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Mechanical Engineering ME 481 Vehicle Design Fall 2000

Lecture Notes

By Richard B. Hathaway, Ph.D., PE Professor Mechanical and Aeronautical Engineering

Section 1 Energy Consumption and Power Requirements in Design

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Aerodynamics and Rolling Resistance
GENERAL FORMULAS - AERODYNAMIC Dynamic Pressure:

Pd
Drag Force:

1  v2 2
1  v 2 A f ( RE ) 2

Fd

FdAero Power

1  v 2 Cd A 2

Fd

1 (1.2) Cd A ( v  v0 ) 2 2

P=
Cd = A= v= coefficient of drag projected frontal area (m2) vehicle velocity (m/sec)

 3 V A f(RE) (2)
f(RE) V0 =  = air density  1.2 kg/m3 = Reynolds number headwind velocity

ENGLISH UNITS
-6 3 HP aero = (6.93 X 10 ) C d A V

where: A = area (ft2)

V = velocity (MPH)

Cd = drag coefficient

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SIUNITS

     1 kW  1 .2  V 3  PKW = Cd A  3  1000 W   (2)   3600          1000  
-6 P aero = (12.86 x 10 ) x C d A V (V  V0 ) 2

P V Cd

= power (kw) = velocity (KpH) = drag coefficient

A V0 

= area (m2) = headwind velocity = 1.2 kg/m3

GENERAL FORMULAS – ROLLING RESISTANCE
ENGLISH UNITS

HPrr = Crr W x

V 375
W = weight (lbs) V = velocity (MPH)where: Crr = coefficient of rolling resistance
SI UNITS

 9.81   x C rr x M x V Prr =   3600  Prr = (2.72 x 10- 3 ) x C rr x M x V
where: P
M = power (kw) = mass (kg) Crr V = coefficient of rolling resistance = velocity (KpH)

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TRACTIVE FORCE REQUIREMENTS.
Vehicles require thrust forces, generated at the tires, to initiate and maintain motion. These forces are usually referred toas tractive forces or the tractive force requirement. If the required tractive force (F) is broken into components the major components of the resisting forces to motion are comprised of acceleration forces (Faccel = ma & I forces), Gradeability requirements (Fgrade), Aerodynamic loads (Faero) and chassis losses (Froll resist ). F = Faero + Froll resist + Fgrade + Faccel = (/2) Cd A v2 + Crr m g+ %slope m*g + m a = (/2) Cd A v2 + m g{Crr + % slope + a/g} in SI units: A = frontal area (m2) v = velocity (m/s) m = Crr = coefficient of roll resistance (N/N) usually approx .015 Cd = coefficient of aero drag for most cars .3 - .6 % slope = Rise/Run = Tan of the roadway inclination angle Steady state force are equal to the summation of Faero + Froll resist + Fgrade Fss   Faero  Frollresist  Fgrade 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) requirements, including steady state acceleration. VEHICLE ENERGY REQUIREMENTS. The energy consumption of a vehicle is based on the tractive forces required, the mechanical efficiency ofthe drive train system, the efficiency of the energy conversion device and the efficiency of the storage system. Examples of the above might best be demonstrated with the following. Storage efficiency: A flywheel used for energy storage will eventually lose its total energy stored due to bearing and aerodynamic losses. A storage battery may eventually discharge due to intrinsic losses in thestorage device. These losses can be a function of the % of the total system capacity at which the system is currently operating. A liquid fuel usually has extremely high storage efficiency while a flywheel may have considerably les storage efficiency. Both however have the storage efficiency a function of time. mass (kg)

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 E fianl  E  x 100 Storge Efficiency  store   initial  Einitial  

Conversion efficiency: An internal combustion engine changes chemical energy to mechanical energy. The system also produces unwanted heat and due to moving parts has internal friction which further reduces the system efficiency. A storage battery has an efficiency loss during the discharge cycle and an efficiency loss during the charge cycle. These efficiencies may be a function of the...