If I understand correctly, wind force increases quadratically as airspeed increases

Correct. Anyway we speak more correctly of "aerodynamic" force.

Therefore, all other things being equal, lift should also increase quadratically.

Not really. The aerodynamic force depends not only on the speed but also on:

1. the fluid density
2. the dimension of the aerodynamic body
3. the shape of the body
4. the angle with which the airspeed hits the body, more or less in a linear manner. This angle is termed "angle of attack" and called $\alpha$. Comprimibility effects (Mach > 0.3) and structural deformations modify this simple linear relationship but the main idea still holds.

In general the equation expressing an aerodynamic force looks something like this:

$F=½ \rho V^2 S C_F$

Where:

• $\rho$ is the fluid density - see previous point 1.
• $V$ the speed
• $S$ a surface which is used as reference area (for an airplane it is normally the wing area, for a car is the frontal surface) - see previous point 2.
• $C_F$ is the part depending on the shape of the body and $\alpha$ - see previous point 3. and 4.

If for example we consider the lift, then that equation becomes:

$L=½ \rho V^2 S C_L$

Where $C_L$ (lift coefficient) has the following shape (underlined in blue):

As you can see, $C_L$ increases linearly with $\alpha$ (till a certain point called stall) and can be used to change lift as needed.

Let's do a simple example: if the speed doubles, its effect on $L$ becomes four time as big. If we reduce $\alpha$ from 10° to 2° then the $C_L$ decreases from 0.8 till 0.2) i.e. four times, compensating for the increase in $V$.

If I understand correctly, wind force increases quadratically as airspeed increases

Correct. Anyway we speak more correctly of "aerodynamic" force.

Therefore, all other things being equal, lift should also increase quadratically.

If everything remains exactly the same then yes.

Anyway this is not how an airplane deals with higher speed. The aerodynamic force depends not only on the speed but also on:

1. the fluid density
2. the dimension of the aerodynamic body
3. the shape of the body
4. the angle with which the airspeed hits the body, more or less in a linear manner. This angle is termed "angle of attack" and called $\alpha$. Comprimibility effects (Mach > 0.3) and structural deformations modify this simple linear relationship but the main idea still holds.

In general the equation expressing an aerodynamic force looks something like this:

$F=½ \rho V^2 S C_F$

Where:

• $\rho$ is the fluid density - see previous point 1.
• $V$ the speed
• $S$ a surface which is used as reference area (for an airplane it is normally the wing area, for a car is the frontal surface) - see previous point 2.
• $C_F$ is the part depending on the shape of the body and $\alpha$ - see previous point 3. and 4.

If for example we consider the lift, then that equation becomes:

$L=½ \rho V^2 S C_L$

Where $C_L$ (lift coefficient) has the following shape (underlined in blue):

As you can see, $C_L$ increases linearly with $\alpha$ (till a certain point called stall) and can be used to change lift as needed.

Let's do a simple example: if the speed doubles, its effect on $L$ becomes four time as big. If we reduce $\alpha$ from 10° to 2° then the $C_L$ decreases from 0.8 till 0.2 i.e. four times, compensating for the increase in $V$.

If I understand correctly, wind force increases quadratically as airspeed increases

Correct. Anyway we speak more correctly of "aerodynamic forces".

Therefore, all other things being equal, lift should also increase quadratically

Not really. The aerodynamic force depends also on the angle with which the airspeed hits the aerodynamic body, more or less in a linear manner. This angle is called "angle of attack" and is normally indicated with an $\alpha$. Changes in altitude ($\rho$), comprimibility effects (Mach > 0.3) and structural deformations modify this simple linear relationship but the main idea still holds i.e. at higher speed you need lower $\alpha$.

In general the equation expressing an aerodynamic force looks something like this:

$F=½ \rho V^2 S C_F$

Where:

• $\rho$ is the fluid density
• $V$ the speed
• $S$ a surface which is used as reference (for an airplane it is normally the wing area, for a car is the frontal surface)
• $C_F$ is the part depending on the $\alpha$ (and other parameters like the Mach number).

If for example we consider the lift, then that equation becomes:

$L=½ \rho V^2 S C_L$

Where $C_L$ has the following shape (underlined in blue):

As you can see, $C_L$ increases linearly with $\alpha$ (till a certain point called stall) and can be used to change lift as needed. For example if the speed doubles, its effect on $L$ becomes four time as big. If we reduce $\alpha$ from 10° to 2° then $C_L$ decreases exactly of four times (from 0.8 till 0.2) compensating for the increase in $V$.

If I understand correctly, wind force increases quadratically as airspeed increases

Correct. Anyway we speak more correctly of "aerodynamic" force.

Therefore, all other things being equal, lift should also increase quadratically.

Not really. The aerodynamic force depends not only on the speed but also on:

1. the fluid density
2. the dimension of the aerodynamic body
3. the shape of the body
4. the angle with which the airspeed hits the body, more or less in a linear manner. This angle is termed "angle of attack" and called $\alpha$. Comprimibility effects (Mach > 0.3) and structural deformations modify this simple linear relationship but the main idea still holds.

In general the equation expressing an aerodynamic force looks something like this:

$F=½ \rho V^2 S C_F$

Where:

• $\rho$ is the fluid density - see previous point 1.
• $V$ the speed
• $S$ a surface which is used as reference area (for an airplane it is normally the wing area, for a car is the frontal surface) - see previous point 2.
• $C_F$ is the part depending on the shape of the body and $\alpha$ - see previous point 3. and 4.

If for example we consider the lift, then that equation becomes:

$L=½ \rho V^2 S C_L$

Where $C_L$ (lift coefficient) has the following shape (underlined in blue):

As you can see, $C_L$ increases linearly with $\alpha$ (till a certain point called stall) and can be used to change lift as needed.

Let's do a simple example: if the speed doubles, its effect on $L$ becomes four time as big. If we reduce $\alpha$ from 10° to 2° then the $C_L$ decreases from 0.8 till 0.2) i.e. four times, compensating for the increase in $V$.