Spool and Card
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The Spool and the Card

by Ed Seykota, 1999

 

The spool-and-card levitator is a good illustration for lift since it is graphic, easy to construct and nicely isolates the phenomenon. It is a cute and curious device in which air flows down through a spool and onto a card below. The downward flow of air lifts the card up against the spool. Yes, that's right, it actually lifts it! The author constructed a larger laboratory-grade model of the levitator and used it to make measurements of pressure, airflow and lift. He also built a mathematical model of it based on the Theory of Radial Momentum. Result: the Radial Momentum model explains the levitator both qualitatively and quantitatively.

 

When you blow down through the spool of thread, the index card adheres to the bottom of the spool. (A sewing pin up through the center of the card can help to keep it centered.) Contrary to popular belief, Bernoulli's Principle does not explain the phenomenon. The Theory of Radial Momentum does.

 

Momentum is the tendency of an object in motion to stay in motion. Radial Momentum is the tendency of a group of objects (or a fluid) that is radiating out from a center of radiation, to continue to radiate. Radial Momentum is the sum of the momenta of all the objects with respect to their center of radiation. An explosion in outer space radiates mass in all directions. In this case, the linear and angular momenta are zero while the Radial Momentum is the sum of the momenta of all the particles from the center. Like linear momentum and angular momentum, Radial Momentum also remains constant until some force acts upon it. A group of objects may have linear, angular and Radial Momentum all in superposition. Classical physics often deals with linear momentum and angular momentum. Radial Momentum, which also obeys the classical laws, is generally overlooked. It is a very important piece of physics that explains lift and other pressure drop phenomena.

When a group of objects with Radial Momentum radiates away from the center of radiation, it occupies more space and therefore becomes less dense and, in the case of a fluid, develops less pressure. This is the fundamental principle behind pressure drop and lift: radiating fluid becomes less dense and loses pressure. Most instances of pressure decrease in nature occur as a result of Radial Momentum. Other mechanisms use angle-of-attack and/or pistons.

The levitator works by Radial Momentum. The small central valve just under the central well, between the spool and the card is the bottleneck that controls the flow. It has a cylindrical shape, entrains the air to flow radially and invests the air with Radial Momentum. This Radial Momentum carries the air out in expanding rings. As it expands it becomes less dense and loses pressure. Eventually, counter pressure and friction absorb the Radial Momentum and limit the radius of the effect.

Detail of Spool and Card

Air enters the spool at the top and flows into the well and out through the valve. Radial Momentum carries the air out between the spool (green) and the card (yellow). As the air expands into larger rings, it loses density and pressure. It is this radial expansion of the air and not the air velocity (as many textbooks indicate) that accounts for lift.

 

Your lungs provide a high and consistent flow of air. The gap between the spool and the card is small. The air comes out of the valve with high Radial Momentum. As the air expands, its pressure falls. It is this momentum-induced expansion of the air (and not its velocity) that motivates the pressure drop. The ambient pressure below the card elevates the card. Incidentally, this may decrease the gap even further, and increase the valve escape velocity, drawing the card up, even tighter to the spool.

Of course, many good things come to an end, including levitating cards. In this case, no real lungs can maintain a constant flow against an arbitrarily small valve. Your lungs would have to deliver unlimited pressure. Also, at velocities near and above the speed of sound, valves tend to choke on the shock wave and this limits velocity. So as the gap becomes smaller and smaller, the valve escape velocity and the mass flux through the valve eventually stop increasing. Your lungs and the valve both set limits on Radial Momentum. Absent the limits, if you could blow with an infinite pressure through an infinitely small orifice, you would create, in the theoretical limit, a suction cup.

Once the air leaves the valve area and radial Momentum begins to carry it into larger and larger rings, two counter-effects combine to reduce Radial Momentum and limit the radius of the effect. First, as low-pressure air in the gap flows toward the circumference of the spool, it experiences a positive pressure gradient that slows the air; this reduces the Radial Momentum. Second, as the air flows along between the face of the spool and the face of the card, it experiences drag or skin friction, both from the viscosity of the air and from its colliding with the roughness on the walls. Skin friction is a surface phenomenon, generally independent of the size of the gap, so for very small gaps it can become overwhelming and determine the equilibrium position for the card. Valve and friction effects do not directly motivate lift; they act against it. Still, a numerical model of the levitator does not come to equilibrium without their inclusion.

During construction of the levitator model, the author discovers that while the theory and mathematics of Radial Momentum are both straightforward and relatively simple, the theories and mathematics for valves and air friction are rather complex. Most of the work in building the fluid-mechanics model of the levitator lies in obtaining accurate equations to describe valve and friction phenomena. Still, a theory had better be able to predict behavior pretty well, especially if you are using it to pin the tail on a couple hundred years of fallacious thinking, so including all the details is essential. All in all, the levitator model is not perfect fit. In fluid dynamics, almost nothing fits exactly. The model is pretty close, however, and far better than the Bernoulli-based models. In addition, it provides an open, detailed and rigorous look under the hood at the workings of Radial Momentum.

This web site presents a catalog of several other experiments, many of which use standard textbook devices to demonstrate Bernoulli's Principle. In each and every case, the author shows how radial Momentum accounts for the behavior while Bernoulli's Principle does not.