Energy Consumption & Power Requirements of A Vehicle

P M V SubbaraoProfessor

Mechanical Engineering Department

Know the Requirements Before You develop an Engine…..

Resistance Force : Ra

• The major components of the resisting forces to motion are comprised of :

• Aerodynamic loads (Faero) • Acceleration forces (Faccel = ma & I forces)• Gradeability requirements (Fgrade)• Chassis losses (Froll resist ).

grraero FFFmaF

Aerodynamic Force : Flow Past A Bluff Body

Composed of:1. Turbulent air flow around vehicle body (85%)2. Friction of air over vehicle body (12%)3. Vehicle component resistance, from radiators and air

vents (3%)

Aerodynamic Resistance on Vehicle

2

21 VPd

(Re)21 2 fAVFd

ACVF dd2

21

20, )()2.1(

21 VVACF ddesignd

VF = P designd ,

Dynamic Pressure:

Drag Force:

Aero Power

Cd =

coefficient of drag

=

air density 1.2 kg/m3

A =

projected frontal area (m2)

f(Re)

= Reynolds number

v =

vehicle velocity (m/sec)

V0 =

head wind velocity)(862 0

2VV V A C )10 .(1 = P d-6

aero

P

= power (kw)

A = area (m2)V

= velocity (KpH)

V0 = headwind velocityCd

= drag coefficient

= 1.2 kg/m3

Purpose, Shape & Drag

Shape & Components of Drag

Some examples of Cd:

• The typical modern automobile achieves a drag coefficient of between 0.30 and 0.35.

• SUVs, with their flatter shapes, typically achieve a Cd of 0.35–0.45. • Notably, certain cars can achieve figures of 0.25-0.30, although sometimes

designers deliberately increase drag in order to reduce lift.• 0.7 to 1.1 - typical values for a Formula 1 car (downforce settings change for

each circuit) • 0.7 - Caterham Seven • at least 0.6 - a typical truck • 0.57 - Hummer H2, 2003 • 0.51 - Citroën 2CV • over 0.5 - Dodge Viper • 0.44 - Toyota Truck, 1990-1995

• 0.42 - Lamborghini Countach, 1974 • 0.42 - Triumph Spitfire Mk IV, 1971-1980 • 0.42 - Plymouth Duster, 1994 • 0.39 - Dodge Durango, 2004 • 0.39 - Triumph Spitfire, 1964-1970 • 0.38 - Volkswagen Beetle • 0.38 - Mazda Miata, 1989 • 0.374 - Ford Capri Mk III, 1978-1986 • 0.372 - Ferrari F50, 1996 • 0.36 - Eagle Talon, mid-1990s • 0.36 - Citroën DS, 1955 • 0.36 - Ferrari Testarossa, 1986 • 0.36 - Opel GT, 1969 • 0.36 - Honda Civic, 2001 • 0.36 - Citroën CX, 1974 (the car was named after the term for drag

coefficient) • 0.355 - NSU Ro 80, 1967

• 0.34 - Ford Sierra, 1982 • 0.34 - Ferrari F40, 1987 • 0.34 - Chevrolet Caprice, 1994-1996 • 0.34 - Chevrolet Corvette Z06, 2006 • 0.338 - Chevrolet Camaro, 1995 • 0.33 - Dodge Charger, 2006 • 0.33 - Audi A3, 2006 • 0.33 - Subaru Impreza WRX STi, 2004 • 0.33 - Mazda RX-7 FC3C, 1987-91 • 0.33 - Citroen SM, 1970 • 0.32064 - Volkswagen GTI Mk V, 2006 (0.3216 with ground effects) • 0.32 - Toyota Celica,1995-2005 • 0.31 - Citroën AX, 1986 • 0.31 - Citroën GS, 1970 • 0.31 - Eagle Vision • 0.31 - Ford Falcon, 1995-1998 • 0.31 - Mazda RX-7 FC3S, 1986-91 • 0.31 - Renault 25, 1984 • 0.31 - Saab Sonett III, 1970 • 0.30 - Audi 100, 1983 • 0.30 - BMW E90, 2006 • 0.30 - Porsche 996, 1997 • 0.30 - Saab 92, 1947

• 0.195 - General Motors EV1, 1996 • 0.19 - Alfa Romeo BAT Concept, 1953 • 0.19 - Dodge Intrepid ESX Concept , 1995 • 0.19 - Mercedes-Benz "Bionic Car" Concept, 2005 ([2]

mercedes_bionic.htm) (based on the boxfish) • 0.16 - Daihatsu UFEIII Concept, 2005 • 0.16 - General Motors Precept Concept, 2000 • 0.14 - Fiat Turbina Concept, 1954 • 0.137 - Ford Probe V prototype, 1985

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 resistance5. Simplifying approximation:

WCF rrrr

ROLLING RESISTANCE

V M C )10 (2.72 = P

V M C 36009.81 = P

rr3-

rr

rrrr

where:

P

= power (kW)

Crr

= coefficient of rolling resistance

M

= mass (kg)

V

= velocity (KpH)

Rolling resistance of a body is proportional to the weight ofthe body normal to surface of travel.

MgFrr

147101.0 VCrr

Contact Type 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

Grade Resistance

Composed of – Gravitational force acting on the vehicle

gg WF sin

gg tansin

gg WF tanGg tan

WGFg

For small angles,

θg W

θg

Fg

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 translational mass (Fma). • If rotational mass is added it adds not only rotational

inertia but also translational inertia.

ra = k m = I =

dtd I = T

tire

vehiclewheelwheel

2wheeli

a r

k m = r

a k m = rT = F 2

tire

222

2tire

2

tire

ii

= angular acceleration k = radius of gyration t = time T = Torque

m = mass = ratio between rotating component and the tire

Transient Force due to Rotational Mass

Therefore if the mass rotates on a vehicle which has translation,

a m + mr

k = F tr2tire

22

i t&r

m +

r

k m a + Slope% + C gm + V A C = F t2tire

22

rrrt2

dtire

2

Resistance power, Presistance V FP tireceresis tan

P resi

stan

ce

Vehicle Speed

Power Demand Curve

Gr F = T tiretire

PE

)( r G

RPM = hkm tirePE 377.0/

The Powering Engine Torque is:

The speed of the vehicle in km/h is:

rtire = Tire Rolling Radius (meters)

G = Numerical Ratio between P.E. and Tire

Ideal capacity of Powering Engine: kWNTP PEPE

600002

Ideal Engine Powering Torque

Drive System Efficiency

• Drive train inefficiencies further reduce the power available to produce the tractive forces.

• These losses are typically a function of the system design and the torque being delivered through the system.

actual

PEdrivemech P

PEfficiencyMechanical

nredredreddrivemech ......21

Actual Capacity of A Powering engine

kWNTPPmech

PE

mech

PEactual

600002

auxtyre

tyretyrePE PkWN

rFP

600002

Correction for Auxiliary power requirements:

MATLAB for Vehicle Torque Requirement

MATLAB Model for Transmission System

MATLAB Model for Engine Performance

Engine Characteristic Surface

Requirements of Vehicle on Road & Engine Power

Urban Driving Cycle

Engine RPM during Urban Driving Cycle

Engine Fuel Consumption During Urban Driving Cycle

Inverse of Carnot’s Question

• How much fuel is required to generate required power?• Is it specific to the fuel?• A Thermodynamic model is required to predict the fuel

requirements.• Carnot Model• Otto Model• Diesel Model• A Geometric Model is required to implement the

thermodynamic model.