Fuel Cells
323
11.2 Power and Energy Requirements of the FCV
To assess the energy and power requirements of an electric automobile, it
is appropriate to quantitatively estimate the power and energy required for
driving a modern ICEV (Shukla 2005; Shukla, Aricò, and Antonucci 2001) as
follows. Neglecting relatively minor losses due to road camber and curvature, the power required at the drive wheel (P traction ) may be expressed as
,
P traction = P grade + P accel + P tires + P aero
(11.1)
where P grade is the power required for the gradient,
P accel is the power required for acceleration,
P tires is the rolling-resistance power consumed by the tire, and
P aero is the power consumed by aerodynamic drag.
The first two terms in Equation 11.1 describe the rates of change of potential
(PE) and kinetic (KE) energies associated during climbing and acceleration,
respectively. The power required for these actions may be estimated from
the Newtonian mechanics as follows:
P grade = d(PE)/dt = Mgν sinθ,
(11.2)
and
P accel = d(KE)/dt = d(1/2Mν 2 )/dt = Mav.
(11.3)
In Equations 11.2 and 11.3, M is the mass (kg) of the car, v its velocity (m/s),
a its acceleration (m/s 2 ), and tanθ is the gradient. The potential and kinetic
energies acquired by the car as a result of climbing and acceleration represent
reversibly stored energies and, in principle, may be recovered by appropriate regenerative methods wherein the mechanical energy is converted and
stored as electrical energy.
The last two terms in Equation 11.1 describe the power required to overcome tire friction and aerodynamic drag that are irreversibly lost, mainly as
heat and noise and cannot be recovered. The power required here may be
estimated from the following empirical relations:
P tires = C t Mgν,
(11.4)
and
P = 0.5dC A(v + w) 2 v.
(11.5)
aero
a
In Equations 11.4 and 11.5, C t and C a are dimensionless tire friction and
aerodynamic drag coefficients, respectively, d the air density (kg/m 3 ), w the
323
11.2 Power and Energy Requirements of the FCV
To assess the energy and power requirements of an electric automobile, it
is appropriate to quantitatively estimate the power and energy required for
driving a modern ICEV (Shukla 2005; Shukla, Aricò, and Antonucci 2001) as
follows. Neglecting relatively minor losses due to road camber and curvature, the power required at the drive wheel (P traction ) may be expressed as
,
P traction = P grade + P accel + P tires + P aero
(11.1)
where P grade is the power required for the gradient,
P accel is the power required for acceleration,
P tires is the rolling-resistance power consumed by the tire, and
P aero is the power consumed by aerodynamic drag.
The first two terms in Equation 11.1 describe the rates of change of potential
(PE) and kinetic (KE) energies associated during climbing and acceleration,
respectively. The power required for these actions may be estimated from
the Newtonian mechanics as follows:
P grade = d(PE)/dt = Mgν sinθ,
(11.2)
and
P accel = d(KE)/dt = d(1/2Mν 2 )/dt = Mav.
(11.3)
In Equations 11.2 and 11.3, M is the mass (kg) of the car, v its velocity (m/s),
a its acceleration (m/s 2 ), and tanθ is the gradient. The potential and kinetic
energies acquired by the car as a result of climbing and acceleration represent
reversibly stored energies and, in principle, may be recovered by appropriate regenerative methods wherein the mechanical energy is converted and
stored as electrical energy.
The last two terms in Equation 11.1 describe the power required to overcome tire friction and aerodynamic drag that are irreversibly lost, mainly as
heat and noise and cannot be recovered. The power required here may be
estimated from the following empirical relations:
P tires = C t Mgν,
(11.4)
and
P = 0.5dC A(v + w) 2 v.
(11.5)
aero
a
In Equations 11.4 and 11.5, C t and C a are dimensionless tire friction and
aerodynamic drag coefficients, respectively, d the air density (kg/m 3 ), w the