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→Lift and Drag Coefficients
# We should tabulate performance figures and draw polar graphs using indicated airspeed.
# We do not need to adjust the performance tables or polar graphs to compensate for non-standard atmospheric conditions.
=== Components of lift and drag coefficients ===
To proceed with the discussions, it is necessary to quote these without proof. Indeed, these formulae cannot be proven. There are complicated aerodynamic theories that derives these, however, while the success in doing so is remarkable, the theories themselves rely on rigorous assumptions and extensive modelling, so the derivations cannot really be called proofs. You are advised to understand the following as experimental correlations.
\[ C_L = C_{L0} + C_1 \alpha \]
\[ C_D = C_{D0} + \frac{k}{\pi A} C_L^2 \]
It is, however, necessary to explain the physical rationale in detail.
The lift coefficient \( C_L \) can be decomposed as follows:
# \( \alpha \) is the angle-of-attack.
# \( C_{L0} \) is the lift coefficient at zero angle-of-attack. This term equals to zero if the aerofoil is symmetric, greater than zero if the aerofoil is cambered, and smaller than zero if the aerofoil is cambered the wrong way.
# \( C_1 \) can be thought as an empirical factor. It is rather close to \( 2\pi \).
# The lift coefficient increases proportionally with the angle-of-attack up to the point where the wing stalls.
The drag is more complex: the drag on an aeroplane has three components:
# Friction drag, this is the drag caused by the air sticking onto the glider and trying to slow it down. Imagine flying a glider in honey which is quite sticky. The friction drag coefficient \( C_{DF} \) is approximately a constant for a given glider.
# Pressure drag, this is the drag associated with the glider trailing a wake. This is also known as the form drag because it is related to the form of the glider being not fully aerodynamic. You would intuitively think that a Land Rover Discovery has more drag than a Jaguar fastback: because the Discovery is not streamlined while the fastback is, and this is what pressure drag is about. The pressure drag coefficient \( C_{DP} \) is approximately a constant for a given glider, because its form does not change in flight.
# Induced drag, this is the drag caused by having lift. There is no free lunch in aerodynamics and wherever you have lift you must have drag, no matter how well your design is. The induced drag coefficient \( C_{DI} \) takes the following form:
\[ C_{DI} = \frac{k}{\pi A} C_L^2 \]
Where \( A \) is the aspect ratio of the wings (how slender the wings are), and \( k \) is a factor that depends on the wing design. This drag component increases quadratically with \( C_L \).
