Induced drag relation with speed

In summary, induced drag is the aerodynamic drag that occurs due to the generation of lift, and it is inversely related to the square of the speed of the aircraft. As speed increases, induced drag decreases because the amount of lift produced for a given angle of attack becomes more efficient. Conversely, at lower speeds, induced drag is higher, making it a significant factor during takeoff and landing phases. Understanding this relationship is crucial for optimizing aircraft performance and fuel efficiency.
  • #1
Owells
2
0
Hi everyone. I was wondering if you guys could explain me why I saw people say that:
Induced drag changes for a factor of 1/V2
Induced drag coefficient for a factor of 1/V4

If I don't make any mistakes, Drag = 1/2 rho * S * V² * Cd.

Manipulating the formula I find, 1/Cd = 1/2 rho * S * V² * Drag so here we can see that Cd inversely proportional to V², not V⁴.
And I still find that Drag is proportional to V² so why it's different with Induced Drag and Cdi ?
 
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  • #2
The drag coefficient doesn't change with speed. It includes everything that influences drag EXCEPT density, some predefined reference area, and speed.
 
  • #3
Yes, maybe I misspoke, I know that drag is influenced by the design of the airfoil ect but let's pretend that we study an airfoil, I learnt that the drag formula was the same that the lift formula. So I don't understand why Induced drag change for a factor of 1/V² and why Cdi for a factor of 1/V⁴
 
  • #4
Owells said:
... so why it's different with Induced Drag and Cdi ...
There are two different forms of drag mechanism.

The profile drag is due to airflow passing the wing, that also generates lift.

The induced drag is due to airflow around the wingtip, the end of the wing. That unwanted flow is normally from below the wing, to above the wing.
 
  • #5
I understand better now.

The induced drag ##F_{di}## is ##\frac{1}{2} \rho C_{di}A_i v^2##. We already said ##C_{di}## includes everything that influences the drag force but ##\rho A_i## and speed. The lift force influences the induced drag force. No lift force, no induced drag force. Double the lift, you will [approximately] double the induced drag force. If this is what we observed then ##C_{di}## is proportional to the lift force ##\frac{1}{2}\rho C_L A_L v^2## or:
$$F_{di} = \frac{1}{2} \rho \left(C_{di*} \frac{1}{2}\rho C_L A_L v^2\right) A_i v^2$$
$$F_{di} = \frac{1}{4} \rho^2 C_{di*} C_L A_L A_iv^4$$
Where ##C_{di*}## is a coefficient including everything that is affecting the induced drag force excluding the lift coefficient, reference areas, density, and speed.
 
  • #6
jack action said:
The drag coefficient doesn't change with speed.
In general it does, but there are problems where we neglect this.
 
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FAQ: Induced drag relation with speed

What is induced drag and how is it related to speed?

Induced drag is a type of aerodynamic drag that occurs as a byproduct of lift. It is inversely related to speed; as the speed of an aircraft increases, the induced drag decreases. This is because at higher speeds, the aircraft requires less angle of attack to generate the same amount of lift, leading to a reduction in the vortices and, consequently, induced drag.

Why does induced drag decrease with increasing speed?

Induced drag decreases with increasing speed because at higher speeds, the aircraft can generate the necessary lift with a lower angle of attack. A lower angle of attack reduces the strength of the wingtip vortices, which are the primary source of induced drag. Therefore, as speed increases, the induced drag decreases.

How can pilots minimize induced drag during flight?

Pilots can minimize induced drag by flying at higher speeds where induced drag is naturally lower. Additionally, using winglets or other aerodynamic devices can help reduce the strength of wingtip vortices, further minimizing induced drag. Maintaining an optimal angle of attack and properly managing the aircraft's weight and balance also contribute to reducing induced drag.

What is the relationship between induced drag and lift coefficient?

Induced drag is directly proportional to the square of the lift coefficient. This means that as the lift coefficient increases, induced drag increases quadratically. The lift coefficient is higher at lower speeds to generate the necessary lift, which results in higher induced drag. Conversely, at higher speeds, the lift coefficient is lower, leading to reduced induced drag.

How does induced drag affect fuel efficiency in aircraft?

Induced drag has a significant impact on fuel efficiency. Higher induced drag at lower speeds requires more thrust to maintain flight, leading to increased fuel consumption. By flying at speeds where induced drag is minimized, aircraft can achieve better fuel efficiency. Efficient aerodynamic designs and the use of winglets also help in reducing induced drag, thereby improving overall fuel efficiency.

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