Resistances to vehicle motion &

Need for a gearbox

K.G.MaheswaranK.G.Maheswaran

Physics rule of motion

• Object is in static status

It needs a larger force to overcome friction

• Object starts moving• Object starts moving

the needed driving force becomes smaller and smaller, and the speed becomes faster and faster

Single stage gear reducer.

Engines need to operate at a relatively high rotational speed, which is inappropriate for starting, stopping, and slower travel.

The transmission reduces the higher engine speed to the slower wheel speed, increasing torque in the process

A diagram comparing the power and torque bands of a "torquey" engine versus a "peaky" one

When we are to roll from standstill, we need torque(force) to move the vehicle.

In this case we want our 1st gear (the largest in size,also the ‘torque-giving’ gear) to provide us increasedtorque by converting the extra engine speed into force.

As we go faster, the load increases on gear as it’s madeto rotate faster but it’s not designed for it. It getsstressed, engine growls and we push 2nd gear which issmaller and faster. This way we go on as speedincreases because beyond a certain limit, the gearboxcannot bear the increased rotation and we keep ontransferring the role to next gear

Resistance to motion

Resistance a vehicle faces while attempting to move from a stall condition or while accelerating

To sustain motion-This resistance must be overcome by the powerplant of the engine

Power produced < Resistance to motionPower produced < Resistance to motionVehicle will gradually slow down.

We must have experienced the slowing down of bicycles if we stop pedaling.

The bicycle also slows down if we go uphill or if wind blows from front. A poorly inflated tire also causes the vehicle to groan more and slow down. These are the resistances that force the vehicle to slow down under their effect.

Broadly the resistances can be categorized into the following categories:Aerodynamic dragGradient resistanceRolling resistanceInertiaAll the above produce a restraining force working against the tractiveforce. The tractive force must be greater than or equal to the resistive forces in order to maintain a sustainable motion. We can balance them as

F = F = F + F + F + FF = F req = FA + FG + FR + FI

whereFA= Force due to air resistanceFG = Force due to gradient of a slopeFR = Force due to rolling resistanceFI = Force due to moving or static inertia

The last one FI comes into the picture only when the vehicle accelerates or decelerates, while the first three always offer a resistance even when the vehicle is moving at a constant speed

Air resistance/ Aerodynamic drag:When a body travels within a dense medium, the molecules of themedium collide with the moving object and thereby absorb some ofthe energy. This is felt as a resistance to the moving object. If themedium is denser, then the resistance is more. Also when theobject moves at a faster speed, the resistance increasesproportionately. Mathematically it can be expressed as:

FA = Cd × A × V²

whereCd = Co−efficient of drag

= 0.6A = Frontal Area Of VehicleV = Velocity of the vehicle

AERODYNAMIC LIFT

Flow seperation and reattachement

AFTER FLOW WAKE

CD for various shapes of truck leading edges

• When the vehicle travels uphill, a component of its weightworks in a direction opposite to its motion.

• If some energy is not supplied to overcome this backwardforce, then the vehicle would slow down, stall and roll

Gradient resistance:

force, then the vehicle would slow down, stall and rollbackwards.

• If the vehicle is trading uphill at a slope of θ, then theweight of the vehicle, W has two components: oneperpendicular to the road surface (with a value W·Cosθ) and the other along the road surface (with a valueW·Sin θ).

• The component along the road surface is the one thattries to restrict the motion

The gradient resistance is given by: FG = W·Sin θ

θ

Rolling resistance• When a vehicle rolls, it rolls with its tires in contact with the road

surface

• Relative motion of two hard surfaces produces a friction.

• Further, neither the road, nor the tire are perfectly rigid. Hence, bothflex under the load slightly.flex under the load slightly.

• As there is a gradual deformation at the contact between the roadand the tire, greatest at the bottom most point and least at the entryand exit points, the slip of the tire w.r.t. the road produces anothertype of loss of energy which results in a resistance.

• Rolling resistance is composed of the following components:

• Tire Rolling resistance: FR,T

• Road rolling resistance: FR,Tr

• Resistance due to tire slip angle: FR,αR,α

• Resistance due to bearing friction and residual braking: FR,fr

• Hence the rolling resistance offered may be written as:

FR = FR,T + FR,Tr + FR,α + FR,fr

• The tire rolling resistance FR,T is a result of the resistance due to flexure of the tire, air resistance on the tire and friction of tire with the road. These three can be summed up and written as:up and written as:

FR,T = FR.T.flex + FR.T.A + FR.T.fr.

• In a simplified manner the total rolling resistance can be related to the vertical load on the wheels and can be written as:

Co−efficient of rolling friction, kR or Crr= FR/FZ.w

Contact Type KR OR Crr

Steel wheel on rail 0.0002...0.0010

Car tire on road 0.010...0.035

Car tire energy safe 0.006...0.009

Tube 22mm, 8 bar 0.002

Race tyre 23 mm, 7 bar 0.003

Touring 32 mm, 5 bar 0.005

Tyre with leak protection 37 mm, 5 bar / 3 bar 0.007 / 0.01

Rolling Resistance And Drag Forces Versus Velocity

Inertial or Transient Forces

• Transient forces are primarily comprised of acceleration related forces where a change in velocity is required.

These include:• The rotational inertia requirements (FI ) and the • The rotational inertia requirements (FI ) and the

translational mass (Fma).

• If rotational mass is added it adds not only rotational inertia but also translational inertia.

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Vehicle Speed