Upgrade of the MGB Electric Sports Car

Analysis by Warren Winovich

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Acceleration. Acceleration is determined from the solution of the general equation of motion,.The solution gives velocity in term of time for the top speed and the characteristics of the vehicle that give the "time constant".

V/Vf = 1 - 2/(1 + e2t/c)

where Vf is the top speed, t is the time after starting, and c is the time constant of the electric car. The time constant is found from the initial acceleration and the final (top) speed. That is,

c = Vf / a0

In turn, the initial rate of acceleration is determined from the starting torque of the motor, the drive weight, tire radius, and the rolling force coefficient for zero velocity.

a0 = (gc) x G0 , ft/sec2

The "G-force", G0 is given by

G0 = (Tstart / WxR) - r0, #/lbm

The acceleration parameters shown above are derived from the specifications of the motor and electric car. These specifications are listed below.

starting torque, Ts112 #-ft
overall gear ratio, (G/R) 8:1
drive weight, W2635 pounds
tire/wheel radius, R0.958 foot
rolling force, r00.0075 #/lb
top speed, Vf55 mph (or, 80.67 ft/sec)

From these specifications, find:

G0 = (336/2635x0.958) - 0.0075 = 0.1256 #/lb

a0 = (32.174) x (0.1256) = 4.04 ft/sec2

c = (80.67)/(4.04) = 19.968 seconds

The relation for velocity as a function of time becomes:

V/Vf = 1 - 2/(1 + e2t/19.968), where Vf = 55 mph

The relation for distance in terms of time is found by the mathematical process of integration of the velocity equation in terms of time. (A final result of the process is given here to provide the quarter-mile time and final speed.)

Acceleration performance results.

0 to 30 mph12.218 seconds
0 to 50 mph30.397 seconds
quarter mile29.155s @ 49.37 mph

Comparison of quarter-mile time with that of other electric cars.

Modelquarter mile result
MGB sports car 6729.155s @ 49.37 mph (upgraded version)
MGB (lead-acid pack)29.437s @ 49.12 mph (drive wt: 2700 lbm)
Saturn coupe 9219.942s @ 70.45 mph (AC Propulsion make)
Th!nk Ford 0220.644s @ 56.72 mph (drag competition)
Toyota RAV 4 0421.914s @ 64.65 mph (drag competition)

All models are direct-drive transmissions. The motor ratings of the three commercial models are about 30 kW, continuous; and, the rating of the motor installed in the MGB sports car is 15 kW. The lower starting torque of the MGB electric car accounts for the lower quarter-mile time and speed.

The times to speed and distance for the MGB electric car are deemed quite adequate for normal driving conditions.

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