PhD Thesis - Cranfield University

Chapter 4
where sgn[vxT] is a the signum function of the vehicle tangential velocity, vxT and is given
as,
⎧1
if v xT ≥ 0
sgn[ v xT ] = ⎨
(4.5)
⎩ − 1 if v xT ≤ 0
C 0 and C 1 are rolling resistance coefficients. Typical values of C 0 ranges between 0.004 and
0.002 [1], while typical C 1 values are several magnitudes less than C 0.
Aerodynamic Drag Force, F AD
The aerodynamic drag force, F AD acting on a vehicle is due to the viscous friction of the
surrounding air acting on the vehicle surface and the pressure distribution induced by the
downwash of trailing vortices behind the vehicle. The force opposes the motion of the
vehicle and is influenced by the frontal area, shape and protrusions of the vehicle shell
design. As there are multiple factors that contribute to this resistive force, it is commonly
approximated using a prismatic vehicle body with a frontal area. The stagnation pressure
caused by the product of the frontal area and ambient air density is multiplied by a constant
drag coefficient. The total aerodynamic drag force is then expressed to include the vehicle
and headwind velocity as,
2
{ } ( 5 . 0 v A C +
FAD xT
D F xT
] sgn[ v
v = ρ (4.6)
0 )
where ρ is the air density in kg/m 3 , C D is the aerodynamic drag coefficient, A F is the vehicle
equivalent frontal area in m 2 , vxT and v 0 are the vehicle tangential velocity and head wind
velocity respectively and are in m/s. The air density parameter ρ is temperature, altitude
and humidity dependent. However, a value of 1.25kg/ m 3 for ρ is typical. For accurate
values of the aerodynamic drag C D , the use of wind tunnels or CFD simulations are
required. Typical figures of C D for passenger vehicles ranges from 0.19 to 0.3 [95] and 0.8 to
1.5 for larger vehicles such as busses and trucks [2].
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