The difference between buoyant lift and aerodynamic lift is static vs. dynamic. A lighter-than-air craft generates lift at a standstill, whereas a winged aircraft only generates lift with moving air. So I don’t think it’s particularly useful to try to explain both lift mechanisms in terms of the "same’ phenomenon.
Water does compress/rarefy when passing over a hydrofoil, but the density change is miniscule compared to the density changes associated with an airfoil generating an equal amount of lift. A density change/equilibrium argument would have to be very complicated to deal with that difference, whereas a fluid momentum transfer analysis handles things quite nicely.
Lifting bodies should work just fine in a hypothetical truly incompressible liquid.
The problem with this explanation is that for an airfoil, the lion’s share of lift is associated with the reduced pressure over the top of the wing, rather than the increased pressure on the bottom. Were this not so, aerodynamic stall would only cause a minor reduction in lift instead of a major one.
Well, sort of. That it is moving faster results in a difference in an effective pressure differential (due to angle of attack) giving rise to lift, but the essential condition is the difference in pressure; you could achieve the same effect by blowing high pressure air directly below the wing creating lift that is equivalent (in terms of effect) even though the wing has no net airflow.
There are really three mechanisms to atmospheric flight: There is aerodynamic lift (due to a flow separation and pressure differential over an aerofoil) in forward flight as in a conventional aircraft; direct thrust which has a positive net force vector through the flying body’s center-of-mass in the up direction; and buoyancy (a vehicle with a net mass which is less than the air it discplaces) as in a balloon or zepplin, or low enough mass to surface to be buoyed by dynamic air currents. Most flying objects have some combination of the first two in various modes of flight, and small insects may combine all three.
It is certainly possible to collect radiant solar energy and use it to heat air which will become buoyant and produce work; see solar convective air heating, which can be used to produce convective currents in buildings designed for it without using forced (blown) air. However, although this will cause air to move, generating a significant amount of pressure to drive a turbine or other mechanical engine to produce significant net thrust is not really feasible without some kind of adiabatic (ideally insulated) chamber because the temperature of the air as it increases in pressure will get much hotter than the effective temperature of air focused by a fresnel or other lightweight lens system. Systems like the Ivanpah Solar Electric Plant in Southern California use a central collector which is capable of very high temperature operation from which sunlight is focused by a distributed field of heliostats. This achieves sufficient high temperature operation to be thermodynamically efficient but requires a large field array to concentrate enough energy.
Oh, yes, there have been a few solar sail demonstration missions. Japan’s IKAROS was probably the most successful, demonstrating both deployment and propulsion.
I’m not saying you’re wrong here, indeed this is the best and simplest explanation of how an airfoil works. We already have the various forms of flight explained in the simplest way, and several posters have eloquently summarized these.
I’m looking for a single explanation for all these forms of flight, whether it’s the simplest or not. Indeed we can treat a rocket as a single object and apply Newton’s Third Law of Motion directly, works just fine even without moving through a fluid medium. I just don’t see where the Third Law can be used to describe the flight of a hot air balloon.
Here I disagree, the airfoil requires both low pressure above and high pressure below. Just having low pressure above and the same low pressure below, we have no lift. The momentum transfer from the fluid is equal up and down, thus adding up to zero. And again, I’m not saying we can’t describe airfoil mechanics using pressure, just that we can’t describe all the forms of flight in the OP using pressure.
… except for the OP’s #6 … I read the Wikipedia article until it said that the momentum of the photon was exactly equal to it’s energy divided by the speed of light. This old Newtonian mind doesn’t understand a vector value being exactly equal to a scalar value. Every 18th Century physicists would laugh in your face if you said that.
So I make no claim that fluid density can describe solar sails, just that fluid density can be used to describe the other six. Thus providing a single explanation for all these six other forms of flight.
If you get right down to it, you could say that all forms of flight are due to having a greater pressure below than above. It’s just a question of how you cause the pressures to be different.
In post #38 you spoke of changes in density as the relevant phenomenon, but I have pointed out that changes in density are not necessary for the creation of aerodynamic/hydrodynamic lift. In fact, Bernoulli’s equation works fine if you treat density as a constant value; you get a perfectly cromulent relationship between pressure (i.e. lift) and fluid velocity.
Likewise with buoyant lift. I can posit a hypothetical lighter-than-air object that is incompressible yet still produces a lifting force based on the density of the object and the density of the air (with no reference to changes in or “restoration” of fluid density).
I remember reading an article on insect flight - they can remarkably hover, fly backward, etc. using simple wings.
A very high-speed video analysis shows the insects “paddling” through the air. on the upward/forward stroke, the wings are flat to the stroke and generate lift like an airplane wing. At the front, the wing turns about 90 degrees and becomes a paddle, pushing air down and back on the back/down stroke.
I assume this works because the air is very viscous at insect scale, and the ratio of weight /wingload /muscle power required works.
Right, the actual relationship according to special relativity is the magnitude of the momentum is equal to its energy divided by c. The direction of the momentum vector is of course the same as the direction of its velocity vector.
BTW, it seems a little pedantic to me to object to the way the wiki article expresses it. If someone tells you that they were driving 50 miles per hour, do you tell them that they’re making no sense, because velocity is a vector?
That’s what I started with, but this fails with a hot air balloon, pressure is the same on either side of the fabric, the balloon is vented on the bottom. This is strictly due to different densities. So I went back through and substituted density for pressure and found the statements still made sense. Pressure is proportional to density.
I didn’t say that in post #38, if I said that anywhere please change it to differences in density as the relevant phenomenon. Your link relates to barotropic conditions, which means “density is a function of pressure only.” So if we treat density as constant, then pressure is constant. So, pressure differences in an incompressible fluid where density is constant is hardly obvious. Your only lift will have to come from the Chronos apparatus.
Ah … there must be something special about photon momentum. In classical physics, the magnitude of the momentum vector is more typically called it’s kinetic energy, and is expressed in Joules. For a photon, this is expressed as Joule-seconds per meter. Something about that special stuff I know nothing about.
<snark>Dude, I know 50 mph is below the speed limit, you were driving northbound in the southbound lanes, your velocity vector was pointed the wrong direction.</snark>
But seriously, Wikipedia isn’t entitled to such an obvious mistake, it’s just four little words “the magnitude of the” momentum vector. If that’s even true, I sure as hell ain’t going to assume that being I know absolutely nothing about photons. So I’m asking here …
The explanation still works fine. The pressure differential is on the top surface. Just inside the fabric, the pressure is higher than just outside.
As you note, the bottom is at the same pressure, since otherwise there would be a gas flow. But that’s all right.
Imagine you have two tubes of fluid with different densities–mercury and water, maybe. Fill the tubes so that the pressure at the bottom is equal–you could connect the two tubes and there would be no flow. But at any elevation above that, the pressure in the low-density fluid will be higher than that of the high-density fluid. Put a membrane between the two tubes and it will have a force on it towards the high-density fluid.
Same thing with the hot-air balloon. The upper surface has a pressure differential, which is why it’s under tension and lifts the rest of the balloon.
Apologies, I linked to the compressible flow equation; I intended to link to the incompressible flow equation, which shows that if density is held constant, there still is a proportional relationship between pressure and the square of velocity - in other words, an incompressible fluid will generate lift when it moves over an airfoil/hydrofoil body.
You’re looking at the inside and the outside. You need to look at the top and the bottom. Buoyancy exists precisely because the fluid pressure on the bottom of an object is greater than on the top.
The only place where the magnitude of the momentum vector is equal to kinetic energy is for massless particles like photons, and then only if you’re treating c as 1. In Newtonian physics, they’re completely different quantities.
No … if mass is equal, then equal force on each tube produces equal acceleration. If you have equilibrium at surface gravity, then you will have equilibrium at any gravity.
We need a force that causes the pressure inside the top to be larger than outside, and if it’s vented at the bottom (or anywhere for that matter) then the pressure force is out. The fluid will flow until it achieves equilibrium with gravity, and the air does flow out of the vent. Think of the force required to lift a propane cylinder, maybe the fabric can’t withstand that force without ripping.
I certainly apologize if I’ve inferred you’re wrong, you’re not. Your explanation is perfectly adequate for a hydrofoil. Water is as incompressible as to make no difference. An airfoil moves through air, which is compressible … so density is proportional to pressure … and the OP isn’t asking about flight through an incompressible fluid.
The mass for a column of a given height is not equal due to the differing densities.
Also, varying gravity has nothing to do with buoyancy. The difference in gravity at balloon altitudes is infinitesimal.
You seem to be thinking that the pressure is constant within the volume of the balloon–it’s not, since it doesn’t account for the weight of the column of gas. The pressure at the bottom is equal due to the vent. But the pressure at the top is not, because cold air weighs more than hot air. The cold air undergoes a faster decrease in pressure with altitude, and so at the top of the balloon there is a differential.
:dubious: So…you’re looking for one single explanation for all types of lift - even if it’s overly complicated, even if it doesn’t explain lift in incompressible fluid media, even if there are other, simpler, long-established explanations that nicely explain lift in both compressible and incompressible fluid media.
The units of relativistic momentum are the same as classical momentum. Classically, momentum is mass times velocity, so the units are kilogram-meters/second. That’s the same as joule-seconds per meter (since a joule is a kilogram-meter^2 per second^2).
As Chronos mentioned, kinetic energy is not the magnitude of momentum. Not sure where you got that idea. Classically, KE is 1/2 mass times the square of the magnitude of the velocity vector.