# a) Maximum power available at the back wheel

Automotive Assignment3

a)Maximum power available at the back wheel

=Engine power x Drivetrain efficiency = 57KW x (1 – 0.05) = 54.15KW

b)Theoretical maximum speed of mph on level ground

Itinvolves balancing of power at the rear wheels with losses

54.15KW= Drag force + Rolling resistance +Power into hills

DragForce x Velocity = Drag power loss, From Drag = ½ (density x Cdx Area x Velocity2x Velocity)

Also,Rolling resistance power = Rolling resistance x Velocity

Powerinto hills = 0, on the level ground

TheMax power is therefore given by (½ x air density x area) x Velocity3+ Rolling resistance x velocity + 0

Solvingthis equation give theoretical maximum speed as 38.1m/s or 85.22mph

c)Theoretical maximum speed of mph in 1 in 16 hill

Theprocess above is repeated, but the power loss due to climbing is notzero

Energyuphill = Mass x gravity x height

Poweruphill = mass x gravity x change in height per unit time

Forcedue to gravity on the slope = mass x gravity x 1/6 = 1274N

Usingthe relationship established in (b) above, the max speed uphill isobtained as 26.3m/s or 58.83mph

d)The maximum tractive force that each of the rear tires could provideunder acceleration before slipping occurs.

Tractiveforce = coefficient of friction x downward force

=60%x 1300 x 9.8 = 7644N

e)Maximum usable tractive force at each of the rear tires if full powerwas applied at 30mph

Thisforce will be the minimum of ( force due to engine power, tire force)

=Min (54.15/30, 7644)

=Min (4041N, 7644) = 4041N

f)Wind resistance at 30mph

=½ x density x Cdx area x Velocity2

=0.5 x 1.2 x 0.8 x 2.5 x 13.4=215N

g)Acceleration at 30 mph

F=Ma

Netimpulse force = Tractive force –drag force – rolling resistance

7644N– 215N – 150N= 7276N

Acceleration=7276/1300 = 5.6m/s2

h)Acceleration at 30mph up a 1 in 6 hill

Netimpulse force = Tractive force –drag force – rolling resistance –weight due to gravity

=5976N and acceleration = 4.6m/s2

References

RAJAMANI,R. (2012). Vehicledynamics and control.New York, Springer.

PACEJKA,H. B., &amp BESSELINK, I. (2012). Tireand vehicle dynamics.Oxford, UK, Butterworth-Heinemann.http://www.books24x7.com/marc.asp?bookid=47135.