Resistance Forces on A Vehicle P M V Subbarao Professor Mechanical Engineering Department Estimation of Vehicle Demands ….

Resistance Forces on A Vehicle The major components of the resisting forces to motion are comprised of : Acceleration forces (F accel = ma & I  forces) Aerodynamic loads (F aero ) Gradeability requirements (F grade ) Chassis losses (F roll resist ).

Force System on A Rolling Wheel

Road Conditions & Rolling Resistance 4

Rolling Resistance Composed primarily of 1.Resistance from tire deformation (  90%) 2.Tire penetration and surface compression (  4%) 3.Tire slippage and air circulation around wheel (  6%) 4.Wide range of factors affect total rolling resistance The magnitude of this force is Approximated as: Rolling resistance of a vehicle is proportional to the component of weight normal to the surface of travel

Standard Formula for Rolling Resistance where: P= power (kW) Crr= coefficient of rolling resistance M= mass (kg) V= velocity (KpH)

Contact Type C rr Steel wheel on rail Car tire on road Car tire energy safe Tube 22mm, 8 bar0.002 Race tyre 23 mm, 7 bar0.003 Touring 32 mm, 5 bar0.005 Tyre with leak protection 37 mm, 5 bar / 3 bar / 0.01 Typical Values of Coefficient of Rolling Resistance

Effect of Road Condition on C rr 8

Rolling Resistance And Drag Forces Versus Velocity

Grade Resistance Composed of –Gravitational force acting on the vehicle For small angles, θgθg mg θgθg Fg

Total Vehicular Resistance at Constant Velocity AR = air resistance [N] RR = rolling resistance [N] GR = gradient resistance [N] TR = total resistance [N]

Resistance Vehicle Speed Steady State Demand Curve

Vehicle Speed vs. Engine Speed V =velocity, km/hr r =wheel radius, m N crank =crankshaft rpm i =driveline slippage GOGO =Overall gear reduction ratio

Typical Engine Torque-Power SS

Steady State Demand Vs Available Effort 15

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 (F I  ) and the translational mass (F ma ). If rotational mass is added to a translating vehicle, it adds not only rotational inertia but also translational inertia.

Inertial Resistance 17 where: F IR = inertia resistance [N] m eff-vehicle = Vehicle mass + Equivalent mass of rotating parts [kg] a = car acceleration [m/s 2 ], (from 0 to 100 km/h in: 6 s (4.63 m/s 2 ), 18 s (1.543 m/s 2 )) m vehicle = Vehicle mass [kg] m eq = Equivalent mass of rotating parts [kg]

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 = angular accelerationk = radius of gyration Equivalent Mass of Rotating Parts Torque due to any rotating part (ex. Wheel) wheels and axles = 78% of total polar inertia propeller shaft = 1.5% Engine = 6% Flywheel and clutch =14.5%

Therefore the equivalent mass of all rotational parts including losses is represented as:

Required Torque & Power at Wheels Tractive Effort demanded by a vehicle):

Vehicle Dynamics Model

Transmission System Model

Torque Requirements Model

Engine Model

Pune Urban Drive Cycle

Engine RPM during Urban Driving Cycle

Engine Fuel Consumption During Urban Driving Cycle

Kinetic Energy Available during Braking per Driving Cycle kJ

Inertial Energy in A Sub Cycle Duration : 450 to 475 sec Time in seconds Inertial Energy, J

Inertial Energy in A Sub Cycle Duration :1105 to 1139 sec

Fuel Savings due to Idling Logic

Idling Engine During Braking : Fuel Consumption

Fuel Consumption over Pune Drive Cycle

Braking Methods Vs Fuel Economy A planned gradual stop, say at a traffic light where you would prefer saving fuel over engine braking - you may press the clutch and / or shift to neutral and brake simultaneously. Caveat - if you are using fuel cut-off, you need not shift to neutral or press clutch. Just use clutch to avoid engine stalling. Slowing down to slightly lower speeds, say while abandoning an overtaking maneuver - Clutch is not required as long as you don't drop too low on engine speed. Panic braking from high speed to stop or very slow speed - don't touch the clutch even if you risk stalling the engine and use maximum engine braking.

Stop-and-go braking like in bumper to bumper traffic - press clutch and brake to avoid engine stalling. Track / rally circuit - brakes first and eyes on tachometer. As soon as you close on in-gear idle (which you should know better than your birthday if you are racing), press the clutch and downshift gears. Re-engage clutch as soon as you have finished shifting. Coasting downhill - brakes first and use clutch only to shift gears.

Braking Vs Safety The driver is trying to achieve two things by braking Slow down the vehicle or bring it to stop within a desirable time span so that everyone is safe As long as the first one is achieved, avoid engine stall If you do not apply clutch while braking, vehicle gets more braking assistance due to engine resistance.

You are trying to slowdown the vehicle from say 80kmph or more for a normal stop At 80kmph or more you would normally be driving in top gear. Your engine is not going to stall in the same gear till you come down to say 40kmph. In this case apply brake without clutch till you reach that speed and then move to the lower gear(usually 4th) and release the clutch. Keep braking till you reach around 25 kmph and apply clutch and bring the vehicle to stop. The second part is applicable if you were driving at less than say 50kmph. You don't need to change the gear. Keep applying the brakes and apply clutch when you feel engine running too slow.

Emergency stop/slowdown at any speed Just apply brake without clutch. You need maximum braking even at the cost of engine stalling. Even if you are at a very high speed (100kmph or more), lowering the gear is not a great idea. Disengaged clutch (even if it is for very short duration) would lower your total braking effectiveness.

Driving downhill Lower the gear to a comfortable one (usual theory advises the same gear in which you would go uphill at the same place. However my experience say it would be too slow, you may want to run in the next higher gear) and apply brakes without clutch. This will help to avoid over heating of your brakes.

Braking N Safety In general, if we're talking normal driving situations the rule of thumb you should follow is to keep the car in gear for the most amount of time. Downshifting is good, but most people do not downshift when stopping. This can either just be laziness, but it's also driven by the fact that when you need to slow down reasonably fast you might just not have enough time to row through the gears. Best way to do is, brake in gear until the car about the slowest speed for whatever gear it is in, then clutch in, go into neutral and keep braking further.