Vehicle dynamics
1) An electrically driven road vehicle of mass 450kg has four wheels, of effective diameter
400mm, radius of gyration 125mm, and mass 9kg.The armature of the electric motor has a
mass of 65kg, a radius of gyration of 100mm, and rotates at 4 times the speed of the road
wheels. The rolling resistance to motion of the vehicle is to be assumed constant at
225N.Determine the acceleration of vehicle if it is allowed to run freely down a slope whose
inclination to the horizontal is sin-10.2. (0.91m/s2).
2) A motor vehicle has a mass of 1000kg and the moments of inertia of the road wheels and rear
axle are together 8.4kgm2. The effective diameter of the road wheels is 620mm. Find the
acceleration on the level at an instant when the engine output torque is 100Nm and the overall
speed reduction ratio is 14.Take the air and road resistance as 200N at this speed, and the
transmission efficiency as 88 per cent. (3.47m/s2)
3) A 10-t truck is driven at a steady speed of 40km/h on a level road, against a tractive resistance
of 200N/t. The wheels are 1.2m in diameter, the engine runs at 1800rev/min, and the
transmission efficiency may be taken as 0.85. Calculate the engine power and the gear ratio in
use, engine to wheels. With the throttle fully open and the engine giving three times this
power, at the same speed, estimate the maximum truck speed in km/h up a 10 0 slope, and the
gear ratio required. Under these conditions, what is the overall efficiency as a weight- lifting
machine? (26.15kW; 10.18;12.6km/h;32.3;76.1%)
4) A motor car, of total mass 1400kg, running in top gear at 55km/h, passes on to a rising of 1 in
20 at that speed. The road and other resistances may be taken as constant at 270N/t. With
conditions unchanged, the speed falls uniformly to 40km/h in a distance of 360m. An
intermediate gear is then engaged for which the speed ratio between the engine and the road
wheels is 9:1 and the transmission efficiency is 85%. The engine is then developing a torque
of 85Nm. Determine: (a) The tractive efforts before and after the gear change, given that the
road wheels are 750mm in diameter, (b) The time between the start of retardation and the
recovery of the original speed of 55km/h, and (c) The powers being developed by the engine
when the car is retarding and accelerating through 50km/h, given that the transmission
efficiency in top gear is 94%. (851N; 1.735kN; 36s; 12.56kW; 28.35kW)
5) A car has mass of 800kg, the moment of inertia of the wheels is 6.7kgm2 and that of the
engine parts is 0.2kgm2. The effective diameter of the road wheels is 620mm and the
maximum engine torque is 65Nm at an engine speed of 2000rev/min. The gear ratio is 13.5 to
1 and the engine is developing full torque at 2000rev/min. The efficiency of the transmission
is 88%. If the resistance to motion in N is given by R 135 0.09v2, where v is the speed in
km/h, find: (a) The road speed and (b) The acceleration of the car. (17.3km/h;1.935m/s2)
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1) An electrically driven road vehicle of mass 450kg has four wheels, of effective diameter
400mm, radius of gyration 125mm, and mass 9kg.The armature of the electric motor has a
mass of 65kg, a radius of gyration of 100mm, and rotates at 4 times the speed of the road
wheels. The rolling resistance to motion of the vehicle is to be assumed constant at
225N.Determine the acceleration of vehicle if it is allowed to run freely down a slope whose
inclination to the horizontal is sin-10.2. (0.91m/s2).
2) A motor vehicle has a mass of 1000kg and the moments of inertia of the road wheels and rear
axle are together 8.4kgm2. The effective diameter of the road wheels is 620mm. Find the
acceleration on the level at an instant when the engine output torque is 100Nm and the overall
speed reduction ratio is 14.Take the air and road resistance as 200N at this speed, and the
transmission efficiency as 88 per cent. (3.47m/s2)
3) A 10-t truck is driven at a steady speed of 40km/h on a level road, against a tractive resistance
of 200N/t. The wheels are 1.2m in diameter, the engine runs at 1800rev/min, and the
transmission efficiency may be taken as 0.85. Calculate the engine power and the gear ratio in
use, engine to wheels. With the throttle fully open and the engine giving three times this
power, at the same speed, estimate the maximum truck speed in km/h up a 10 0 slope, and the
gear ratio required. Under these conditions, what is the overall efficiency as a weight- lifting
machine? (26.15kW; 10.18;12.6km/h;32.3;76.1%)
4) A motor car, of total mass 1400kg, running in top gear at 55km/h, passes on to a rising of 1 in
20 at that speed. The road and other resistances may be taken as constant at 270N/t. With
conditions unchanged, the speed falls uniformly to 40km/h in a distance of 360m. An
intermediate gear is then engaged for which the speed ratio between the engine and the road
wheels is 9:1 and the transmission efficiency is 85%. The engine is then developing a torque
of 85Nm. Determine: (a) The tractive efforts before and after the gear change, given that the
road wheels are 750mm in diameter, (b) The time between the start of retardation and the
recovery of the original speed of 55km/h, and (c) The powers being developed by the engine
when the car is retarding and accelerating through 50km/h, given that the transmission
efficiency in top gear is 94%. (851N; 1.735kN; 36s; 12.56kW; 28.35kW)
5) A car has mass of 800kg, the moment of inertia of the wheels is 6.7kgm2 and that of the
engine parts is 0.2kgm2. The effective diameter of the road wheels is 620mm and the
maximum engine torque is 65Nm at an engine speed of 2000rev/min. The gear ratio is 13.5 to
1 and the engine is developing full torque at 2000rev/min. The efficiency of the transmission
is 88%. If the resistance to motion in N is given by R 135 0.09v2, where v is the speed in
km/h, find: (a) The road speed and (b) The acceleration of the car. (17.3km/h;1.935m/s2)
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