Clearing certain misconception in the common explanations of the aerodynamic lift

TL;DR

This paper clarifies misconceptions about aerodynamic lift, critiques common explanations, and introduces a new theory at zero angle of attack using a novel length scale and circulation theory to better understand lift generation.

Contribution

It proposes a new theory for lift at zero angle of attack involving a novel length scale and challenges vortex-based explanations, enhancing understanding of aerodynamic lift.

Findings

The ratio of the new length scale to wing chord is approximately 0.4930 for typical airfoils.

The proposed theory explains lift at zero angle of attack without vortex generation.

A new equation for the lift coefficient at zero angle of attack is derived.

Abstract

Air travel has become one of the most common means of transportation. The most common question which is generally asked is: How does an airplane gain lift? And the most common answer is via the Bernoulli principle. It turns out that it is wrongly applied in common explanations, and there are certain misconceptions. In an alternative explanation the push of air from below the wing is argued to be the lift generating force via Newton's law. There are problems with this explanation too. In this paper we try to clear these misconceptions, and the correct explanation, using the Lancaster-Prandtl circulation theory, is discussed. We argue that even the Lancaster-Prandtl theory at the zero angle of attack needs further insights. To this end, we put forward a theory which is applicable at zero angle of attack. A new length scale perpendicular to the lower surface of the wing is introduced and it turns out that the ratio of this length scale to the cord length of a wing is roughly $0.4930\pm0.09498$ for typical NACA airfoils that we analyzed. This invariance points to something fundamental. The idea of our theory is simple. The "squeezing" effect of the flow above the wing due to camber leads to an effective Venturi tube formation and leads to higher velocity over the upper surface of the wing and thereby reducing pressure according the Bernoulli theorem and generating lift. Thus at zero angle of attack there is no need to invoke vortex and anti-vortex pair generation. In fact vortex and anti-vortex pair generation cannot be justified. We come up with the equation for the lift coefficient at zero angle of attack: \[C_l = \frac{1}{c}\int_0^c dx \left(\frac{h_c^2}{(h_c - f(x))^2}-1\right).\] Here $C_l$ is the lift coefficient, $h_c$ is our new length scale perpendicular to the lower surface of the wing and $f(x)$ is the functional profile of the upper surface of the wing.