A wing can vary not only in chord but also in the orientation and aerodynamic zero-lift direction of its sections across the span. These spanwise changes are called twist.

Choose one reference line whose orientation is common to the entire wing. Let

• $\alpha$ be the free-stream angle relative to that common reference;
• $\alpha_{geom}(y)$ be the local geometric orientation of the section chord line relative to the same reference;
• $\alpha_{L=0}(y)$ be the local section's zero-lift angle measured relative to its chord line.

Then the local chord-line angle of attack before accounting for downwash is

$$\alpha+\alpha_{geom}(y).$$

Geometric twist

The spanwise variation of

$$\boxed{\alpha_{geom}(y)}$$

is the geometric twist.

For a symmetric wing:

• washout means $\alpha_{geom}$ decreases toward the tips;
• washin means $\alpha_{geom}$ increases toward the tips.

Washout therefore points the tip sections to a lower local geometric angle than the inboard sections for the same overall wing orientation.

Aerodynamic twist

Sections can also have different camber or flap settings, so their zero-lift angles can vary with span even if all chord lines are geometrically parallel.

Define the aerodynamic twist angle

$$\boxed{ \alpha_{aero}(y) =\alpha_{geom}(y)-\alpha_{L=0}(y) }.$$

Then the local angle above the section's zero-lift direction, before induced downwash, is

$$\boxed{\alpha+\alpha_{aero}(y)}.$$

This decomposition is useful because section lift depends on angle relative to the zero-lift line, not on chord orientation alone.

A wing can therefore acquire aerodynamic twist through

• geometric rotation of the sections;
• spanwise changes in camber or airfoil shape;
• flap or control-surface deflection that changes $\alpha_{L=0}$.

Include induced angle

A finite lifting wing generates downwash. If $\alpha_i(y)$ is the induced angle, the effective section angle relative to its zero-lift line is

$$\boxed{ \alpha_{eff,0}(y) =\alpha+\alpha_{aero}(y)-\alpha_i(y) }.$$

In the linear section regime,

$$\boxed{ c_l(y)=a_0(y) \left[\alpha+\alpha_{aero}(y)-\alpha_i(y)\right] }.$$

Thus geometric twist, section camber, and induced downwash enter the local lift law through one effective angular combination.

The common reference line is arbitrary

The numerical values of $\alpha$ and $\alpha_{geom}$ depend on the chosen wing-wide reference line.

If that reference line is rotated by a constant angle, $\alpha$ and every $\alpha_{geom}(y)$ shift in compensating ways. The physical combination

$$\alpha+\alpha_{geom}(y)$$

does not change.

Similarly, the actual local angle relative to the zero-lift line,

$$\alpha+\alpha_{aero}(y),$$

is independent of this bookkeeping choice.

Twist is therefore a spanwise difference in section orientation, not an absolute numerical angle tied to one arbitrary datum.

Worked example

Suppose a wing has the following section data:

At the center,

$$\alpha_{geom}(0)=2^\circ,$$

$$\alpha_{L=0}(0)=-2^\circ.$$

At the tip,

$$\alpha_{geom}(tip)=-1^\circ,$$

$$\alpha_{L=0}(tip)=-3^\circ.$$

The geometric angle has decreased by

$$3^\circ$$

toward the tip, so the wing has geometric washout.

The aerodynamic twist angles are

$$\alpha_{aero}(0) =2^\circ-(-2^\circ) =\boxed{4^\circ},$$

and

$$\alpha_{aero}(tip) =-1^\circ-(-3^\circ) =\boxed{2^\circ}.$$

Now let the overall free-stream angle be

$$\alpha=3^\circ,$$

with induced angles

$$\alpha_i(0)=1.0^\circ,$$

$$\alpha_i(tip)=1.5^\circ.$$

The center section sees

$$\alpha_{eff,0}(0) =3+4-1 =\boxed{6.0^\circ},$$

while the tip sees

$$\alpha_{eff,0}(tip) =3+2-1.5 =\boxed{3.5^\circ}.$$

If both sections had the same lift-curve slope, the tip would therefore carry a substantially smaller section lift coefficient.

Why twist matters

Twist changes the spanwise loading without necessarily changing the planform outline. It is therefore one of the principal ways to

• shape the circulation distribution;
• alter induced drag;
• redistribute structural loading;
• control which wing regions approach stall first.

The aerodynamic effect is determined by the combined variation of geometry, zero-lift angle, and induced downwash—not by geometric twist alone.