About Lift and C_l Distributions

The section lift coefficient is related to the section lift by:

So that if we know the lift distribution and the planform shape, we can find the C_l distribution.

The lift and lift coefficient distributions are directly related by the chord distribution. Here are some examples:


The lift and C_l distributions can be divided into so-called basic and additional lift distributions. This division allows one to examine the lift distributions at a couple of angles of attack and to infer the lift distribution at all other angles. This is especially useful in the process of wing design.

From the discussion of lifting line theory and Weissinger theory, we saw that the distribution of lift could be written:


where:
α_r is the angle of attack at the root
θ is the twist angle
{l₁} is the wing lift distribution with no twist and with α_r = 1
{l₂} is the lift distribution at zero angle of attack and unit twist.

The lift distribution may also be written in a more conventional way:


Here, the distributions {l_a} and {l_b} are the wing lift distributions with no twist at C_L = 1 and with unit twist at zero lift respectively. The first term, C_L {l_a}, is called the additional lift. It is the lift distribution that is added by increasing the total wing lift. θ {lb} is called the basic lift distribution and is the lift distribution at zero lift.

Why is this useful? Consider the following example.

We can use the data at these two angles of attack to learn a great deal about the wing.
From the expression above:

or:

The additional lift distribution, C_L {l_a} may be interpreted graphically as shown below.

The additional lift coefficient distribution at C_L = 1.0 is plotted below. Note that it rises upward
toward the tip -- this is indicative of a wing with a very low taper ratio or a wing with sweep-back.

The basic lift distribution is negative near the tip implying that the wing has washout.