Welcome.
In this lecture, we start analyzing the forces acting
on a vehicle when it's driving with the purpose
to determine how much traction force the power train need
to produce.
We start by analyzing the rolling resistance
from the tires and the aerodynamic resistance,
as they are always present when the vehicle is driving.
Only the forces in the longitudinal direction
will be analyzed, since they influence the power train.
Forces in other directions are neglected,
as they mainly influence the steering and suspension.
When the vehicle is stationary on a flat road,
there is no longitudinal forces acting on the vehicle.
When the vehicle move forward, the tires
cause rolling resistance.
All the wheels have rolling resistance,
but for our analysis, it is sufficient to only analyze
the total rolling resistance force.
We choose to illustrate the rolling resistance force only
at the rear wheel in this picture.
The rolling resistance is 0 at standstill.
When the speed is non-zero, it can
be calculated as the rolling resistance coefficient
multiplied with the normal force between the vehicle
and the road.
The normal force is vehicle mass times
gravity times cosine for the road angle.
The rolling resistance is approximately
independent of speed, as shown in this diagram.
It changes slightly with road angle,
since the normal force decrease if the road becomes very steep.
The rolling resistance is always opposing the driving direction,
which means that it change sign when the driving is
in reverse direction.
The rolling resistance coefficient
should typically be as low as possible
to keep energy consumption low.
And it typically is only about 0.01.
Once the vehicle move a little faster,
there is also aerodynamic resistance,
which is caused by the air as it's
forced to flow around the vehicle when it's driving.
Aerodynamic forces occur all around the vehicle,
but here, we illustrate them as one concentrated force acting
on the rear of the vehicle.
The aerodynamic resistance mainly
is caused by higher air pressure in front
of the vehicle and lower pressure behind it.
When the vehicle speed increases,
more air has to pass the equal per second,
leading to higher aerodynamic drag force.
At the speed around 75 kilometer per hour,
the aerodynamic force is similar in size
to the rolling resistance for a typical car.
As the speed increase even further,
the aerodynamic force increases more and more quickly.
The aerodynamic resistance is 0 at standstill.
It can be calculated as the aerodynamic drag coefficient
times the front area of the vehicle times the air
density times the vehicle speed squared divided by 2.
The drag force increase with the square of the vehicle speed,
as is shown in this diagram.
It is opposing the driving direction
and it is independent of the road angle and the vehicle
mass.
The aerodynamic drag coefficient should be as low as possible
and typically is about 0.25 to 0.35 for a modern car.
For trucks and buses, it is higher--
about 0.7.
In this lecture, we have presented
two forces which are always present when
a vehicle is driving.
It is rolling resistance, which is rather
constant with the vehicle speed, and aerodynamic drag,
which increases with the square of the speed.
At low speed, rolling resistance is
bigger than aerodynamic drag.
And for a modern car, the aerodynamic resistance
is bigger, above roughly 70 kilometers per hour.
Before we go on to analyze the force needed for acceleration,
test what you have learned about rolling
resistance and aerodynamic resistance in the following
exercises.
Thank you for watching.