This short article, written to be published in the CGC News, is an excerpt from my lecture titled Introductory Aerodynamics for Glider Pilots delivered to the Cambridge University Gliding Club on 27/02/2021.
Unceasing debate surrounds the topic of lift generation, both in folk science, and, to a lesser extent, in the academic community. A wealth of written material and explainer videos of, at best, varied correctness exists. In this article, we shall summarise the common misconceptions and (at least partially) incorrect theories of lift generation and explore how lift generation may be explained in a physical manner.
Incorrect lift theories are explored in detail by the Glenn Research Centre of NASA, whose educational webpages can be found on Google. In summary, the incorrect lift theories known to the author include:
- Equal transition time theory, which asserts that the air separated at the leading edge meets up at the trailing edge in the same amount of time. This has no physical underlying and it can be proven by a wind tunnel experiment that the top surface air overtakes the bottom surface air despite the longer distance.
- Skipping stone theory, which says lift is generated by the air impinging on the bottom surface at an incidence and, therefore, gets deflected downward. This takes no account of the top surface which might be generating 80% of the total lift, thus, it cannot explain the phenomenon of stall as the skipping stone effect should be more pronounced with increased incidence well beyond the stall incidence.
- Venturi effect theory, which says the top surface of the aerofoil is so shaped to pinch the streamtube to create a local venturi, despite there is no solid boundary above the aerofoil for it to pinch against. The local venturi exists, but it is part of the global potential field established around the aerofoil, which is of an extensive nature.
- Partial vacuum theory, which says air on top of the aerofoil is somewhat rarefied due to the larger surface area to cover in motion (linked to the equal transition time assertion), thus a partial vacuum is created. This has no physical underlying and the best way to falsify this would be to consider a hydrofoil where lift is generated in a fluid that is very nearly incompressible.
Lift explanations, whether they fall into one of the incorrect theories or not, can be broadly divided into the Newtonian camp and the Bernoulli camp. The Newtonian camp sees lift as resulting from the 3rd law (law of equal and opposite reaction) when the aerofoil accelerates the air downward, thus impressing a force on it. They need to explain the cause of such acceleration. The Bernoulli camp sees lift as the pressure difference existing across the top and bottom surfaces of the aerofoil. In explaining this pressure difference, they invoke the Bernoulli’s equation (but often without considering the prerequisites of its application to the flow field in detail). The difficulty they encounter, then, is to explain why air flows at a faster speed on the top surface. It should be noted that neither Issac Newton nor Daniel Bernoulli sought to explain lift in their careers, and their names are borrowed merely for convenience.
Very recently a third camp has emerged, led by the effort of Professor Holger Babinsky of the University of Cambridge, who explains the sub-atmospheric pressure on the top surface and the high pressure on the bottom surface by considering centrifugal-motion-induced transverse pressure gradient (known in the subject as a streamline curvature method, think about a tornado). This is, in my opinion, a more elegant and generally applicable explanation of the pressure differences, and certainly better than using the Bernoulli’s equation. The difficulty is, of course, explaining why the flow curves around the aerofoil in such a way.
When the flow is well attached such that the viscous effects are confined to within the boundary layers, such that a potential field exists for the external domain, all the above explanations are correct and equivalent, and they are just different perspectives of viewing the same flow field and extracting information from it. However, many people deviate to unphysical arguments because they try to ‘break the loop’ and establish a chain of causes and results to explain the features of the flow field, in an ‘A leads to B and B leads to C’ style. Some may argue that high velocity leads to low pressure which leads to lift, but subsequently get stuck in explaining the cause of the high velocity which the others will say results from the pressure gradient, thus the argument goes around in circles rendering additional assertions (which are invariably wrong) necessary.
Provided the flow follows the aerofoil, any of the explanations are applicable. The difficulty is fundamentally in explaining why the flow follows the aerofoil, and it can be stated that it is simply the solution of the full viscous governing equations of gas dynamics (additional inputs are needed if the inviscid governing equations are to be used). Three equations must be solved simultaneously (conservation of mass, momentum, and energy) thus three variables must be solved for simultaneously. Two of those variables must be kinetic (thermodynamic) such that the state of the substance can be fixed, and the remaining one must be kinematic to represent motion. Pressure, for example, is a thermodynamic variable and velocity can be the kinematic variable. It is noted that the thermodynamic variables are all scalars while the kinematic variable should invariably be a vector. Their distributions are related in such ways that conform to the governing equations and they cannot be solved for independently. Thus, it is fundamentally incorrect and fruitless to seek to break the loop of arguments. It is simpler to accept that the flow field gets established around the aerofoil, when it is not stalled, in the very form that we commonly see.
I strongly discourage people to think down the Bernoulli route, as opposed to many aviation books and training material. This is because:
- The Bernoulli’s equation applies to steady, inviscid, incompressible flow. The user must understand each of the conditions and be able to justify why such approximations in the regions where they intend to use the equation are appropriate.
- Perhaps the single most important source of confusion, the Bernoulli’s equation applies along a streamtube and not generally otherwise. However, in the explanation of lift, it is necessary to relate different streamtubes and apply the Bernoulli’s equation across the flow field. This is not automatically wrong but it requires the flow to be irrotational, which cannot be determined without great difficulty in the absence of vector calculus, as an irrotational flow can go around in circles whereas a rotational flow can go in a straight line. People who fail to understand this condition attempt to demonstrate Bernoulli equation by blowing over the top of a piece of paper and watch it rise: this does not demonstrate the Bernoulli equation because, should the piece of paper be vertically hanging, no movement will occur. Physically this is because the jet created by blowing is more energised than the surrounding air such that it has a higher velocity without having to trade in its pressure.
To summarise, provided that the flow follows the aerofoil, lift may either be viewed as the reaction of accelerating the air downward, or as the aggregate (integral) effect of the pressure difference existing across the top and bottom surfaces. In the latter view, the pressure gradient may either be explained by the streamline curvature or by using the Bernoulli’s equation, although the latter is not encouraged due to the need to understand the conditions and prerequisites to use Bernoulli’s equation across streamlines. A simple argument to explain why the flow follows the aerofoil, however, is not yet available. Despite this lack of understanding, the advancement of aeronautics over the past century was not inhibited and we see continued improvement in glider efficiency over time.
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