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B. Arizmendi et al.
corresponding increase in power consumption is expected. The limitation of these
effects is crucial in the critical flight stages, which include take off, approaching,
and landing. In critical missions, the limitation of thrust available can cause severe
concerns and may not suffice to satisfy regulated margin of safety requirements.
Bragg [63] elaborated a high order model which physically represents the effects
of ice on aircraft flight. The value of any aircraft performance, stability, or control
parameter if ice has been accreted can be calculated as follows:
C (A),iced =
1 + η ice k
CA
C (A) ,
(15.10)
where C (A) and C (A)iced represent any arbitrary performance, stability or control
parameter to be derived under the uniced and iced aircraft. η ice represents the
severity of the icing encounter and k
CA measures the aerodynamic effects of ice
accretion on the parameter of interest, which is constant for a given aircraft and
it is dependent on the presence of ice protection systems, on the geometry and
configuration of the aircraft and on the specific icing conditions. The severity
parameter depends on the collection efficiency, the accumulation factor, and the
freezing fraction that will be presented next. The freezing fraction represents the
type of ice that it is formed and it can be obtained as follows:
f =
mass of water freezing
mass of water impinging
.
(15.11)
Freezing fractions close to the unit represent rime ice formation, whereas values
close to zero correspond to no accretion. Then, the accumulation parameter A c is a
non-dimensional parameter that corresponds to the width of ice that would accrete
over a flat plate placed perpendicular to the free stream over a time t. It can be
calculated as follows:
A c =
V ∞ LWC t
ρ ice c
,
(15.12)
where t represents the time and c represents the chord length of the airfoil and LWC
accounts for the liquid water content. The collection efficiency β will be explained
in more detail in the Sect. 15.3.3.2. It can be calculated as:
β =
Mass of water droplets impinging
Mass of water in the body projected area
.
(15.13)
The general form for the increase in drag ΔC D has the following general form:
ΔC D = Z 1 A C β g(f ),
(15.14)
where Z 1 is a constant and the function g decreases linearly as f differs from
0.2, where it presents a peak. Since the curve is linearly dependent on A c β
then the performance drop will increase over time if no ice protection system is
B. Arizmendi et al.
corresponding increase in power consumption is expected. The limitation of these
effects is crucial in the critical flight stages, which include take off, approaching,
and landing. In critical missions, the limitation of thrust available can cause severe
concerns and may not suffice to satisfy regulated margin of safety requirements.
Bragg [63] elaborated a high order model which physically represents the effects
of ice on aircraft flight. The value of any aircraft performance, stability, or control
parameter if ice has been accreted can be calculated as follows:
C (A),iced =
1 + η ice k
CA
C (A) ,
(15.10)
where C (A) and C (A)iced represent any arbitrary performance, stability or control
parameter to be derived under the uniced and iced aircraft. η ice represents the
severity of the icing encounter and k
CA measures the aerodynamic effects of ice
accretion on the parameter of interest, which is constant for a given aircraft and
it is dependent on the presence of ice protection systems, on the geometry and
configuration of the aircraft and on the specific icing conditions. The severity
parameter depends on the collection efficiency, the accumulation factor, and the
freezing fraction that will be presented next. The freezing fraction represents the
type of ice that it is formed and it can be obtained as follows:
f =
mass of water freezing
mass of water impinging
.
(15.11)
Freezing fractions close to the unit represent rime ice formation, whereas values
close to zero correspond to no accretion. Then, the accumulation parameter A c is a
non-dimensional parameter that corresponds to the width of ice that would accrete
over a flat plate placed perpendicular to the free stream over a time t. It can be
calculated as follows:
A c =
V ∞ LWC t
ρ ice c
,
(15.12)
where t represents the time and c represents the chord length of the airfoil and LWC
accounts for the liquid water content. The collection efficiency β will be explained
in more detail in the Sect. 15.3.3.2. It can be calculated as:
β =
Mass of water droplets impinging
Mass of water in the body projected area
.
(15.13)
The general form for the increase in drag ΔC D has the following general form:
ΔC D = Z 1 A C β g(f ),
(15.14)
where Z 1 is a constant and the function g decreases linearly as f differs from
0.2, where it presents a peak. Since the curve is linearly dependent on A c β
then the performance drop will increase over time if no ice protection system is