A vehicle of the following data is equipped with a 4-speed AT. The ratios are: 2.84(1"), 1.60(2), 1.0(3),

0.7(4th). The final drive ratio is 2.84. The torque converter has the characteristics as shown. The engine

WOT output torque is also shown. The vehicle is being driven on level ground in the first gear with the

torque converter unlocked.

a) Present the differential equation system with the initial condition for the WOT performance simulation

model of the vehicle in the first gear. Assume the vehicle is launched at engine idle RPM.

b) Determine the engine angular acceleration and vehicle acceleration when the vehicle is just launched

from stand still.

c) Starting from time zero and using a step size of t-0.2, solve the differential equation system for one

step, i.e., find the engine RPM and vehicle speed 0.2 second after launch.

Vehicle Data

Front axle weight: 1290 lbs

Center of gravity height: 18 inch

Air drag coefficient: 0.31

Tire radius: 10.0 in.

Powertrain efficiency: 0.92

Torque 250

(ft.Ib)

200

150

100-

50

TORQUE RATIO

..

.6

1000

K CAPACITY FACTOR

100

180

260

240

330

200

100

160

140

120

100

2:

60

40

0

torque

Rear axle weight: 1240 lbs.

Wheelbase: 100 in.

Frontal projected area: 20 square feet

Roll resistance coefficient: 0.02

Mass moment of inertia of engine-impeller: 0.3 lbs.ft²

Max. Torque

TORQUE RATIO

Max. Power

IMPELLER SPEED

EFFICIENCY

2000 3000 4000 5000 6000 7000

PERFORMANCE BASED ON 300 LB. FT.

CONSTANT INPUT TORQUE

SPEED RATIO

.7

82228 29 2

100

10

60

30

20

1.0

PERCENT

EFFICIENCY

237.5 (HP)

190

142.5

95

Power

47.5

'Mex. Torqne:

3200

3000

RPM

2000

2500

Max. Powers

2400

2200

2000

1800

1600

1400

1200

1000

8:00

600

IMPELLER SPEED-RPM

400

200 HP at 5500RPM

199 ft.Mbat 3850RPM

0