Falling objects with different mass, air resistance, and speed

[Yora]

I was just thinking about objects with different mass falling always at the same speed when you have no air resistance to fight against. And I was imagining three identical bottles of which one is filled with water, one with air, and one has a vacuum.

Without air resistance all would fall at the same rate. The first bottle and the water in it would fall at the same speed, so they both are the same speed as the other two bottles. The water also would excert no pressure on the bottom of tbe bottle as the bottle moves out of the way at the same speed as the water wants to move to the bottom.

But when you account for air resistance it is only the rigid bottle that encounters it. The water is effectively riding in the bottles wind shadow. So does the water cause a pressure on the bottom of the bottle? And does this lead to an increased acceleration for the bottle?

I imagine any such effect would be too small to notice by throwing bottles from a height so in our everyday experience averything with the same air resistance would appear to fall at the same speed. But is there really such a force on the bottle or is it counteracted by an opposite force within the material of the bottle?

[halfeye]

I was just thinking about objects with different mass falling always at the same speed when you have no air resistance to fight against. And I was imagining three identical bottles of which one is filled with water, one with air, and one has a vacuum.

Without air resistance all would fall at the same rate. The first bottle and the water in it would fall at the same speed, so they both are the same speed as the other two bottles. The water also would excert no pressure on the bottom of tbe bottle as the bottle moves out of the way at the same speed as the water wants to move to the bottom.

But when you account for air resistance it is only the rigid bottle that encounters it. The water is effectively riding in the bottles wind shadow. So does the water cause a pressure on the bottom of the bottle? And does this lead to an increased acceleration for the bottle?

I imagine any such effect would be too small to notice by throwing bottles from a height so in our everyday experience averything with the same air resistance would appear to fall at the same speed. But is there really such a force on the bottle or is it counteracted by an opposite force within the material of the bottle?
Compare a feather to a cannon ball.

Now compare weightless bottles, to weightless bottles containing a feather and a cannon ball (with no extra space in them).

[Caesar]

I was just thinking about objects with different mass falling always at the same speed when you have no air resistance to fight against. And I was imagining three identical bottles of which one is filled with water, one with air, and one has a vacuum.

Without air resistance all would fall at the same rate. The first bottle and the water in it would fall at the same speed, so they both are the same speed as the other two bottles. The water also would excert no pressure on the bottom of tbe bottle as the bottle moves out of the way at the same speed as the water wants to move to the bottom.

But when you account for air resistance it is only the rigid bottle that encounters it. The water is effectively riding in the bottles wind shadow. So does the water cause a pressure on the bottom of the bottle? And does this lead to an increased acceleration for the bottle?

I imagine any such effect would be too small to notice by throwing bottles from a height so in our everyday experience averything with the same air resistance would appear to fall at the same speed. But is there really such a force on the bottle or is it counteracted by an opposite force within the material of the bottle?

The positive acceleration felt by the bottle towards the ground is independent of the bottle's mass. The decceleration felt by the bottle due to air resistance is entirely dependent on a) the density of the air, b) the speed of the bottle, and c) the shape of the bottle. We assume a) is constant for simplicity, and we find that b) is dependent only on the aforementioned positive acceleration and c). From this we conclude that it is only the shape of the bottle that has any effect, as we have already ruled out changes in mass from having any effect on the acceleration.

[BannedInSchool]

But when you account for air resistance it is only the rigid bottle that encounters it. The water is effectively riding in the bottles wind shadow. So does the water cause a pressure on the bottom of the bottle? And does this lead to an increased acceleration for the bottle?
The water is still being accelerated by gravity, and without air resistance would fall faster than the bottle with air resistance, so yes. The bottle is the water's parachute, and there is a force between the two.

Edit: Okay, not *necessarily* the way I phrased that, but there's till the force of gravity downward on the water, and the force of air resistance up on the bottle, and for them both to accelerate at the same rate there must be a force between the bottle and the water to balance things out.

[Yora]

Actually there is a better example that shows the difference in a very visible way: Instead of a bottle take a balloon. Balloons filled with air fall pretty slow through air. At the same volume filled with water they fall much faster.

And from that would follow that a lead ball falls faster than an aluminium ball in an atmosphere.

But is my explanation correct? Is it because the water is shielded from the air by the balloon?

[Grinner]

I imagine any such effect would be too small to notice by throwing bottles from a height so in our everyday experience averything with the same air resistance would appear to fall at the same speed. But is there really such a force on the bottle or is it counteracted by an opposite force within the material of the bottle?

I say it's counteracted by an opposite force.

If the water is really accelerating at a rate greater than that of the bottle, then there are two options as to how events may proceed. Either it will accelerate through the bottle, or it will push against the bottle. If it pushes against the bottle, the downward force of the bottle will increase, but the air resistance, which depends partially on velocity, will also increase. So....Now I guess we just need to do the math to find how much the counteracting forces increase?


Actually there is a better example that shows the difference in a very visible way: Instead of a bottle take a balloon. Balloons filled with air fall pretty slow through air. At the same volume filled with water they fall much faster.

And from that would follow that a lead ball falls faster than an aluminium ball in an atmosphere.

But is my explanation correct? Is it because the water is shielded from the air by the balloon?

That's not a straight analogy, though. In the first, you have a balloon filled with a gas falling through a gaseous medium and a balloon filled with a heavier medium falling through a gaseous medium. In the second, you have two solid substances falling through a gaseous medium. It's like comparing how quickly a solid and a liquid fall through a liquid.

[Caesar]

Actually there is a better example that shows the difference in a very visible way: Instead of a bottle take a balloon. Balloons filled with air fall pretty slow through air. At the same volume filled with water they fall much faster.

And from that would follow that a lead ball falls faster than an aluminium ball in an atmosphere.

But is my explanation correct? Is it because the water is shielded from the air by the balloon?

You cant use that example to understand a relatively heavy mass in a relatively heavy bottle because you end up in a situation where air resistance becomes highly significant, in fact much more so than gravity, and we call this regime "bouyancy". In your bottle example, it is gravity which is the most significant factor.

[halfeye]

Terminal velocity depends on mass and surface area.

The shape of the bottle defines the surface area.

The contents of the bottle define the mass.

If you define the bottle as massless, and the contents as entirely enclosed, then the equation is simplified.

A massive bottle, with contents of air plus other contents complicates things a bit, but it's still mass versus surface area.

[factotum]

You cant use that example to understand a relatively heavy mass in a relatively heavy bottle because you end up in a situation where air resistance becomes highly significant, in fact much more so than gravity, and we call this regime "bouyancy". In your bottle example, it is gravity which is the most significant factor.

But that contradicts what you said earlier? According to your earlier example the balloon filled with air should accelerate as fast as the one filled with water, assuming they're roughly the same shape. This is clearly not the case, so there's another factor involved that you ignored in your first post. Call it buoyancy, call it what you will, it still has to be taken into consideration here.

[Binks]

I think you might be trying to get too complicated with your analogy. Let's put it another way. Instead of filling the glass bottle with water, let's fill it with more glass, solid all the way through. Does the glass inside the bottle, which is not encountering air resistance because only the surface glass is, exert force on the surface glass?

Yes, and that force is transmitted through the bottle and countered by the air resistance. It's exactly the same situation regardless of what mass you fill the bottle with, a bottle full of mass X will have a greater terminal velocity, a larger amount of air resistance required to counter-act the gravitational acceleration on it, than a bottle of mass X-1.

As halfeye said, terminal velocity (which is the velocity at which the force of air resistance = the force of gravitational acceleration) is determined by shape (surface area / other factors) and mass (and how much air there is, but that should be the same for all the bottles). If all the bottles have the same shape, the ones with greater mass (water filled > air filled > vacuum) will have a greater terminal velocity and fall faster through air.

The pressure on the bottle from its contents is exactly the same as the pressure on the bottle from the air resistance (since they are equal and opposite countering forces in this example). The mass of its contents (+ its own mass, but again, assuming identical bottles in all respects save their contents) and the friction of the air it is falling through cancel out at terminal velocity, that's what terminal velocity is.

You can see the difference in force between a bottle with water and one without at any altitude sufficient for the air bottle to reach its terminal velocity.

[gomipile]

Yes, the pressure measured inside the bottom of the bottle when the air resistance is F will be equal to the pressure if the bottle was sitting on a table on a planet/moon where the local gravitational acceleration is F/m. Here, I have m as the total mass of bottle+ fluid.

So, once the bottle reaches terminal velocity(say, on Earth) the bottle will have the same internal pressures as if it were sitting on a table(on Earth,) because at terminal velocity, by definition, F_resistance=mg.

[Yora]

Now that I think about it, it's actually easy: Drag affects only the surface od an object regardless of it's mass.

So a sphere of lead would fall faster than a sphere of aluminium (same surface, more mass). But the same spheres ground into dust would fall almost the same speed. (Not sure if drag still applies at the scale of individual atoms,)

[BlueHerring]

Now that I think about it, it's actually easy: Drag affects only the surface od an object regardless of it's mass.

So a sphere of lead would fall faster than a sphere of aluminium (same surface, more mass). But the same spheres ground into dust would fall almost the same speed. (Not sure if drag still applies at the scale of individual atoms,)If you ground the spheres up fine enough, your powder would actually start to experience Brownian motion, where there's momentum transfers between the individual air molecules and the powder. Keep in mind, though, that since each particle in the powder still feels the pull of gravity, your powder will still fall to the ground, but all of your powder particles might not reach the ground at the exact same time.

[gomipile]

This all comes down to the difference between body forces and contact forces. Gravity is a body force, and air resistance is a contact force.

Unfortunately, many university Physics I courses don't seem to emphasize this distinction effectively. At least, I've met several people who passed calculus-based Physics I who didn't understand the difference between body and contact forces.

[halfeye]

Now that I think about it, it's actually easy: Drag affects only the surface od an object regardless of it's mass.

So a sphere of lead would fall faster than a sphere of aluminium (same surface, more mass). But the same spheres ground into dust would fall almost the same speed. (Not sure if drag still applies at the scale of individual atoms,)

That's because mass increases with increasing volume (which has a cubic relation to linear size), whereas air resistance increases with surface area (which has a square relation to linear size), and the ratio of volume to surface area (therefore) increases with increasing size.

[Larrx]

Now that I think about it, it's actually easy: Drag affects only the surface od an object regardless of it's mass.

So a sphere of lead would fall faster than a sphere of aluminium (same surface, more mass). But the same spheres ground into dust would fall almost the same speed. (Not sure if drag still applies at the scale of individual atoms,)

The first part of this makes no sense. If drag only affected the surface, and not the inside, than the surface of objects would experience less acceleration than the insides. So the surface would peel off of objects whenever they fell. This is not what we experience. Falling objects of the sort we're discussing here here fall as a single unit, affected exactly the same throughout, whether due to being rigid or to being sealed containers.

For the second part . . . it's density that gives the lead ball the edge, not mass (which falls faster? A hot air balloon, or a needle?), it's profile not surface area (which flies further, a paper airplane, or a crumple?), dust isn't atoms (if you're dealing with individual atoms you're effectively talking about a gas and we'd probably be wise to take off our physics hats and put on our chemistry ones). I'm not super good at dynamics with gases, but given that when everything gets back to an equilibrium state the lead gas would rest below the aluminum, I'd guess the lead still falls faster.

On to the OP!

Even a simplistic model of air resistance has at least two terms. Linear drag, which depends on shape and how 'sticky' the sides of the thing are(basically friction), and quadratic 'push', which depends on profile and density (as the falling thing has to shove air out of the way). There's actually a lot more going on (we probably can't ignore buoyancy, what with the op using a vacuum bottle as an example), but that should do for now.

So does the water push on the bottom of the bottle, and make it go faster? Probably, I guess? It experiences less acceleration from air resistance than the air filled bottle(because it's more dense), so something's going on. Seems reasonable.

[Binks]

The first part of this makes no sense. If drag only affected the surface, and not the inside, than the surface of objects would experience less acceleration than the insides. So the surface would peel off of objects whenever they fell. This is not what we experience. Falling objects of the sort we're discussing here here fall as a single unit, affected exactly the same throughout, whether due to being rigid or to being sealed containers.
No. In fact the surface experiences more acceleration than the interior of the ball. Some of that acceleration just happens to counter the other acceleration, creating a lower overall total acceleration. And it won't shed unless its tensile strength is lower than the force it is experiencing. If that is the case, however, it will definitely fall apart as a result of the differing forces, there is a reason we use high tensile materials for high acceleration situations.


For the second part . . . it's density that gives the lead ball the edge, not mass
Density is irrelevant except as a secondary factor, it is determined by mass and volume, and terminal velocity is determined by mass and surface area, which is related to the volume of the object. For two balls of equal volume and design all that matters is their mass.

[Caesar]

But that contradicts what you said earlier? According to your earlier example the balloon filled with air should accelerate as fast as the one filled with water, assuming they're roughly the same shape. This is clearly not the case, so there's another factor involved that you ignored in your first post. Call it buoyancy, call it what you will, it still has to be taken into consideration here.

You are mistaken, and I think it is because you are conflating acceleration with speed.

The two bottles will indeed fall with the same acceleration. This means they will match speed, up to a point. Now two forces will oppose this free fall: bouyancy and drag from air resistance. Lets ignore bouyancy for now as it is typically very insignificant for any object that is considered to be "falling". That leaves drag, which happens to be dependent on the instantaneous speed of the object, and the surface area (a complex cross section but lets not get into flow dynamics here), as well as the density of the air (which again, we ignore for simplicity).

For a falling object, you have the situation where the gravitational acceleration increases the objects falling speed which in turn increases the drag. At some point, the drag is high enough to cancel any further acceleration, so the object stops speeding up but continues to fall at a constant rate, known as the terminal velocity. Up until now, the mass of the object hasnt been important. We have F = ma = GmM/r^2 => a = GM/r^2 or in other words, the acceleration of the falling object is only dependent on the mass of the earth (big M). (You can run this same equation the other way and find the earth accelerates towards the object, but this acceleration is miniscule because of the ratio of the small mass to the planetary radius.) Anyhow, you can see mass of the object (little m) isnt in play.

But it is. Objects have inertia, and the drag is trying to slow our object down against this inertia (and the acceleration of gravity). So now in our case of a bottle full of air, and a bottle full of water or lead or whatever, the heavy bottle keeps accelerating past the point where the lighter bottle stopped. It has a higher terminal velocity, because as mentioned above in this thread, terminal velocity is dependent on the objects mass, because of inertia. So if you let two objects fall for long enough, they will fall at the same speed with the same acceleration, but eventually the light one stops accelerating before the heavy one, and the heavy one ends up with a higher terminal velocity. It "falls" faster. But only after a long enough distance.

Galileo didnt have enough distance to test this; the leaning tower of Pisa is not that high. (Actually he did his measurements on an inclined plane in his laboratory, and used the rhythmic sound of the spheres rolling over cuts in the plane to qualify his results, but I digress.) But at that point, what was of interest was the acceleration of objects, not their terminal velocities, because quite frankly, nothing was high enough at that point in time, we hadnt even invented hot air balloons yet.

If you throw bouyancy into this, you aren't even talking about falling anymore but instead the force required to displace molecules of different mass.

[Caesar]

A good thought device to see this (and indeed the one Galileo started his research with) is as follows:

Assume lighter objects fall slower than heavier objects (by fall, I mean acceleration not terminal velocity). A sphere of lead falls faster than a sphere of wood, all other things being equal. Ok, so if we tie the two spheres together with a piece of string, the sphere of wood should act as a parachute for the sphere of lead, correct? But! The two spheres together weigh more than either sphere alone, so now in fact our two spheres tied together should fall faster than either sphere alone. Contradiction. The assumption is false, and by symmetrical argument we find all objects must fall at the same speed regardless of their mass: a lighter object cannot fall faster than a heavier object, either.

[DavidSh]

Now for extra credit, repeat the same argument with charged bodies moving in response to an electric field.

[Lord Torath]

An interesting effect of this regards powerless airplanes. If you're flying your Cessna out over the lake, and suddenly you lose you engine, should you start throwing things out to lighten your plane? It depends on which way the wind is blowing. If you are flying into the wind, you want that wind to have as small an effect as possible, so you should not try to lighten your load. If you are flying with the wind, then you want the wind to carry you as far as possible, so, yes, you should dump your fuel, empty the bathroom tanks, toss your binoculars, and do everything you can to lighten your plane.

For a given airframe, a heavier plane will glide farther into a headwind than a lighter plane, while a lighter plane will glide farther with a tailwind. My Aerodynamics professor walked us through the equations, and pointed out that the crew of the Memphis Belle was likely sabotaging themselves by ditching their guns and ammo as they limped back across the English Channel (most likely into a prevailing headwind) in the movie.

[5a Violista]

On the other hand, a partially-filled bottle will fall weird compared to a full bottle and an empty bottle, especially if they're rotating around anything that's not their first and third principal axes. With the water sloshing around inside the bottle, the bottle will move around its center of mass in a weird way, which would make its spinning more unpredictable and offbeat, which would change the frontal surface area in interesting ways, which will alter the air resistance which will make it pretty cool and erratic.

[NichG]

There are many equivalent ways to talk about the same setup. What's going on here is that you can make different choices as to what constitutes 'an object', and making different choices results in different stories for the same dynamics (and the same eventual mathematics).

Lets say I have a falling sphere of material. I can tell the story where the sphere is an object, it has a mass, and as a result of its mass there is a force from gravity on 'the sphere' proportional to that mass, leading to the sphere as a whole having a certain acceleration. If there's air resistance, then 'the sphere' experiences that resistance force, and its terminal velocity is the balancing of that resistance force to the force from gravity.

I could also say that the sphere is made up of a number of bits of matter, each of which has its own mass (such that they add up to the total mass of the sphere), and each of which independently experiences forces due to gravity, air resistance, etc. However, because the sphere stays together, that means that these bits of matter are constrained to move at the same average velocity, have the same average acceleration, etc. They can oscillate around that, but if they didn't obey that constraint then the sphere would disintegrate. So it turns out that doing all the detailed accounting of each bit and the forces on it, I get a new force which sums to zero over the sphere, but locally is non-zero in order to enforce that constraint. This force can be interpreted as 'tension' or 'pressure' or whatever - the point is, whatever physical mechanism holds the sphere together is exerting forces in order to make that happen, and those forces create local deformations around the average that sum up to zero (compression, shear, etc).

The end result I get is the same as if I treat the sphere as 'an object'.

So with the water in the bottle, I can tell the story where I have 'a bottle filled with water' as an object (total mass = bottle mass + water mass, total force from gravity = water force + bottle force, total air resistance, etc). I can also tell the story where the bottle and water are distinct. But because the water cannot escape the bottle, all deviations between those stories are very strictly bounded (at most, the water could move from one side of the bottle to the other).

So you can say 'the water is in the bottle's wind shadow', much like you can say 'the second micrometer of the bottle is in the first micrometer's wind shadow'. The question is, what does telling the story that way let you express more easily versus treating the whole as a rigid object (since the descriptions are equivalent here)? I would tend to go with the rigid object description unless there were some way for that to be broken in an interesting fashion by what was going on (the water could escape, the bottle was big enough that the motion of its contents during the fall doesn't reach a static configuration before the fall ends, etc).

[gomipile]

Seriously, familiarize yourselves with these:

https://en.wikipedia.org/wiki/Body_force
https://en.wikipedia.org/wiki/Contact_force

The main part of this discussion is just the distinction between these two types of forces in one dimensional dynamics.

[Larrx]

No. In fact the surface experiences more acceleration than the interior of the ball. Some of that acceleration just happens to counter the other acceleration, creating a lower overall total acceleration. And it won't shed unless its tensile strength is lower than the force it is experiencing. If that is the case, however, it will definitely fall apart as a result of the differing forces, there is a reason we use high tensile materials for high acceleration situations.

Grr? Acceleration is the second derivative of position with respect to time. If two things have different 'that' then (Barring them intersecting somewhere, shut up) they will be in different places as time marches on.

Do you mean forces? Forces add and subtract, acceleration is just a thing.

Material strength doesn't even factor in. If Bob is traveling at 30 miles/hour, and sarah is traveling at three miles/hour, then it doesn't matter how strong their hand grips are. You already told us that they're traveling at different speeds to different places. Their hands have been shorn off at the wrist.




Density is irrelevant except as a secondary factor, it is determined by mass and volume, and terminal velocity is determined by mass and surface area, which is related to the volume of the object. For two balls of equal volume and design all that matters is their mass.

I guess I tried to present it in the most understandable way?

Okay, trying again.

Terminal velocity is not, in any way, determined by surface area. I'm going to hope that you get that air resistance is the thing that makes terminal velocity happen, so that I can use some examples that people might intuitively understand. Look at cars and planes. The ones that are supposed to 'cut through' the air the fastest. Look at arrows. They can be as long as they want, right? Sometimes the longer the better. If a dinner plate and an arrow had the same surface area(easy!), which would you chose if you wanted to rain death on your foes?

Terminal velocity is also not determined by mass. You can check this yourself. Just drop stuff. If you see variation, it's because the thing has such little mass that it's affected strongly by wind. Wind and air resistance are not the same physical thing.

Mass and surface area is related to volume, I guess. I mean, we need to know the shape of the thing. If we don't know that, then (given mass and volume) there are an unlimited number of answers. If the set of answers is 'anything', then I don't think it nails stuff down in the way you present.

You say that "For two balls of equal volume and design all that matters is their mass", and I agree, but the real difference between those two things is density. If you change the parameters of the experiment, you will quickly come to find that mass, and surface area, and such are less relevant.

I'm not sure how to explain this better? We have built warships that are more massive than your hometown, and they float just fine. We have airliners that are more massive than your house, and they sail through clouds unconcerned. But now we have to talk about buoyancy and Bernoulli forces and stuff, and that's not right.

I guess the takeaway is that, for air resistance, if you want to estimate or predict what's going to happen then you look at the density of the thing(not mass), and it's shape(not surface area). Pay attention to the profile it presents as it passes through the medium, and take it from there.

[Dodom]

No. In fact the surface experiences more acceleration than the interior of the ball. Some of that acceleration just happens to counter the other acceleration, creating a lower overall total acceleration. And it won't shed unless its tensile strength is lower than the force it is experiencing. If that is the case, however, it will definitely fall apart as a result of the differing forces, there is a reason we use high tensile materials for high acceleration situations.


Density is irrelevant except as a secondary factor, it is determined by mass and volume, and terminal velocity is determined by mass and surface area, which is related to the volume of the object. For two balls of equal volume and design all that matters is their mass.

Exactly. A good demonstration would be to observe a ball of water falling. Air resistance quickly rips it apart. Solids are subjected to the same forces, but have enough rigidity not to show it visibly.
Forces applied to a part of an object are transmitted to the rest of the object, I don't get why it's being debated. Otherwise we couldn't receive a high five without our hand being knocked off!

[Lord Torath]

Terminal velocity is the point at which the deceleration due to drag equals the acceleration due to gravity. Gravity is primarily dependent on the mass of the earth, with the mass of the falling object being negligible. The drag force is dependent on the geometry of the falling object, its velocity, and the properties of the fluid it is falling through. The deceleration due to the drag force equals the drag force divided by the mass of the falling body (F=ma => a=F/m)

So yes, terminal velocity is dependent on the mass of the falling object.

[halfeye]

Grr? Acceleration is the second derivative of position with respect to time. If two things have different 'that' then (Barring them intersecting somewhere, shut up) they will be in different places as time marches on.

Do you mean forces? Forces add and subtract, acceleration is just a thing.

Material strength doesn't even factor in. If Bob is traveling at 30 miles/hour, and sarah is traveling at three miles/hour, then it doesn't matter how strong their hand grips are. You already told us that they're traveling at different speeds to different places. Their hands have been shorn off at the wrist.



I guess I tried to present it in the most understandable way?

Okay, trying again.

Terminal velocity is not, in any way, determined by surface area. I'm going to hope that you get that air resistance is the thing that makes terminal velocity happen, so that I can use some examples that people might intuitively understand. Look at cars and planes. The ones that are supposed to 'cut through' the air the fastest. Look at arrows. They can be as long as they want, right? Sometimes the longer the better. If a dinner plate and an arrow had the same surface area(easy!), which would you chose if you wanted to rain death on your foes?

Terminal velocity is also not determined by mass. You can check this yourself. Just drop stuff. If you see variation, it's because the thing has such little mass that it's affected strongly by wind. Wind and air resistance are not the same physical thing.

Mass and surface area is related to volume, I guess. I mean, we need to know the shape of the thing. If we don't know that, then (given mass and volume) there are an unlimited number of answers. If the set of answers is 'anything', then I don't think it nails stuff down in the way you present.

You say that "For two balls of equal volume and design all that matters is their mass", and I agree, but the real difference between those two things is density. If you change the parameters of the experiment, you will quickly come to find that mass, and surface area, and such are less relevant.

I'm not sure how to explain this better? We have built warships that are more massive than your hometown, and they float just fine. We have airliners that are more massive than your house, and they sail through clouds unconcerned. But now we have to talk about buoyancy and Bernoulli forces and stuff, and that's not right.

I guess the takeaway is that, for air resistance, if you want to estimate or predict what's going to happen then you look at the density of the thing(not mass), and it's shape(not surface area). Pay attention to the profile it presents as it passes through the medium, and take it from there.

Mass is directly related to density, density is mass/volume.

Yeah, shape is important, but with spheres aka balls, that's a given, and they're picked as examples because the shape is known.

If all that matters is density and cross section, where did the area rule come from? There is friction along the surface as well as due to pushing the air displaced aside, an infinitely long thin arrow would not be the fastest.

Bouyancy and Bernoulli forces aren't right? what do you mean? this may or may not be the place for them, but I think they are right for physics.

[Yora]

On the other hand, a partially-filled bottle will fall weird compared to a full bottle and an empty bottle, especially if they're rotating around anything that's not their first and third principal axes. With the water sloshing around inside the bottle, the bottle will move around its center of mass in a weird way, which would make its spinning more unpredictable and offbeat, which would change the frontal surface area in interesting ways, which will alter the air resistance which will make it pretty cool and erratic.

In case of a "bottle shaped" bottle, shouldn't air resistance eventually cause the bottle to fall either top first or bottom first? Like a flag will follow the direction of the wind?

[gomipile]

In case of a "bottle shaped" bottle, shouldn't air resistance eventually cause the bottle to fall either top first or bottom first? Like a flag will follow the direction of the wind?

Typically, yes. However, It should be possible to make a (still radially symmetrical) bottle which isn't all that stable when falling. Also, since air resistance is a fluid effect, and turbulence is possible, some shapes might have "flutter modes," other vortex shedding modes, etc. which prevent truly stable falling orientations from existing.

[Larrx]

Mass is directly related to density, density is mass/volume.

Yeah, shape is important, but with spheres aka balls, that's a given, and they're picked as examples because the shape is known.

If all that matters is density and cross section, where did the area rule come from? There is friction along the surface as well as due to pushing the air displaced aside, an infinitely long thin arrow would not be the fastest.

I'm not sure what area rule you're referencing, but an arbitrarily long (and arbitrarily thin) object will fall much faster in a medium than any other shape with the same surface area.

There is friction along the surface, but that force is the same regardless of how long the surface is (to a good approximation).

I understand that density and mass have a mathematical relation to one another, but saying that mass is the important quantity could confuse people who can't easily convert one to the other. Someone might assume that simply making something more massive would make it reach the ground sooner, and that's not true. If you drop 1 gram of feathers, it will fall at the same speed as 2 grams of feather. "But wait!" someone might cry. "What if you pack twice as many feathers into the same size sphere as the first time! Then it will fall faster!" And yeah, sure. But that's density.




Bouyancy and Bernoulli forces aren't right? what do you mean? this may or may not be the place for them, but I think they are right for physics.

I meant that this wasn't the place for them :smile:

[halfeye]

I'm not sure what area rule you're referencing,

This one:

https://en.wikipedia.org/wiki/Area_rule


, but an arbitrarily long (and arbitrarily thin) object will fall much faster in a medium than any other shape with the same surface area.

However, the mass must vary if the surface area stays the same. If I take a cube of uniform density with sides of 2 length units, it has a surface area of 24 square length units. If I then take that and make it into a long thin shape with rectangular surfaces with a length of 8 units, and a width and height of one, which has the same volume and thus mass, the surface area has risen to 34 square length units.


There is friction along the surface, but that force is the same regardless of how long the surface is (to a good approximation).

I understand that density and mass have a mathematical relation to one another, but saying that mass is the important quantity could confuse people who can't easily convert one to the other. Someone might assume that simply making something more massive would make it reach the ground sooner, and that's not true. If you drop 1 gram of feathers, it will fall at the same speed as 2 grams of feather. "But wait!" someone might cry. "What if you pack twice as many feathers into the same size sphere as the first time! Then it will fall faster!" And yeah, sure. But that's density.
It is also mass. Mass is a preceding factor in any discussion of density, you have to take volume into account too, but so long as you've dealt with mass and volume, you have dealt with density.

[Larrx]

This one:

https://en.wikipedia.org/wiki/Area_rule



"longitudinal cross-sectional area" Like me, they are talking about profile. (look how skinny all the pictures are!)



However, the mass must vary if the surface area stays the same. If I take a cube of uniform density with sides of 2 length units, it has a surface area of 24 square length units. If I then take that and make it into a long thin shape with rectangular surfaces with a length of 8 units, and a width and height of one, which has the same volume and thus mass, the surface area has risen to 34 square length units.

True, but I have held from the outset that mass is irrelevant (or nearly so. so nearly that it can, and often is, ignored).


It is also mass. Mass is a preceding factor in any discussion of density, you have to take volume into account too, but so long as you've dealt with mass and volume, you have dealt with density.

It's not preceding. You don't have to do math in any particular order, and the first element is not more important. If you vary mass and volume proportionally, than nothing changes (picture several lead balloons tied together with string). If you vary volume and mass proportionally, than the same thing happens. If you vary them disproportionally, then there will be an effect. Because you're changing density. This isn't wordplay. If someone wants to know what hits the ground the fastest than this is the knowledge they need.

[halfeye]

"longitudinal cross-sectional area" Like me, they are talking about profile. (look how skinny all the pictures are!)

Somewhere in the range 10:1 to 20:1, not infinity:1


True, but I have held from the outset that mass is irrelevant (or nearly so. so nearly that it can, and often is, ignored).

It's not preceding. You don't have to do math in any particular order, and the first element is not more important. If you vary mass and volume proportionally, than nothing changes (picture several lead balloons tied together with string). If you vary volume and mass proportionally, than the same thing happens.

This is ridiculous. Surface area depends on size, the bigger something is, the less surface area it has relative to its volume. You can't ignore mass and do serious calculations, whether you like mass or not.

[5a Violista]

This is ridiculous. Surface area depends on size, the bigger something is, the less surface area it has relative to its volume. You can't ignore mass and do serious calculations, whether you like mass or not.
In certain calculations and situations, yes you can ignore mass (due to it being insignificant) and do serious calculations. More importantly, in many calculations you don't even have to know the mass. There's no point in ignoring the mass because the mass doesn't even matter in many physical situations.

The Buckingham π Theorem (https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem) is one of the ways you can determine whether or not the mass is important in the calculations. (Summary: you put all the units together in proportion to each other, equal to a nondimensional variable. Sometimes, mass is not present in the equation and, thus, doesn't matter. Other times it doesn't and in those cases, mass matters. This theorem shows this through unit cancellation.)

In addition:
Any intensive property calculation or equation (as opposed to extensive property calculations (https://en.wikipedia.org/wiki/Intensive_and_extensive_properties)) is, by definition, independent of mass. A whole category of serious calculations are performed using intensive calculations. You don't even have to know the mass to perform these calculations.

Other times the mass cancels out with itself and because the mass is always equal to the mass and is never equal to zero, it divides out and thus doesn't matter.

You easily can ignore mass and do serious calculations because the mass simply doesn't matter. Air resistance falls into one of these situations: The drag force is dependent on the density of the fluid, the flow velocity, the drag coefficient, and the reference area. The drag coefficient is largely dependent on the shape, as well as the Reynold's Number (which is dependent on the speed, kinematic viscosity of the fluid, and a characteristic length) and the Mach Number (which is dependent on the fluid speed and its speed of sound) and the flow direction. Note how "mass" is not listed even once. (Feel free to look up the equations if you doubt me).
The air resistance calculations can be done independently of the mass. You don't have to know or calculate the mass at all.

Now, the mass does affect the force due to gravity and the inertia. In a freefalling object, terminal velocity occurs when the drag force equals the force due to gravity. However, air resistance is neither defined nor dependent on gravity or inertia. Claiming that "air resistance is dependent on mass because it equals gravity in freefall" is as nonsensical as claiming "gravity is dependent on velocity because it equals air resistance in freefall".

[halfeye]

In certain calculations and situations, yes you can ignore mass (due to it being insignificant) and do serious calculations. More importantly, in many calculations you don't even have to know the mass. There's no point in ignoring the mass because the mass doesn't even matter in many physical situations.

The Buckingham π Theorem (https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem) is one of the ways you can determine whether or not the mass is important in the calculations. (Summary: you put all the units together in proportion to each other, equal to a nondimensional variable. Sometimes, mass is not present in the equation and, thus, doesn't matter. Other times it doesn't and in those cases, mass matters. This theorem shows this through unit cancellation.)

In addition:
Any intensive property calculation or equation (as opposed to extensive property calculations (https://en.wikipedia.org/wiki/Intensive_and_extensive_properties)) is, by definition, independent of mass. A whole category of serious calculations are performed using intensive calculations. You don't even have to know the mass to perform these calculations.

Other times the mass cancels out with itself and because the mass is always equal to the mass and is never equal to zero, it divides out and thus doesn't matter.

You easily can ignore mass and do serious calculations because the mass simply doesn't matter. Air resistance falls into one of these situations: The drag force is dependent on the density of the fluid, the flow velocity, the drag coefficient, and the reference area. The drag coefficient is largely dependent on the shape, as well as the Reynold's Number (which is dependent on the speed, kinematic viscosity of the fluid, and a characteristic length) and the Mach Number (which is dependent on the fluid speed and its speed of sound) and the flow direction. Note how "mass" is not listed even once. (Feel free to look up the equations if you doubt me).
The air resistance calculations can be done independently of the mass. You don't have to know or calculate the mass at all.

Now, the mass does affect the force due to gravity and the inertia. In a freefalling object, terminal velocity occurs when the drag force equals the force due to gravity. However, air resistance is neither defined nor dependent on gravity or inertia. Claiming that "air resistance is dependent on mass because it equals gravity in freefall" is as nonsensical as claiming "gravity is dependent on velocity because it equals air resistance in freefall".

Yes, sometimes you can ignore mass, as in level flight, if you ignore lift, which at 1.0 mach and above you probably more or less can.

Terminal velocity? no, you can't ignore mass. This forum thread is about terminal velocity.

[5a Violista]

((So I just double checked the opening post, and it doesn't mention terminal velocity – instead, it mentions acceleration, and by definition terminal velocity happens when the acceleration is zero. Terminal velocity isn't even brought up until post 8. So, while I feel it would be acceptable to say "I was talking exclusively about terminal velocity" – in which case, we were talking about different things – it would be incorrect to make the blanket statement that the entire thread is about terminal velocity.))

Since the first poster hasn't posted here in around four days, I think all their questions have been answered. If we wanted to create a discussion exclusively about terminal velocity and its interactions with mass, I feel creating a new thread about it would be best.

[Lord Torath]

The drag force on an object is dependent only on the surface geometry of the object, the properties of the fluid it is moving through (or the fluid that is moving past it), and the relative velocity of the object to the fluid. Drag force is completely independent of the mass of the object. If your bottle is full of air, water, or lead, the drag force on the bottle for a given flow orientation and fluid velocity is the same. Nothing inside the bottle can interact with the fluid flowing past the bottle, so it can't affect the drag force (unless you've got a leaky bottle - or a magnetic field that penetrates the bottle wall to interact with the moving fluid - in which case you need another set of equations to describe its behavior).

The acceleration (or deceleration as the case may be) due to that drag force does depend on the mass of the object, via the formula Force = mass x acceleration. Acceleration = Force / mass.

If you want to model the acceleration of the fluids inside the bottle acting on the bottle itself, it would be equal to the difference between the acceleration due to gravity and net acceleration the bottle is experiencing. If the drag deceleration is 0.25 G, the bottle itself is accelerating at 0.75 G, so the fluid inside would exert a force equal to its mass x 0.25 G on the bottle itself. I think. I haven't plugged numbers in yet, but there should be no difference in the net forces acting on a 2 kg bottle, or a 1 kg bottle with 1 kg of water inside it.

[Larrx]

Somewhere in the range 10:1 to 20:1, not infinity:1


The point of my . . . point? was not to reference the exact ratio between width and surface area(I just thought it might be a helpful observation), but instead to point out that in the 'surface area is king' arguments and formulae it is not the mathematical definition of surface area to which they are referring. Rather, they are discussing a much narrower concept. I call this 'profile' for clarity, but longitudinal cross-sectional area means the same thing. You'll find this to be true throughout the literature. I swear, I'm not making this up.


This is ridiculous. Surface area depends on size, the bigger something is, the less surface area it has relative to its volume. You can't ignore mass and do serious calculations, whether you like mass or not.

I love mass. It is literally my favorite measurable quantity (special shout out to temperature). The idea that there is a number to measure inertia is unbelievably cool. And it interacts with so much basic 'this is how the world works, who knew?' stuff. Awesome. Newton is still my favorite scientist, and he pretty much defined mass. So cool.

That being said, it just isn't relevant in every situation, and this is one of those times.

So point by point:

"Surface area depends on size" . . . I don't know what you mean by size, but if you mean two objects with identical geometry (just scaled up or down versions of each other), then sure, I guess? Seems a simplistic definition though.

"The bigger something is, the less surface area it has relative to its volume" . . . again, this is only true if the geometries are the same. Why are we taking that as a given, when it defiantly is not in any discussion of air resistance? An air-filled balloon (of the sort you might find at a child's birthday party) will have a much larger surface area than a pea sized piece of rubber made of the same amount of material.

A thought exercise: If you drop a marble, you can measure how it falls through air. If you hold a marble in each hand and drop them simultaneously, would you expect them to reach the ground faster or slower than if you had dropped only a single one? They'd fall exactly the same, right? If you dropped a hundred at once, you'd still expect the same result. Since they're falling at the same rate, they couldn't speed each other up or slow each other down even if you welded them together. You can change the mass up or down willy nilly without changing the measured result. This is why I say mass doesn't factor into this particular calculation. Also, saying I don't like mass is mean. Me and mass are BFFs. What if mass heard you!?

"But wait!" you exclaim. "Imagine a small marble, and a larger (but still spherical) object of the same material! The larger one would fall faster! Mass!"

To which I would reply, "Yeah, I know, and that's why I have also been stressing the idea of profile (as opposed to surface area) in every post. You'll note that profile is proportional to the square root of radius, while surface area is proportional to the cube root. So while the density of the larger sphere hasn't changed, something very much like density has. The ratio of mass to profile is really the quantity we're interested in. It's a lot like density though, you can see why I shorthanded it, right?

[halfeye]

The point of my . . . point? was not to reference the exact ratio between width and surface area(I just thought it might be a helpful observation), but instead to point out that in the 'surface area is king' arguments and formulae it is not the mathematical definition of surface area to which they are referring. Rather, they are discussing a much narrower concept. I call this 'profile' for clarity, but longitudinal cross-sectional area means the same thing. You'll find this to be true throughout the literature. I swear, I'm not making this up.

You swear? evidence, padawan.


I love mass. It is literally my favorite measurable quantity (special shout out to temperature). The idea that there is a number to measure inertia is unbelievably cool. And it interacts with so much basic 'this is how the world works, who knew?' stuff. Awesome. Newton is still my favorite scientist, and he pretty much defined mass. So cool.

That being said, it just isn't relevant in every situation, and this is one of those times.

So point by point:

Are you swearing again, or is this just an oath?


"Surface area depends on size" . . . I don't know what you mean by size, but if you mean two objects with identical geometry (just scaled up or down versions of each other), then sure, I guess? Seems a simplistic definition though.

Simpler definitions make arguments easier to understand. Oversimplification is a problem to be avoided.


A scientific theory should be as simple as possible, but no simpler. -- AlbertEinstein

... (formating)


"The bigger something is, the less surface area it has relative to its volume" . . . again, this is only true if the geometries are the same.

Why wouldn't they be the same? It is true of every case of the geometries being the same. If the shape/geometries are the same, for every possible geometry, bigger means less surface area per volume.


Why are we taking that as a given, when it defiantly is not in any discussion of air resistance? An air-filled balloon (of the sort you might find at a child's birthday party) will have a much larger surface area than a pea sized piece of rubber made of the same amount of material.

That is not what's being talked about, and you know it. The mass involved is the balloon plus the air, not just the balloon.


A thought exercise: If you drop a marble, you can measure how it falls through air. If you hold a marble in each hand and drop them simultaneously, would you expect them to reach the ground faster or slower than if you had dropped only a single one? They'd fall exactly the same, right? If you dropped a hundred at once, you'd still expect the same result. Since they're falling at the same rate, they couldn't speed each other up or slow each other down even if you welded them together.

Nope, if you weld them together, the surface area changes. This only becomes apparent at high velocities, but the terminal velocity of the blob would be higher.


"But wait!" you exclaim. "Imagine a small marble, and a larger (but still spherical) object of the same material! The larger one would fall faster! Mass!"

Volume.


To which I would reply, "Yeah, I know, and that's why I have also been stressing the idea of profile (as opposed to surface area) in every post. You'll note that profile is proportional to the square root of radius, while surface area is proportional to the cube root. So while the density of the larger sphere hasn't changed, something very much like density has. The ratio of mass to profile is really the quantity we're interested in. It's a lot like density though, you can see why I shorthanded it, right?

Nah. I can't say I do. If profile is density, why isn't mass = volume? Simplification is great, Einstein for one was all for it, but there are limits.

[Lord Torath]

Regarding the cross-sectional area, this is generally used in supersonic jets. Drag is generally less if the cross-sectional area is the about the same all the way through the aircraft. This is why you see supersonic jet bodies narrow where wings and engines are located.

[Larrx]

You swear? evidence, padawan.

I'm not linking all the things. One (apparently unread, or misunderstood) Wikipedia post was presented to me as a rebuttal, and I refuted it. I believe my posts stand on their own, and I have tried to provide the context necessary for them to be understood. Your mileage may vary.



Are you swearing again, or is this just an oath?


I honestly don't know what this means.


Simpler definitions make arguments easier to understand. Oversimplification is a problem to be avoided.



... (formating)


They do! That's why I've made an effort to use colloquial language, and easily observed phenomena, to make my points. "Surface area depends on size," is, unfortunately one of the oversimplifications that you claim should be avoided. It's actually an issue critical to the discussion at hand. Two items with the same volume could have vastly different surface areas. Two items with the same mass could have vastly different surface areas. Two items with the same density could have vastly different surface areas. Two items with the same profile could have vastly different surface areas. When you claim that size and surface area have some dependency, I honestly don't know what you mean in the context of this conversation. That is not simplifying for comprehension, it's simple not communicating what you're trying to say.


Why wouldn't they be the same? It is true of every case of the geometries being the same. If the shape/geometries are the same, for every possible geometry, bigger means less surface area per volume.


Why would they? 'Bigger' is not a term that gets bandied about the science labs very often, and I earnestly don't know what you mean by it. If sphere A has radius r and sphere B has radius R and r<R then sphere B will have a larger surface area. If A has less 'stuff' inside than B, but B is a sphere, and A is a thin sheet, than A will have more surface area despite being 'smaller.'


That is not what's being talked about, and you know it. The mass involved is the balloon plus the air, not just the balloon.

Strangely, I do know what we're talking about. I am not using tactics or lies or misdirection to convince you or anyone of wrong things. Let me try again. Assume you should add the mass inside the balloon into the total mass (which I was always doing). It still works just like I said! The deflated balloon falls fastest. One half filled falls faster than one fully filled. One overfilled falls slowest of all. In all cases the mass increased, but they fell slower. This is your own argument, and it still holds mass as irrelevant at best, and the opposite of what you claim at worst. You can try this at home. Balloons are really cheap.


Nope, if you weld them together, the surface area changes. This only becomes apparent at high velocities, but the terminal velocity of the blob would be higher.
Sigh . . . it was a figure of speech? Tie them together with string then. Same result.



Volume.
Wait, is your stance now that things with more volume fall faster. That's . . . so crazy I don't even know how to respond.



Nah. I can't say I do. If profile is density, why isn't mass = volume? Simplification is great, Einstein for one was all for it, but there are limits.

I never said (even a little bit) that profile was density. What I was trying to convey was that, if we wanted a good shorthand, than the ratio of mass to profile (density isn't even in the equation!) would be a good number to look at. You seem upset, and I don't think you're actually reading my posts. Did I do something wrong?

Why is this hard? This isn't like some strange esoteric rejiggering of numbers that lets us figure out how much Jupiter weighs. This is physics you can touch. A well crafted paper airplane flies forward more swiftly than it falls down (it's surface area is constant, but it's profile favors forward over down). A diver sinks more deeply than a belly flopper. If you hold your hand out the window of a moving car, and hold your palm flat, with fingers outstretched, parallel to the ground . . . and then perpendicular (the surface area still constant!) you will feel the difference. Try cupping your hand! Even more force! All examples of constant mass and constant surface area and radically different results. This is physics you can touch.

[halfeye]

I'm not linking all the things. One (apparently unread, or misunderstood) Wikipedia post was presented to me as a rebuttal, and I refuted it. I believe my posts stand on their own, and I have tried to provide the context necessary for them to be understood. Your mileage may vary.

My mileage certainly does vary. I don't know you, and you don't know me. The average person on the internet is a loudmouthed ignoramus, if you want not to be that gal, show either clear workings or backup.


They do! That's why I've made an effort to use colloquial language, and easily observed phenomena, to make my points. "Surface area depends on size," is, unfortunately one of the oversimplifications that you claim should be avoided.

With the qualification that the shape must remain the same, it's not an oversimplification at all, it's simply true. It is a funamental fact about the way things change with changes in size. It's what makes flying model aeroplanes different than flying full size ones. It's what make viruses and bacteria able to spread via the air, while elephants can't.


It's actually an issue critical to the discussion at hand. Two items with the same volume could have vastly different surface areas. Two items with the same mass could have vastly different surface areas. Two items with the same density could have vastly different surface areas. Two items with the same profile could have vastly different surface areas.

The first three are correct, I'm not sure what you mean by the last, since I don't understand what you mean by a profile.


When you claim that size and surface area have some dependency, I honestly don't know what you mean in the context of this conversation. That is not simplifying for comprehension, it's simple not communicating what you're trying to say.

I don't understand what you're not understanding. The shapes have to stay constant, but so long as they do, then surface area increases as a square function of increasing linear size, and volume (and thus mass given a static density) increases as a cube function of increasing linear size. You said that for a shape of static surface area, longer and thinner was more effective at passing through the air. I pointed out that given the surface area stayed the same, then as the shape got longer, the volume and thus the mass declined. So, if the mass is constant it's not clear that making something longer and thinner indefinitely consistently decreases the air resistence, because the surface area rises, and some drag is due to friction.



Why would they? 'Bigger' is not a term that gets bandied about the science labs very often, and I earnestly don't know what you mean by it. If sphere A has radius r and sphere B has radius R and r<R then sphere B will have a larger surface area. If A has less 'stuff' inside than B, but B is a sphere, and A is a thin sheet, than A will have more surface area despite being 'smaller.'

True, but I think it's irrelevant.



Sigh . . . it was a figure of speech? Tie them together with string then. Same result.

If it's a figure of speach, it shouldn't be used as an argument in a serious discussion. Tying them together with string will also change things, in that case the surface area of the string will be added, and slow them down.



Wait, is your stance now that things with more volume fall faster. That's . . . so crazy I don't even know how to respond.

Things with the same shape, same density, and larger size have less surface area per unit mass, so yes. As above, elephants can't fly.




I never said (even a little bit) that profile was density. What I was trying to convey was that, if we wanted a good shorthand, than the ratio of mass to profile (density isn't even in the equation!) would be a good number to look at. You seem upset, and I don't think you're actually reading my posts. Did I do something wrong?

Trolling is wrong. I don't think you're trolling, but I can't 100% rule it out yet.

[Larrx]

My mileage certainly does vary. I don't know you, and you don't know me. The average person on the internet is a loudmouthed ignoramus, if you want not to be that gal, show either clear workings or backup.

Okay, let me introduce myself. I'm just a guy that has done some post-graduate work in physics. I don't have a job in the field, and I certainly didn't specialize in either aeronautics or re-entry. But it comes up, you know? Every entry level physics class proclaims 'Ignoring air resistance!' as a prereq. It gets you curious. So I looked into it. It turns out that it is intensely complicated, and equations with that included can often not be solved analytically.

I'm sure that it makes you feel better to refer to me as a padawan, or a loudmouthed ignoramus, or a gal (there are tons of bright young women in science by the way, why is that an insult in your head?), but I can't show clear workings on this site. I mean, I guess I could. I could load up LaTeX, and write out the equation, and take a screenshot, and place it here. But why? Almost no one would understand it, and literally no one would be able to solve it.


With the qualification that the shape must remain the same, it's not an oversimplification at all, it's simply true. It is a funamental fact about the way things change with changes in size. It's what makes flying model aeroplanes different than flying full size ones. It's what make viruses and bacteria able to spread via the air, while elephants can't.


You did not include that qualification. So I was left to wonder. Model airplanes are not significantly different from real ones, assuming they are made of similar materials. And the reason cells can propagate like perfumes is because of wind, and not because of the difference between or similarity to elephants.



The first three are correct, I'm not sure what you mean by the last, since I don't understand what you mean by a profile.


Earnestly? Imagine a shape. For this exercise we'll use a sphere. It is traveling through a medium. Some portion of its surface area presses against it directly. Some portion of its surface area drags along experiencing friction, and some portion is in the 'shadow' of the preceding parts. So for the sphere, the friction part is very small, the top part is in the shadow, and the bottom half is the profile.

make sense?




I don't understand what you're not understanding. The shapes have to stay constant, but so long as they do, then surface area increases as a square function of increasing linear size, and volume (and thus mass given a static density) increases as a cube function of increasing linear size. You said that for a shape of static surface area, longer and thinner was more effective at passing through the air. I pointed out that given the surface area stayed the same, then as the shape got longer, the volume and thus the mass declined. So, if the mass is constant it's not clear that making something longer and thinner indefinitely consistently decreases the air resistence, because the surface area rises, and some drag is due to friction.


You never said that the shapes have to stay constant. Even if you had, your statement would have been unclear. 'Size' isn't a word that does not need clarification. A sheet of paper twice as long would have increased it's 'size' by what? Most would say that the sheet of paper is twice as 'big', but its surface area increased linearly and not quadratically. Its volume increased linearly as well. I did not understand what you meant when you posted that.

As far as my example goes, I did not claim that either the volume or the mass changed. You can change the shape of something without affecting either of those two quantities. If there are two thing, and they have the same mass, and they have the same volume, than the one that is long and thin (with the thin part facing the direction of falling) will fall faster than the fat one.




If it's a figure of speach, it shouldn't be used as an argument in a serious discussion. Tying them together with string will also change things, in that case the surface area of the string will be added, and slow them down.

This is a serious discussion? This is a physics question on a gaming site. I'm trying to give people a metric they can use if a character in their game jumps off a building to try to catch a falling McGuffin. I mean, I know a lot of things, and I'm doing my utmost to be correct, but no one's going to die if we get this wrong.

The thought exercise that your refering to: If you drop one bottle it will fall at a certain rate. If you repeat the experiment, the results will be the same because the air and the bottle and gravity are all still the same and those are all the variables. If you drop two bottles at once, than they will both fall exactly as the single bottle did. Two bottles have twice the mass and twice the surface area of a single bottle, but they fall exactly like a single bottle falls. Even if they were linked together, they would fall exactly as fast as the single bottle. They were doing that before so neither can slow down or speed up the other.



Things with the same shape, same density, and larger size have less surface area per unit mass, so yes. As above, elephants can't fly.

But . . . but . . . you claim that surface area is what slows you down in air. If the elephant has the least surface area/mass it should fly best by your reasoning. And everything we've been doing with planes is just ridiculous . . . we should mount engines on spheres. Spheres have less surface area/mass than wings!

Look, I don't know why we're having this fight, but it's okay to admit that you're wrong. It's better than turning into some sort of cartoon. This isn't some 'which movie is great' argument. This is science. That you can touch.





Trolling is wrong. I don't think you're trolling, but I can't 100% rule it out yet.

Hmm. I didn't start the thread. I didn't realize this was a hot button issue for anyone. I replied with what I believe to be true without regard for, or in an attempt to, antagonize others. I don't think so? I mean, there has to be a reason I keep coming back despite how cantankerous this has become, so the drama must be at least a little bit of a draw. But I don't like it. I would be more at peace if my first response had gone unremarked.

I'm not arguing just to make people angry and watch the world burn. I have knowledge of this topic and I'm just trying to say it so readers hear. I believe that many of the things you have said are wrong, and I can't let it hang there for innocents to find.

So, no . . . I'm not trolling.

[NichG]

This is kind of surreal, I'm not even sure what the point of contention is anymore. Feels like its time to go to the equations.

[halfeye]

This is kind of surreal, I'm not even sure what the point of contention is anymore. Feels like its time to go to the equations.

I wouldn't like equations, but it certainly does seem to be heading into the surreal.


Okay, let me introduce myself. I'm just a guy that has done some post-graduate work in physics. I don't have a job in the field, and I certainly didn't specialize in either aeronautics or re-entry. But it comes up, you know? Every entry level physics class proclaims 'Ignoring air resistance!' as a prereq. It gets you curious. So I looked into it. It turns out that it is intensely complicated, and equations with that included can often not be solved analytically.

I'm sure that it makes you feel better to refer to me as a padawan, or a loudmouthed ignoramus, or a gal (there are tons of bright young women in science by the way, why is that an insult in your head?)

Padawan is more or less student or beginner, it's not intended solely as an insult, I could have used "Grasshopper" from the Kung Fu TV show, same sort of thing, and I do get the feeling that on the web you are a newbie, which is not in itself bad. I specifically did not call you a loudmouthed ignoramus, I pointed out that a lot of people on the internet behave that way, not so much here, but read the comments section of any other site, then forget it, because it probably will be that bad, if that's not you that's good, but I'm not going to assume it's not without some sort of history. The reason for saying "be that gal" was basically self censorship, it was going to be "be that guy", but then I though I don't know the gender of the person concerned, so what's the PC option?


, but I can't show clear workings on this site. I mean, I guess I could. I could load up LaTeX, and write out the equation, and take a screenshot, and place it here. But why? Almost no one would understand it, and literally no one would be able to solve it.

One or two here might well, unfortunately I'm not one of them.


You did not include that qualification. So I was left to wonder.

In the first instance, I was talking about the general case, so I assumed the shape stayed the same. The second time I referred to this I was very clear that the shape had to stay the same. If you did not pick that up, that's hardly my fault.


Model airplanes are not significantly different from real ones, assuming they are made of similar materials.

With scale models, this is not remotely true, the length of a 1:24 scale spitfire would be about 2ft, but the mass would not be about 1/24th the weight of the real thing.


And the reason cells can propagate like perfumes is because of wind, and not because of the difference between or similarity to elephants.
So the wind can carry elephants? Tornados maybe, otherwise not.



Earnestly? Imagine a shape. For this exercise we'll use a sphere. It is traveling through a medium. Some portion of its surface area presses against it directly. Some portion of its surface area drags along experiencing friction, and some portion is in the 'shadow' of the preceding parts. So for the sphere, the friction part is very small, the top part is in the shadow, and the bottom half is the profile.

make sense?

So it is the side shot of the head of the guy gazing manfully into the distance.


You never said that the shapes have to stay constant.

I certainly did, maybe not the first time the issue was mentioned but every time since.


As far as my example goes, I did not claim that either the volume or the mass changed. You can change the shape of something without affecting either of those two quantities.

You can, but not if the surface area is also invariant.


If there are two thing, and they have the same mass, and they have the same volume, than the one that is long and thin (with the thin part facing the direction of falling) will fall faster than the fat one.

I don't dispute that in the case of say a sphere and a dart, however there seems to be a limit, because the surface area keeps on increasing as the object becomes longer and thinner.


This is a serious discussion? This is a physics question on a gaming site. I'm trying to give people a metric they can use if a character in their game jumps off a building to try to catch a falling McGuffin. I mean, I know a lot of things, and I'm doing my utmost to be correct, but no one's going to die if we get this wrong.

Yeah, hopefully no one will die because of this.


The thought exercise that your refering to: If you drop one bottle it will fall at a certain rate. If you repeat the experiment, the results will be the same because the air and the bottle and gravity are all still the same and those are all the variables. If you drop two bottles at once, than they will both fall exactly as the single bottle did. Two bottles have twice the mass and twice the surface area of a single bottle, but they fall exactly like a single bottle falls. Even if they were linked together, they would fall exactly as fast as the single bottle. They were doing that before so neither can slow down or speed up the other.

This is physics. We can't link things together without affecting their surface area. You seem to be ignoring air resistance.


But . . . but . . . you claim that surface area is what slows you down in air. If the elephant has the least surface area/mass it should fly best by your reasoning. And everything we've been doing with planes is just ridiculous . . . we should mount engines on spheres. Spheres have less surface area/mass than wings!

Lift comes from drag, drag comes from surface area. Elephants don't fly because they have a low surface area, low drag, low lift.


Look, I don't know why we're having this fight, but it's okay to admit that you're wrong.

If I thought I was, I would, but I'm pretty sure I'm not. It may well be that we are arguing at cross purposes, I don't understand what you are trying to prove, if it's not something that I know is wrong.


Hmm. I didn't start the thread. I didn't realize this was a hot button issue for anyone. I replied with what I believe to be true without regard for, or in an attempt to, antagonize others. I don't think so? I mean, there has to be a reason I keep coming back despite how cantankerous this has become, so the drama must be at least a little bit of a draw. But I don't like it. I would be more at peace if my first response had gone unremarked.

I'm not arguing just to make people angry and watch the world burn. I have knowledge of this topic and I'm just trying to say it so readers hear. I believe that many of the things you have said are wrong, and I can't let it hang there for innocents to find.

So, no . . . I'm not trolling.

That's good. I'm not trying to do anything other than correct what seems to be a mistake. There are plenty of people here who would be quite happy to jump on me if I said something untrue, they have before, it will undoubtedly be necessary for them to do so again, unfortunately, but this time it seems we're both right, just not coherently in dialog.

[NichG]

I wouldn't like equations, but it certainly does seem to be heading into the surreal.

...

One or two here might well, unfortunately I'm not one of them.

I'd recommend it. It will make a lot of this less muddy. Talking about it colloquially seems to have produced a ton of overlap in different mathematical meanings of the same English words, like when talking about 'surface area' with respect to lift and drag. The integral that gets you the lift and the integral that gets you the drag care about different facing surfaces of the object, and that's really precisely defined when you look at the integral over the object surface to calculate aerodynamic body forces. The forces in the direction of motion care about the parts of the object that face in that direction (the cross-sectional area), and the forces perpendicular care about the parts of the object that are facing perpendicular to the direction of motion (also a cross-sectional area, but a different cross-section).

The equations also make it a lot clearer what it means that 'you don't need to know the mass of the object' and things like that.

[Icewraith]

I wouldn't like equations, but it certainly does seem to be heading into the surreal.



Padawan is more or less student or beginner, it's not intended solely as an insult, I could have used "Grasshopper" from the Kung Fu TV show, same sort of thing, and I do get the feeling that on the web you are a newbie, which is not in itself bad. I specifically did not call you a loudmouthed ignoramus, I pointed out that a lot of people on the internet behave that way, not so much here, but read the comments section of any other site, then forget it, because it probably will be that bad, if that's not you that's good, but I'm not going to assume it's not without some sort of history. The reason for saying "be that gal" was basically self censorship, it was going to be "be that guy", but then I though I don't know the gender of the person concerned, so what's the PC option?



One or two here might well, unfortunately I'm not one of them.



In the first instance, I was talking about the general case, so I assumed the shape stayed the same. The second time I referred to this I was very clear that the shape had to stay the same. If you did not pick that up, that's hardly my fault.



With scale models, this is not remotely true, the length of a 1:24 scale spitfire would be about 2ft, but the mass would not be about 1/24th the weight of the real thing.


So the wind can carry elephants? Tornados maybe, otherwise not.




So it is the side shot of the head of the guy gazing manfully into the distance.



I certainly did, maybe not the first time the issue was mentioned but every time since.



You can, but not if the surface area is also invariant.



I don't dispute that in the case of say a sphere and a dart, however there seems to be a limit, because the surface area keeps on increasing as the object becomes longer and thinner.



Yeah, hopefully no one will die because of this.



This is physics. We can't link things together without affecting their surface area. You seem to be ignoring air resistance.



Lift comes from drag, drag comes from surface area. Elephants don't fly because they have a low surface area, low drag, low lift.



If I thought I was, I would, but I'm pretty sure I'm not. It may well be that we are arguing at cross purposes, I don't understand what you are trying to prove, if it's not something that I know is wrong.



That's good. I'm not trying to do anything other than correct what seems to be a mistake. There are plenty of people here who would be quite happy to jump on me if I said something untrue, they have before, it will undoubtedly be necessary for them to do so again, unfortunately, but this time it seems we're both right, just not coherently in dialog.

The PC option is most likely "be that person".

A couple things-

Yes, we absolutely can neglect things that result in very small changes to the problem. If you tie two objects together with string, and the string is an order of magnitude or two smaller in terms of mass, surface area, volume, etc, if you drop both objects next to each other in the same way you did when they were not tied together with string, the difference in the result will most likely be within the bounds of measurement error, so it would be difficult to say whether or not it had an effect. So we NEGLECT the effect of the string. If you THROW the two objects and the string is strong enough to not break under the forces, you have dramatically changed their characteristics with the string. If you throw one object while it's attached with string to the other object 1) don't hurt yourself or anyone else or anyone's property 2) you've REALLY changed their characteristics by adding a great deal of spin compared to throwing either object individually.

You can't just talk about "surface area" or similar when it comes to drag and aerodynamics. Think in terms of the profile of the object with respect to the direction of flow.

Consider a cone of arbitrary length and diameter. The same cone will exhibit dramatically different drag characteristics if you have the pointy end or the flat end facing into the direction of flow, regardless of whether you're using a liquid or a gas medium. However, it's the same cone, with the same mass, volume, and surface area. What matters is the shape with respect to the direction of flow. Elephants don't normally fly because they're not the right shape, and they don't generate enough thrust for their mass. But an unfortunate falling elephant will have different terminal velocities depending on which part of the elephant is oriented into the direction of flow.

It's like the difference between scalars and vectors. It's not enough to have "a surface area", you worry about the exposed surface area of an object in a given orientation once you start talking about drag.

[halfeye]

The PC option is most likely "be that person".

If you wanted to be very formal that might work.


A couple things-

Yes, we absolutely can neglect things that result in very small changes to the problem. If you tie two objects together with string, and the string is an order of magnitude or two smaller in terms of mass, surface area, volume, etc, if you drop both objects next to each other in the same way you did when they were not tied together with string, the difference in the result will most likely be within the bounds of measurement error, so it would be difficult to say whether or not it had an effect. So we NEGLECT the effect of the string. If you THROW the two objects and the string is strong enough to not break under the forces, you have dramatically changed their characteristics with the string. If you throw one object while it's attached with string to the other object 1) don't hurt yourself or anyone else or anyone's property 2) you've REALLY changed their characteristics by adding a great deal of spin compared to throwing either object individually.

You can neglect it in a calculation if you need a practical result, but in a discussion of theory, which I believe this is, you shouldn't neglect anything. The effects of a string might be negligible over a short distance, but over a drop that accelerated from nothing to terminal velocity, that slight drag would become significant, if nothing else the thread would be pulled behind the balls and bring them together, so their drags would interact.


You can't just talk about "surface area" or similar when it comes to drag and aerodynamics. Think in terms of the profile of the object with respect to the direction of flow.

Consider a cone of arbitrary length and diameter. The same cone will exhibit dramatically different drag characteristics if you have the pointy end or the flat end facing into the direction of flow, regardless of whether you're using a liquid or a gas medium. However, it's the same cone, with the same mass, volume, and surface area. What matters is the shape with respect to the direction of flow.
The cone is in freefall, so it will assume whichever position results in the least drag, probably with the point first, but I suspect slightly off to one side of central, maybe oscillating somewhat.


Elephants don't normally fly because they're not the right shape, and they don't generate enough thrust for their mass. But an unfortunate falling elephant will have different terminal velocities depending on which part of the elephant is oriented into the direction of flow.

Again the poor elephant will rotate to the position of least drag.

Are you really saying you believe that bacteria etc. are less dense than jellyfish? Bones obviously make vertebrates denser, but the reason jellyfish don't fly is because their surface are isn't big enough to support their weight in air, where bacteria have enough surface area that brownian motion can keep them airborne.


It's like the difference between scalars and vectors. It's not enough to have "a surface area", you worry about the exposed surface area of an object in a given orientation once you start talking about drag.

Yeah, the direction of flow of the air with regard to the motion of a body is important, spins and stalls happen when that goes wrong for aeroplanes.

Really, the ratio of surface area to mass is a very important part of flight. As another example:

https://en.wikipedia.org/wiki/Ballooning_(spider)

Do you think a mile of rope could make an elephant airworthy? even small spiders are not capable of flying by themselves, they need their silk to expand their surface area to weight ratio. A parachute is a way for a human to get a much expanded surface area, for little extra mass. Of course in the case of the human it very much matters how that surface interacts with the air, if the chute doesn't fill out then it doesn't work, but the priciple of an extended surface area is sound.

[gomipile]

The cone is in freefall, so it will assume whichever position results in the least drag, probably with the point first, but I suspect slightly off to one side of central, maybe oscillating somewhat.
[...]
Again the poor elephant will rotate to the position of least drag.



Not necessarily. Imagine a sphere centered on the objects center of mass, and put the drag value in each direction on the point of the sphere in that direction. The cone/elephant/arbitrary object will rotate to where the drag is a local minimum on that sphere, not necessarily to where the drag is lowest.

If while falling it gets perturbed enough to rotate into another minimum's attraction basin, it can switch orientation, of course.

[halfeye]

Not necessarily. Imagine a sphere centered on the objects center of mass, and put the drag value in each direction on the point of the sphere in that direction. The cone/elephant/arbitrary object will rotate to where the drag is a local minimum on that sphere, not necessarily to where the drag is lowest.

If while falling it gets perturbed enough to rotate into another minimum's attraction basin, it can switch orientation, of course.

Yes, I was oversimplifying there, it's rotation away from local drag maxima, not to the absolute drag minimum, if there are intermediate minima it may well halt at one of them.

I'm still mainly interested in the idea that some people seem to have that the ratio of mass to surface area rising with size is not significant for flight. There's a reason that the biggest animals are in the sea, that the elephant is the biggest on the land, and it's essentially the same reason that flying birds have a maximum mass of about twenty kilos:

https://en.wikipedia.org/wiki/Bustard

[5a Violista]

Oh! I think I can answer this question, becaue I was one of the peope saying that mass didn‘t matter when calculating air resistance: actually, as far as I can tell, nobody in this thread had claimed that mass is irrelevant to flight. This thread is about falling, not flight. An elephant can fall just as easily as a whale or a flowerpot or a bottle or an arbitrary lightweight object can fall. This thread asked a question about the force of air resistance (which is, according to the equations I previously explained, is independent from mass) and not about lift or flight or gravity or terminal velocity or inertia or scaling or any of the other things that you have been claiming (rightfully) are related to mass.

That is why people have been claiming that the question asked in this thread is unrelated to mass, while you have been claming that other things are dependent on mass.

[halfeye]

Oh! I think I can answer this question, becaue I was one of the peope saying that mass didn‘t matter when calculating air resistance: actually, as far as I can tell, nobody in this thread had claimed that mass is irrelevant to flight. This thread is about falling, not flight.

Falling is essentially flying, with a direction of straight down.


An elephant can fall just as easily as a whale or a flowerpot or a bottle or an arbitrary lightweight object can fall.

An arbitrarily lightweight object such as a hot air balloon?


This thread asked a question about the force of air resistance (which is, according to the equations I previously explained, is independent from mass) and not about lift or flight or gravity or terminal velocity or inertia or scaling or any of the other things that you have been claiming (rightfully) are related to mass.

Air resistance is independent of mass so long as you are talking about constant speed, or constant acceleration due to some man made force. When the source of acceleration is gravity, then mass becomes important. Firstly the mass of the Earth, which causes the acceleration, then the mass of the object being accelerated. In a lot of cases, you can find the mass of the accelerated object on both sides of the equation and eliminate it. However, this isn't always the case. When it comes to terminal velocity, you have the acceleration due to the attraction between the mass of the Earth and the mass of the object versus the resistance of the air to the passage of the surface of the object, which cancel, so the speed is constant. If you change the shape of an object its terminal velocity will usually change (there are certainly shapes that have identical terminal velocities at the same mass). If you change the mass of an object while keeping it the same shape and size, its terminal velocity will change, and if you change the size of an object while maintaining its density, the terminal velocity will change in that case too.


That is why people have been claiming that the question asked in this thread is unrelated to mass, while you have been claming that other things are dependent on mass.


Falling objects with different mass, air resistance, and speed

Yeah, no mention of mass there. :smalltongue: :smallbiggrin:

[5a Violista]

Yes, the title text has the word "mass" in it. I can see it. Yora's original questions, however, do not, and the answers to them deal largely with stress, material properties, and how air resistance works. Yora didn't explicitly state it but I'm sure implied in the question was the additional question about what affect mass has on falling (hence putting "mass" in the title) but the answer is: mass matters to terminal velocity, but it does not matter to the force from air resistance.

As an answer to your nonsequiter: Yes, hot air balloons can easily fall out of the sky. In spite of what Buzz Lightyear and Woody say, falling is not "essentially flying" except "straight down", unless you're willing to contradict yourself and admit that elephants can fly simply by falling straight down. I see how what you're saying is funny and that you're essentially joking, but I'm still going to correct you and say that air resistance has more to do with drag than lift. Drag is an essential and fundamental part of flying, but it isn't all of flying.

Regarding your larger paragraph: Yes. When you bring in inertia and gravity and terminal velocity, mass matters. Everybody already knows this, and the part of my post that you quoted outright states this. I'm getting the impression that you were just clarifying what I said to other people who will read this thread who know nothing about physics. Is my impression correct?

[halfeye]

Yes, the title text has the word "mass" in it. I can see it. Yora's original questions, however, do not, and the answers to them deal largely with stress, material properties, and how air resistance works. Yora didn't explicitly state it but I'm sure implied in the question was the additional question about what affect mass has on falling (hence putting "mass" in the title) but the answer is: mass matters to terminal velocity, but it does not matter to the force from air resistance.

Mass doesn't matter to the force from air resistance at any given speed for any given shape, however mass does make a difference to the rate of acceleration for a given shape under gravity against air resistance.


As an answer to your nonsequiter: Yes, hot air balloons can easily fall out of the sky. In spite of what Buzz Lightyear and Woody say, falling is not "essentially flying" except "straight down", unless you're willing to contradict yourself and admit that elephants can fly simply by falling straight down.

What I mean about falling being flying but straight down is that the aerodynamics of falling and flying are the same, the only thing that changes is the relationship to the Earth's gravitational field. An aeroplane can fly downwards for a short time, but there will be an incident if it doesn't pull out.


I see how what you're saying is funny and that you're essentially joking, but I'm still going to correct you and say that air resistance has more to do with drag than lift. Drag is an essential and fundamental part of flying, but it isn't all of flying.

Only modern military fighters can sit on their tails and get lift without drag. Aircraft that depend on moving wings for lift (including helicopters and autogiros) get lift as a function of drag.


Regarding your larger paragraph: Yes. When you bring in inertia and gravity and terminal velocity, mass matters. Everybody already knows this, and the part of my post that you quoted outright states this. I'm getting the impression that you were just clarifying what I said to other people who will read this thread who know nothing about physics. Is my impression correct?

It was not clear to me from your post that you knew this, it is by no means clear to me that everyone posting in this thread knows this, if they do fine, we've been wasting our time, but if anybody learned anything that's good.

If anyone doesn't believe bacteria fly, there is this:

http://www.bbc.co.uk/news/health-37152871


Doctors are urging other musicians to be extra hygienic.

They say instruments should be cleaned regularly to prevent the build-up of yeast and other harmful pathogens.

...

"These organisms are around in the air, but they're not usually at a high enough level to cause problems. ...

<edit>

Also consider pollen, as in hayfever. That originates with trees and grasses, but it doesn't fall to the ground at 9.8 m/s^2.

The thing that bothers me at the moment about this discussion, is that people know that 9.8 m/s^2 is the acceleration due to Earth's gravity in a vacuum, but they seem to be assuming that that applies in air.

In air, the terminal velocities of items of different densities are different, but that difference is already present at lower velocities.

Consider a golf ball and a table tennis ball.

Drop them from the same height at the same time and the golf ball ought to hit the ground first because it is much heavier.

Notice how high the table tennis ball bounces, that's an approximate measure of how fast it was going.

Now drop the table tennis ball from twice the height, it will bounce higher, so the first drop didn't take it to terminal velocity.

Therefore, density affects acceleration and speed before terminal velocity is reached.