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Webafrica
01-09-2005, 07:01 AM
Which object has the fastest terminal velocity in the earth's atmosphere and how fast is that?

If its purely shape dependent then a water drop would have been my guess... but I suspect much more comes into play.

Eg the underside of a teardrop with a water surface probably has significant turbulance.

I couldnt find anything conclusive on the web.

Napier
01-09-2005, 07:04 AM
You'd want the object to be dense, and big, and shaped just right. When things get bigger than the thickness of the atmosphere we'd have to argue about what "terminal velocity" meant.

An osmium iridium alloy is the densest IIRC.

And the long unsymmetrically tapered shape of a zeppelin is pretty close to ideal (at least at low velocities - I guess it'd change a little to be best for higher velocities).

Padeye
01-09-2005, 08:02 AM
Zeppelin shape isn't too far off the mark, needs to be pointier on the ends with a very narrow taper for high mach angle. The problem is that the pointed tip will burn away easily from atmospheric heating then it becomes a less aerodynamic shape. I don't know about Iridium alloys but Tungsten is very dense and has a high melting point.

Fuji Kitakyusho
01-09-2005, 09:55 AM
Definitely dense - osmium or iridium as someone already mentioned. This is because buoyancy is a factor. In a vacuum, this wouldn't matter.

Foil shapes, such as NACA foils, teardrops, etc., are good for minimizing drag, but are only effective if they maintain a stable attitude within the airflow. If you drop a shape like this, it won't necessarily remain oriented the same way, without the addition of stabilizing fins or some other mechanism, as you would see in such streamlined projectiles as rockets, bombs and lawn darts. The addition of such appendages will create some additional drag, the magnitude of which is further dependent on the shape of the fin, etc.

For an object which can not be guaranteed to maintain attitude, there are other methods of reducing drag. One common example of this is the golf ball. If you look at fluid flow over a plain sphere, you will notice the flow split from the stagnation point at the leading end, flowing smoothly around the ball, until the flow separates a little bit behind the midpoint of the ball. Behind this flow separation exists turbulent flow (and flow reversal), acting to increase drag. With the addition of dimples, the surface roughness acts to move the separation point further back on the ball, such that if you looked at the flow from behind, the turbulent area would be a much smaller circle than you would see on a plain sphere.

At a guess, I would say that a NACA foil solid-of-revolution with small, foil profiled stabilizing fins at the trailing end, made from an extremely dense alloy, would be the fastest possible free-falling object.

As for its actual speed, terminal velocity occurs when the drag force (or other external forces) on an object produces an acceleration on that object equal and opposite to that of gravity (nominally 9.81 m/s^2 at sea level). When you take the air out of the equation, the only limit as to the speed that can be reached is the height from which the object is dropped, which is limited by the distance at which the earth's gravity well is comparable to gravity produced by other objects such as the sun and moon. In actuality, we can't ignore the air - all we can do is limit the effect of air resistance, but the maximum terminal velocity is dependent on factors such as fluid density, diameter of the falling object, object shape, surface roughness, fluid viscosity (temperature dependent), and so forth, not to mention that once compressibility comes into play (velocity approaching about Mach 0.3 or so), additional energy is lost, and resistance increases phenominally at Mach 1.0 due to the buildup of the sonic pressure wave (sonic boom).

Q.E.D.
01-09-2005, 10:09 AM
When you take the air out of the equation, the only limit as to the speed that can be reached is the height from which the object is dropped...
No, the limit is the escape velocity of the primary body. The higher over the body the object is dropped, the closer its final velocity at impact approaches the escape velocity, ignoring air resistance and other factors.

InvidiousCourgette
01-09-2005, 10:25 AM
No, the limit is the escape velocity of the primary body.
This is only true if the object is "dropped". If the object has an initial velocity relative to the primary body, then the escape velocity is not a limit (in the absence of air). An asteroid is an obvious example.

Xema
01-09-2005, 10:44 AM
If its purely shape dependent then a water drop would have been my guess...

But note that a drop of water tries to assume a spherical shape, but as it falls it soon is distorted by the airflow into a sort of flattened blob.

In other words, once it's falling it never has the classic "teardrop" shape.

LSLGuy
01-09-2005, 11:06 AM
This is only true if the object is "dropped". If the object has an initial velocity relative to the primary body, then the escape velocity is not a limit (in the absence of air). An asteroid is an obvious example.True as far as it goes, but the practical effect of "terminal velocity" gets a little hazy for very fast moving objects.

Terminal velocity implies an equilibrium between gravitational acceleration and antmospheric drag, implying no change in speed over an incremental time interval.

Imagine a meteor approaching at 1 million (cue Dr Evil little finger to mouth) mph. It enters the atmosphere & begins to slow down. It hits the ground still going 900,000 mph. Was that terminal velocity? Probably not. Had the atmosphere been thicker, the speed would have continued to reduce as the air drag force was greater than G.

So the true upper limit for terminal velocity is whatever speed it is where our atmoshpere is just think/dense enough to dissipate all speed in excess of equilibrium prior to ground impact.

Note also that you get a very different answer for an object whose vector is pointed straight down vice a more typical glancing entry trajectory.

Napier
01-09-2005, 02:02 PM
>Definitely dense - osmium or iridium as someone already mentioned. This is because buoyancy is a factor.

Actually it's mostly because you want to minimize the package volume for a given weight. Whatever shape you choose, making the object smaller will always reduce its drag.

There'd be a little buoyancy, too, but given that metals can be something like 20,000 times denser than air, the buoyancy is a pretty tiny effect.

And, by the way, osmium and iridium are both refractory metals, pretty much like tungsten. And like palladium, platinum, uranium, and others. An osmium iridium alloy can get denser than either osmium or iridium alone (though by only a few percent). Tungsten is also close - and much more available.

Mathochist
01-09-2005, 06:52 PM
once it's falling it never has the classic "teardrop" shape.

Not the iconic teardrop shape, no, but I think the argument can be made that it's teardrop-shaped by definition.

Xema
01-09-2005, 07:11 PM
I think the argument can be made that it's teardrop-shaped by definition.

Provided it fell from someone's eye, I'll agree.

Webafrica
01-14-2005, 08:12 AM
Thanks all for the replies, espicially Fuji.

I've wondered why no-one has done any experiments or tried to set speed records. Don't scientists and engineers love that sort of thing? Fastest this and that?

I wonder if they mad bombs "bomb shaped" for the same reason?

Also wonder if it would be possible to break the sound barrier in free fall... That would be an achievement.

Bippy the Beardless
01-14-2005, 10:05 AM
Not the iconic teardrop shape, no, but I think the argument can be made that it's teardrop-shaped by definition.
True, very fast camera pictures of small falling drops of water show they remain very close to spherical as they fall. Here's an article (http://fluidmech.net/tutorials/raindrops/raindrop.htm)

Chronos
01-14-2005, 10:38 AM
Also wonder if it would be possible to break the sound barrier in free fall... That would be an achievement.I think this one has been done, but not at sea level. Remember, as you go up into thinner atmosphere, both terminal velocity and sound speed change with the thinner air.

It looks like Joseph Kittinger (http://centennialofflight.gov/essay/Explorers_Record_Setters_and_Daredevils/Kittinger/EX31.htm) got close to the speed of sound on his record skydive, but not quite. Still, that's pretty impressive for a human jumper.

butler1850
01-14-2005, 10:47 AM
Thanks all for the replies, espicially Fuji.

I've wondered why no-one has done any experiments or tried to set speed records. Don't scientists and engineers love that sort of thing? Fastest this and that?

I wonder if they mad bombs "bomb shaped" for the same reason?

Also wonder if it would be possible to break the sound barrier in free fall... That would be an achievement.

Yes, it's certainly is possible... This guy (http://dropzone.com/news/SpaceParachutingSkydivin.shtml) did it in the 50's by taking a balloon and freefalling out, parachuting when he reached enough atmosphere to slow him down to sub-mach speeds, and provide enough air to allow the parachute to work.

-Butler

BrotherCadfael
01-14-2005, 11:03 AM
A sphere of neutronium?

scr4
01-14-2005, 11:31 AM
Yes, it's certainly is possible [to break the sound barrier in free fall.]... This guy (http://dropzone.com/news/SpaceParachutingSkydivin.shtml) did it in the 50's...
There seems to be some debate about that. This page (http://hypertextbook.com/facts/JianHuang.shtml) (and many others) claim otherwise.

As for the highest terminal velocity - I would expect a small black hole would fall pretty fast.

flight
01-14-2005, 12:38 PM
Sorry to nitpick, but there were some significant problems with an otherwise excellent post.
Definitely dense - osmium or iridium as someone already mentioned. This is because buoyancy is a factor. In a vacuum, this wouldn't matter.
True it would not matter in a vaccuum, but not because of bouyancy. As has already been bointed out, the increase of drag with increasing size (varying linearly with wetted area for lower sppeds) is much more of a concern.
Foil shapes, such as NACA foils, teardrops, etc., are good for minimizing drag, but are only effective if they maintain a stable attitude within the airflow.
Remember, these shapes were designed to minimize drag, while maximizing lift. Thus, they are suboptimal to a design which concerned itself purely with drag.
As for its actual speed, terminal velocity occurs when the drag force (or other external forces) on an object produces an acceleration on that object equal and opposite to that of gravity (nominally 9.81 m/s^2 at sea level).
Actually, neither of the forces is producing an acceleration, as the forces cancel, not the accelerations. For this example it will work out the same, but it is not the same thing.
In actuality, we can't ignore the air - all we can do is limit the effect of air resistance, but the maximum terminal velocity is dependent on factors such as fluid density, diameter of the falling object, object shape, surface roughness, fluid viscosity (temperature dependent), and so forth, not to mention that once compressibility comes into play (velocity approaching about Mach 0.3 or so), additional energy is lost, and resistance increases phenominally at Mach 1.0 due to the buildup of the sonic pressure wave (sonic boom).
Excellent points. To add to what has been said, our projectile should be designed perfectly smooth to maintain laminar flow, though it may cease to be possible at the speeds we are considering. The shape would need to smoothly taper to a point at the rear to prevent an easy onset of recirculation for such a smooth body.

Finally, you really need to say terminal velocity at what altitude. As has been mentioned, a human could break the sound barrier (whether or not it has already happened) in freefall if he were to fall from high enough where the air is thinner. Once he descened to a lower altitude he would slow down to the standard human freefall speed (around 200 mph in a straight arrow position) even if his 'chute didn't open.

Bippy the Beardless
01-14-2005, 03:20 PM
As for the highest terminal velocity - I would expect a small black hole would fall pretty fast.
Wouldn't it be the earth be falling to the black hole with a high terminal velocity? ;)

Sam Stone
01-14-2005, 07:56 PM
A teardrop shape will maximize laminar flow of the air, but it won't give you minimum drag. The reason is because a teardrop shape still has significant frontal area.

My guess for maximum terminal velocity would be a very dense material formed into a needle-shape, with very small stabilizing fins. Or maybe you could do away with the fins if you made the density of the object slightly greater towards the front, so it would have a tendency to fall straight down.

spinky
01-15-2005, 03:59 AM
Definitely dense - osmium or iridium as someone already mentioned. This is because buoyancy is a factor. In a vacuum, this wouldn't matter.Of course it wouldn't matter. But neither would any other factors, since there's no such thing as terminal velocity in a vacuum.

kferr
01-15-2005, 04:16 AM
there's no such thing as terminal velocity in a vacuum.
Other than c. ;)

Desmostylus
01-15-2005, 05:31 AM
Wouldn't it be the earth be falling to the black hole with a high terminal velocity? ;)No, scr4 isn't talking about a conventional black hole. He's talking about small ones, which are speculated to exist (http://usatoday.com/news/science/astro/2002-01-16-black-holes.htm). A small black hole with enough mass to survive long enough to reach the earth's surface might weigh only a few grams, and so there's no question about the earth falling "toward" the black hole, the black hole's not heavy enough. The black hole wouldn't gobble the earth up, either, because small black holes decay very quickly.

Back to the original question, what's wrong with neutrons? Unless they happened to hit an atmospheric nucleus, they won't be slowed down by the atmosphere. They have a half life of around 15 minutes, which is enough time for a 4,000 km fall, and a terminal velocity of around 9,000 m/s (32,000 km/h, 20,000 mph). That's pretty close to the 11,000 m/s escape velocity of the earth.

A longer lived object could achieve a higher terminal velocity, and it's shape and size wouldn't really matter much. A big rock dropped from way outside the atmosphere would achieve most of the 11,000 m/s escape velocity while it was still outside the atmosphere, but once it did hit the atmosphere, it would start to burn up and slow down, so it might impact at say, 10,000 m/s.

But a big rock dropped from higher again, say from the orbit of Pluto, would approach the escape velocity of the earth/sun system, which is around 44,000 m/s (http://en.wikipedia.org/wiki/Escape_velocity) (160,000 km/h, 100,000 mph).

Gaius.Cornelius
01-15-2005, 07:40 AM
I wonder if they mad bombs "bomb shaped" for the same reason?

Well some bombs are certainly designed for maximum terminal velocity. See Tallboy (http://lancastermuseum.ca/s,tallboy.html) for example. This bomb fell at up to 750 mph. And it is exactly the shape that many contributors to this thread have anticipated.

RM Mentock
01-15-2005, 11:59 AM
Imagine a meteor approaching at 1 million (cue Dr Evil little finger to mouth) mph. It enters the atmosphere & begins to slow down. It hits the ground still going 900,000 mph. Was that terminal velocity? Probably not. Had the atmosphere been thicker, the speed would have continued to reduce as the air drag force was greater than G.
In addition to atmospheric friction, you have to take into account lithospheric friction, is all.

flight
01-18-2005, 10:04 AM
A longer lived object could achieve a higher terminal velocity, and it's shape and size wouldn't really matter much. A big rock dropped from way outside the atmosphere would achieve most of the 11,000 m/s escape velocity while it was still outside the atmosphere, but once it did hit the atmosphere, it would start to burn up and slow down, so it might impact at say, 10,000 m/s.

But a big rock dropped from higher again, say from the orbit of Pluto, would approach the escape velocity of the earth/sun system, which is around 44,000 m/s (http://en.wikipedia.org/wiki/Escape_velocity) (160,000 km/h, 100,000 mph).
But you see, we are not talking about impact velocity, but about terminal velocity, which is where the object has zero acceleration. The BIG ROCKS are still decelerating when they hit.

ZenBeam
01-18-2005, 11:51 AM
I don't think this question has an answer unless some constraints are added. For a sphere, just use more material and the terminal velocity will increase. If you specify the mass, make the sphere denser (and hence smaller) and the terminal velocity will increase. If you specify a mass and maximum density, Sam Stone's needle shape can always be made longer and narrower and I suspect its terminal velocity will increase.

MaxTheVool
01-18-2005, 04:34 PM
I also like a needle shape... and another way to keep it straight up and down is to have it be spinning very fast around its axis.

Chronos
01-18-2005, 04:54 PM
Back to the original question, what's wrong with neutrons? Unless they happened to hit an atmospheric nucleus, they won't be slowed down by the atmosphere. They have a half life of around 15 minutes, which is enough time for a 4,000 km fall, and a terminal velocity of around 9,000 m/s (32,000 km/h, 20,000 mph). That's pretty close to the 11,000 m/s escape velocity of the earth.Note that the lifespan of a particle is not a hard-and-fast thing. The average lifespan of a neutron is about fifteen minutes, but a very lucky neutron could, in principle, live for any length of time. However, if it doesn't chance to interact with any nucleus, then it's effectively falling through vacuum, so I don't think that one can meaningfully talk about terminal velocity. If one had a uniform atmosphere of sufficient thickness in a uniform gravitational field and a sufficiently long-lived neutron, then the assumption of no interactions would eventually break down, and eventually one would be able to define an average interaction rate and therefore a terminal velocity. While that terminal velocity would no doubt be very large, I don't know offhand what it would be.

Also incidentally, neutrinos are an even better candidate here. They're only about a billionth the mass of the neutron, but they more than make up for that with their low cross-section for interaction with other matter, and they apparently have an infinite lifespan.

Webafrica
01-23-2005, 09:31 AM
Ok so two things are still unclear to me:

1) Does density affect the speed of the object? With and without the presense of air.
F=MA but is "A" not fixed at 9.8g (or whatever it is).?

2) If we fix mass and density (ie the contraints talked about earlier), can it be calculated say computationally, what the most efficient free fall shape is?

Sam Stone
01-23-2005, 11:37 AM
Ok so two things are still unclear to me:

1) Does density affect the speed of the object? With and without the presense of air.
F=MA but is "A" not fixed at 9.8g (or whatever it is).?


There are two forces acting on a falling object. The first is the force of gravity acting on the mass of object. The second is wind resistance. As an object falls it will start out with a wind resistance of zero, so it will accelerate. As it picks up speed, the force from wind resistance increases. When the two forces balance out, the object has reached terminal velocity and will no longer increase in velocity.

So, if two items have identical wind resistance, the heavier one will fall faster. You can try this by taking two ping-pong balls and injecting one with water. Then drop both of them and see what happens.


2) If we fix mass and density (ie the contraints talked about earlier), can it be calculated say computationally, what the most efficient free fall shape is?


There might be several shapes that are equally efficient. The two most critical parameters are going to be frontal area, and wetted area. Frontal area determines how much air must be 'pushed aside' as the object falls, and wetted area is the total surface area of the object. Air is viscous, and tends to stick to things. So the bigger the object, the more drag created by air sticking to the surface.

zut
01-23-2005, 11:55 AM
Ok so two things are still unclear to me:

1) Does density affect the speed of the object? With and without the presense of air.
F=MA but is "A" not fixed at 9.8g (or whatever it is).?
I assume you mean the density of the object (as opposed to density of the atmosphere). But yes, in general a denser object will have a higher terminal velocity -- I'm reasonably sure all the posters above would abree on that.

Now, let's take a look at the definition (http://searchbox.hyperdictionary.com/dictionary/terminal+velocity) of terminal velocity; one such is "the constant maximum velocity reached by a body falling through the atmosphere under the attraction of gravity. [my italics]" The point is, the definition of terminal velocity requires the presence of an atmosphere; the "terminal velocity" without air is a meaningless concept (or... maybe not meaningless, but you probably shouldn't be calling it terminal velocity).

ZebraShaSha
01-23-2005, 11:58 AM
I also like a needle shape... and another way to keep it straight up and down is to have it be spinning very fast around its axis.

Wouldn't that burn incredibly fast? Or am I just crazy?

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