# Will 3D wing has smaller drag than 2D at same AoA and airflow speed?

We meassure lift and drag for 2D and 3D wing case,we use same airfoil at same AoA and same airflow speed for both case. Wind tunnel can change test section walls width.

2D wing test:

So first we put airfoil in wind tunnel so walls touch arifoil tips(2D wing),at AoA=15degrees and airflow speed=20m/s and meassure lift and drag..

3D wing test:

Now we increase walls width so airflow "act" like 3D wing in test section.We use same AoA=15 and same airflow speed (20m/s) over airfoil like in 2D wing- test. note: AoA=15 is angle between chord line and freestream airflow not angle between chord line and effective airflow at 3D wing

Question is,what will be drag of 3D wing-test compare to 2D wing-test,smaller ,equal or larger?

My logic is that 3D airflow leakage on tips will decrease overall pressure difference at wing ,so lift will be smaller than in 2D wing-test but drag will be also smaller than in 2D-test,because when you integrate smaller pressure difference over airfoil surface you will get smaller drag as well.

(BUT if we must have SAME LIFT IN BOTH TEST,than 3D wing test will have larger drag,because then we must increase AoA at 3D wing to compensate lift reduction caused by airflow leakage,so now when we have increased AoA we also have larger drag..)

3D wing will have less drag,drag decrease when AoA decrease,3D wing "feel" effective AoA,so it fly at smaller "AoA" than 2D wing.

how blue-lift can be larger than red-lift,wing at AoA=10 can not produce larger lift than wing at AoA=20 ??

## Summary

At relatively high Reynolds number (>1 million) and in attached flow, where the boundary layer is thin, 3D wing should always have larger overall drag than a 2D airfoil (infinite span), at the same free-stream incidence angle.

## Why?

The downwash generated from trailing vortices is actually very small compared to the free-stream airspeed; therefore, the reduction in effective AOA is also very small.

This results in three effects:

1. Reduction in lift due to tilting. This effect is exceedingly small, since cosine of a small angle is essentially unity.

2. Reduction in lift and pressure drag due to lower effective AOA. The reduction in lift is small but definitely non-negligible. For unseparated flow around an airfoil, the overall pressure drag is very small to begin with, so the reduction is even smaller.

3. Creation of induced drag due to tilting of the lift vector. This is the main one, since sine of a small angle produces non-negligible linear factor. For example, if the local lift coefficient, $$C_l$$, is 0.4, and we have an effective decrease in AOA of 1.0deg, then $$C_l\cos{\frac{1.0\pi}{180}}\approx 0.9998C_l\approx0.4$$, while the local induced drag coefficient, $$C_{d_i}$$, is $$C_l\sin{\frac{1.0\pi}{180}}\approx0.0175C_l=0.007$$.

By the way, the drag polar you cited doesn't help your argument since it's for the whole wing (at aspect ratio of 6). What you really want to cite is the airfoil drag (from Airfoil Tools):

As you can see, the form drag (includes pressure drag) is a small portion of the overall 3D drag at aspect ratio of 6, in the linear lift range. The pressure drag increase is even smaller.