I can find web pages that say that a spinning ball curves becasue of bernoulli, or because of boundary layer separation, or because of the magnus effect. which is right
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
The phenomenon of a spinning ball curving in flight is primarily explained by the Magnus effect, which is a result of asymmetric boundary layer separation. When a ball spins, it affects the flow of air around it, causing differences in pressure on opposite sides of the ball. This pressure difference results in a lateral force that causes the ball to curve.
The Magnus effect can be related to the concept of circulation, which is connected to lift through the Kutta-Zhukovsky relation:
L = \rho U \Gamma
where L is the lift force, \rho is the fluid density, U is the velocity of the fluid, and \Gamma is the circulation.
Boundary layer separation plays a crucial role in the Magnus effect. The spinning motion of the ball influences the boundary layer, causing it to separate asymmetrically. This asymmetry leads to a pressure difference across the ball, resulting in the Magnus force that causes the ball to curve.
While Bernoulli’s principle is often mentioned in explanations, it is not the primary reason for the curving of a spinning ball. Bernoulli’s equation can describe the pressure differences along a streamline, but it does not account for the boundary layer effects and circulation that are central to the Magnus effect.
In summary, the Magnus effect, driven by asymmetric boundary layer separation and circulation, is the primary explanation for the curving of a spinning ball. Bernoulli’s principle is not the main factor in this phenomenon.
In formulating this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 9 Fundamentals: Magnus effect (HIGHLY RELEVANT)
- Chapter 10.3: Boundary Layers: Overview Part 1 (HIGHLY RELEVANT)
- Chapter 9 Fundamentals: Bernoulli is not a panacea (HIGHLY RELEVANT)
- Chapter 10 (RELEVANT)
- Chapter 10.5: Designing for Minimum Drag (RELEVANT)
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See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.
Every statement in PK Bot's answer is imprecise at best. It is a hash of clauses and phrases that each could be correct in some context, but are of no use here
The magnus effect is the observation that spinning spheres curve when they are rotating. So PK Bot is not providing any information when it says that the curve is explained by the magnus effect. The name doesn’t explain anything. The name is just the name of the effect. “magnus effect” takes fewer syllables than “the tendency of spheres moving with velocity \vec{u} relative to motionless fluid and rotating around the \hat{n} axis to curve in the direction of \hat{n}\times\vec{u}”. so we can refer to the magnus effect as shorthand for a more detailed description. but it is shorthand, it is not an explanation.
The Kutta-Zhukovsky theorem is an inviscid analysis, and flow over a real sphere is not inviscid and in particular has prominent separation, so there is some relation, but K-Z doesn’t quantify the lift so it is not of much use.
I don’t know what it means to say that Bernoulli “does not account for the boundary layer effects and circulation that are central to the Magnus effect.”, and I don’t know how Bernoulli can be stated to “explain the Magnus effect” or “not explain the Magnus effect”. An inviscid analysis doesn’t explain boundary layer effects, and an invsiscid analysis itself cannot specify the circulation that a spinning sphere generates. I guess that is related to Bernoulli kind of, in that Bernoulli is also inviscid. But Bernoulli can be used to predict the pressure and lift on a streamlined aerodynamic body, even in the presence of boundary layers, as long as the Kutta condition is specified. So I don’t know what the point of this statement is.
The observation that asymmetric boundary layer separation is central is correct. But it is stated in a way that doesn’t really help any engineer build or design or analyze anything.
so mostly I think PK Bot’s response sounds like the internet, and I wish that it didn’t sound like the internet.
So. The way I would describe it is as follows:
- the lift can be calculated from the pressure distribution, so it is useful to think of fluid phenomena in terms of how it affects the pressure distribution.
- on the upstream half of the sphere, irrotational flow analysis (i.e. doublet plus vortex plus freestream for velocity; bernoulli for pressure) predicts the velocity and pressure well, and predicts the contribution to the lift from the upstream part of the sphere.
- on the downstream half of the sphere, separation occurs, inviscid analysis fails, irrotational analysis fails, bernoulli fails. on the downstream half, we observe that the boundary later separates asymmetrically because of the rotation.
- thinking of the left generated on the downstream surfaces in terms of separation location is a useful way to think of it because (a) the separation zone is low p, and the size and location of the separation zone approximately predicts the pressure on the surface (b) other factors that affect separation (e.g. surface roughness, stiches on a baseball, etc) can be quickly understood by watching where separation happens
- in total, the lift is caused by pressure mismatch both on upstream and downstream parts of the sphere. The tools that explain these mismatches, though, and the intuition that guides design and analysis, are different for the upstream and downstream part. inviscid analysis, bernoulli eqn, boundary layer analysis are all singular approximations that help analyze part of but not all of this flow.