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→Lift and Drag Coefficients
== Lift and Drag Coefficients ==
=== Definitions ===
In aerodynamics, the lift coefficient (\( C_L \)) and drag coefficient (\( C_D \)) are defined as follows:
* \(S\) is the area of the wing (projected onto the ground), a fixed value for a given glider.
* \( \frac{1}{2} \rho V^2 \) is collectively known as the '''dynamic pressure''', or dynamic head.
=== A comment on the dimension ===
You should notice that, for both coefficients, the unit of both the numerator and the denominator is the unit of force (Newton in SI units). The denominator comprises \( \frac{1}{2} \rho V^2 \) which has the unit of pressure, and \( S \) which has the unit of area, so the product yields a force.
Consequently, both \( C_L \) and \( C_D \) are '''non-dimensional'''. These quantities have no units. Non-dimensional quantities are the language of aerodynamics: it allows us to study the underlying physics without being distracted by how things are measured. A K-21 is heavier than a Junior, therefore, in unaccelerated glide with the same angle-of-attack, the wings of the K-21 produces more lift than the Junior wings. What causes this? Is it because the design of the K-21 is aerodynamically superior? The answer is not necessarily, as the K-21 can be flying faster, for instance, or has larger wings. The comparison only becomes meaningful when the lift is non-dimensionalised into the lift coefficient.
=== A comment on dynamic pressure ===
The true air density and the true airspeed always appear together as a compound quantity \( \frac{1}{2} \rho V^2 \) which is referred to as the '''dynamic pressure''' or '''dynamic head'''.
The density of air is not a constant: it depends on pressure (which most notably depends on altitude) and temperature. This causes a major inconvenience as we have to assert a value to it in order to arrive at any numerical results directly useful for flying: e.g. you do not check any non-dimensional quantities in the cockpit, you read the instruments instead which tells you the airspeed in knots or the altitude in feet.
To overcome this problem, we notice that density only appears within \( \frac{1}{2} \rho V^2 \). Therefore, we can define an equivalent density \( \rho_e \) and an equivalent airspeed \( V_e \) such that:
\[ \frac{1}{2} \rho V^2 = \frac{1}{2} \rho_e V_e^2 \]
We can assert a value to \( \rho_e \) and arrive at a value of \( V_e \) such that, when used together, they produce the same amount of dynamic head, therefore, the aerodynamic effect is exactly the same.
The most reasonable value to assign to \( \rho_e \) would be the density of air at some standard conditions. This can then be implemented into some instrument that tells you \( V_e \) (all this instrument has to do is to measure the dynamic head). So long as all the manuals and polar charts express airspeed in \( V_e \) assuming the same value of \( \rho_e \), the change in true air density will not cause these performance guidelines to vary.
In practise, the instrument that tells you \( V_e \) is the '''air speed indicator (ASI)''', and \( V_e \) is known as '''indicated airspeed'''. Based on the discussions above, you should realise that:
# Indicated airspeed is directly related to the dynamic head.
# The dynamic head is the only way airspeed affects glider aerodynamics.
# Therefore, the glider's aerodynamics is affected only by indicated airspeed, not true airspeed (apart from the never-exceed speed).
# 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.
