum range is found as 46 miles at 20 mph for depth of discharge of 100%. For 60 % depth of discharge, maximum range is 28 miles. At highway velocity of 50 mph, range falls to only 20 miles for complete battery pack depletion. For 60 % depth of discharge, range on highways is 12 miles at 50 mph. By operating the MGB electric sports car to 60 % depth of discharge, a reserve distance of 8 to 14 miles ensures that a return to a home charging station is possible. Of more importance, however, is that long battery lifetime can be achieved when depth of discharge is 60 % - or less. In keeping with improvement in economy, range will be increased if the MGB is driven with a hard-top roof to lower aerodynamic drag. With a hard-top roof, range at 50 mph increases by 25 % - range at 60 % DOD becomes 16 miles, for example.

**Aside from range, the acceleration capability of electric cars to speed and distance is the most widely publicized performance factor. The electric car dragster community schedules regular drag-racing competitions under the auspices of the National Electric Drag Racing Association. Home-built electric car conversions, specially outfitted for dragster competitions with two-speed transmissions, have posted times for the quarter-mile below the so-called " 13-second" barrier.**

__Acceleration of the MGB electric sports car.__Acceleration performance for electric cars ( or any vehicle ) is predicted from the general solution of the non-steady equation of motion. The solution is given in terms of the velocity normalized to the final velocity as determined by the overall qear ratio and motor limits.

V/V

_{f}= 1 – 2/(1 +e

^{2t/c})

This is an exponential equation in which the final velocity, V

_{f}, is approached in an asymptotic fashion with time. For t = 3 x c (where “c” is the time constant of the vehicle ), the velocity is within ½ % of the final value; i.e., V/V

_{f}= 0.995.

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