# Kutta-Zhukovsky

## Explanation of Lift by Kutta-Zhukowsky

It took 150 years before someone dared to challenge the pessimistic mathematical predictions by Newton and d’Alembert, expressed by Lord Kelvin as:

• I can state flatly that heavier than air flying machines are impossible.

In the 1890s the German engineer Otto Lilienthal made careful studies of the gliding flight of birds, and designed wings allowing him to make 2000 successful heavier-than-air gliding flights starting from a little artificial hill, before in 1896 he broke his neck falling to the ground after having stalled at 15 meters altitude. The first powered heavier than-air flights were performed by the two brothers Wilbur and Orwille Wright , who on the windy fields of Kitty Hawk, North Carolina, on December 17 in 1903, managed to get their airplane Flyer off ground using a 12 horse power engine. The mathematicians Kutta and Zhukovsky (called the father of Russian aviation) then quickly modified potential flow around the section of a wing with zero lift/drag by introducing a large scale circulation or rotation of air around a two-dimensional wing section as illustrated in the following figure showing the zero lift/drag potential solution supplemented by large scale circulation into the Kutta-Zhukovsky flow pattern with lift (but no drag):

Kutta-Zhukovsky explanation of the generation of lift by adding large scale circulation to potential flow. We see how the zones of high (H) and low (L) pressure of potential flow with zero net lift, by the circulation are changed to produce net lift by low pressure on top and high pressure from below. Kutta-Zhukovsky suggested that the circulation around the wing section was balanced by a counter-rotating so-called starting vortex behind the wing as shown in the figure, giving zero total circulation according to Kelvin’s theorem. Kutta-Zhukovsky’s formula for lift (proportional to the angle of attack) agreed reasonably well with observations for long wings and small angles of attack, but not for short wings and large angles of attack, and the drag was still zero. Despite these shortcomings, the explanation of lift by Kutta-Zhukovsky, is the only one available in the literature.

## Non-Physical Fiction of Kutta-Zhukovsky

The problem with Kutta-Zhukovsky’s theory is that it is purely fictionalmathematical theory, which does not describe physics: In reality there is

• no large scale circulation around the section of the wing
• no starting vortex behind the wing.

Thus the matematical theory of lift by Kutta-Zhukovsky based on modified potential flow, is non-physicaland does not explain the origin of lift and why it is possible to fly. It rests on the following incorrect logic: Circulation around a wing (=A)  implies lift (=B) and since there is lift (B is true) there must be circulation (A is true). But from A implies B, you can only conclude that B is true if A is true, not that A is true if B is true, since this corresponds to the reverse implication, that B implies A. The incorrect logic is like saying that since eating cakes makes you gain weight, and you have gained weight, you must have eaten a lot of cakes. But you can get fat by eating pasta as well.  This is shown below: lift has another origin than circulation.

## 2 thoughts on “Kutta-Zhukovsky”

1. You say “this is shown below” but then I don’t see it. Where is the explanation for the claim that “lift has another origin than circulation”? For that matter, why do you think the Kutta-Zhukovsky theory predicts 0 drag?

2. See under New Theory. KZ is zero drag potential flow modified by circulation and circulation does not generate drag.