Maximum speed of falling objects?

[Repo Man]

Dear Cecil:

I have this friend and he isn't playing with a full deck, if you know what I mean, and he said if you drop a penny from the top of the Empire State Building and it happened to hit someone in the head it would go through just like that. Is this true? --Joe D., Towson, Maryland

Dear Joe:

I'm explaining this only on condition you don't try the experiment yourself.

Given that the Empire State Building is 1,250 feet tall and ignoring such factors as wind resistance for the moment, a penny dropped from the top would hit the ground in approximately 8.8 seconds, having reach a speed of roughly 280 feet per second.

This is not particularly fast. A low-powered .22 or .25 caliber handgun bullet, to which a penny is vaguely comparable in terms of mass, typically has a muzzle velocity of 800 to 1,100 FPS, with maybe 75 foot-pounds of energy.

On top of this we must consider that the penny would probably tumble while falling, and that the Empire State Building, like all tall buildings, is surrounded by strong updrafts. As a result the penny's descent would be substantially slowed.

Thus while you might conceivably inflict a fractured skull on some hapless New Yorker (or, more likely, some cretinous tourist from Towson), the penny would not "go through just like that." I bet it wouldn't even penetrate the skin. Not that I intend to find out.

For the record, the Empire State folks claim no one has ever dropped anything off their building. Yeah, right.

http://www.straightdope.com/classics/a1_225.html

Dear Cecil:

Every so often you see it on the news: streets full of Middle Eastern men indiscriminately firing guns straight up into the air. If I learned anything from physics class, it's that what goes up must come down. I'm certain the returning projectiles don't float harmlessly to earth and wonder how often they plunge into bystanders. --Kathy Johnson, Madison, Wisconsin

Cecil replies:

Those Middle Eastern men. You want to shake them and say, guys! Is this the safe and sensible way to celebrate? Can't we just say "hooray!" and "whoa, baby"?

But you raise a good point. How dangerous is this really? The question is controversial. Let me lay it out point by point.

Datum 1. At first I thought being struck by a bullet falling straight down would be no worse than getting hit over the head with a two-by-four--not the average guy's idea of fun, but not fatal either. What goes up must come down, but it needn't do so at the same speed. You run up against what's known as "terminal velocity." A bullet fired straight up will slow down, stop, then fall to earth again, accelerating until it reaches a point where its weight equals the resistance of the air. That's its terminal velocity.

For further insight, we turn to Hatcher's Notebook (1962) by Major General Julian S. Hatcher, a U.S. Army ordnance expert. Hatcher described military tests with, among other things, a .30 caliber bullet weighing .021 pounds. Using a special rig, the testers shot the bullet straight into the air. It came down bottom (not point) first at what was later computed to be about 300 feet per second. "With the [.021 pound] bullet, this corresponds to an energy of 30 foot pounds," Hatcher wrote. "Previously, the army had decided that on the average an energy of 60 foot pounds is required to produce a disabling wound. Thus, service bullets returning from extreme heights cannot be considered lethal by this standard."

If 30 foot pounds doesn't mean much to you, the bullet made a mark about one-sixteenth of an inch deep in a soft pine board. About what you'd get giving it a good whack with a hammer. Note that we're talking about bullets shot straight up here. If the bullet is fired more or less horizontally, it may not lose much speed before returning to earth and could easily kill someone.

More... http://www.straightdope.com/classics/a950414b.html

 

[JesseLeigh]

Falling/jumping into water

Evening!

I'm new here, but have been thoroughly enjoying this thread. Great forum, BTW.

Re: falling/jumping into water, I find myself perplexed by the contradictory info on the net.

Forty-one years ago, as a child, I jumped from a ninety foot high diving board (in Aberdeen, Scotland) into (IIRC) twenty-seven feet of water. Some people dove off the board but I wasn't quite brave enough for that. I raised my arms straight in the air above my head, and after jumping, I pointed my toes to make myself as aerodynamic an object as possible. I hurt the bottoms of my feet when I landed on the bottom of the pool, and my lungs were bursting (I forgot to take a breath just before entering the water), but other than that it was certainly a survivable experience. The water was not 'Concrete' as the movie The Guardian said it would be.

I was only eleven at the time but I remember the incident well. I haven't seen the facility for decades so I don't know if it still exists, but my guess would be that it does.

If all the science I've read on the net (and seen in that otherwise terrific movie) is remotely true, I should be dead. I'm not, and can't scientifically find an explanation for that - not to mention the liability issues that would present due to the mere existence of the pool in Aberdeen. :shrug: Any thoughts?

Shalom aleikhem - Jesse.

 

[Cannon]

This is more complicated that you folks seem to think it is. You should not rely on intuition except for qualitative comparisons of various objects. Without some established formulae, you cannot get good numeric answers.

Doing calculations including atmospheric effects is a difficult task. Even if you assume no wind, constant density at all altitudes, and a constant amount of water vapor in the atmosphere, it does not seem easy. In a vacuum, it is easy to calculate final speed at impact with the Earth. For an object with no initial velocity

• Distance = Acceleration * Time² / 2
  
  Acceleration = Approximately 32 Feet / Seconds² or 980 cm / seconds²
  
  Time = SquareRoot( 2 * Distance / Acceleration )
  
  Speed = Acceleration * Time
  
  Speed = SquareRoot( 2 * Distance * Acceleration )

I hope I did the above correctly. The acceleration is actually a variable, but the above is a good approximation for objects falling from less than ten miles above the earth. A reference book I have gives 32.1725 & 980.621 at sea level and 45 degrees latitude. I did a few calculations and rounded the results.

• From 5000 feet: 122 MPH
  From 10,000 feet: 550 MPH
  From 20,000 feet: 770 MPH
  From 5000 meters: 1127 km / hour

The above are for falling in a vacuum.

I have heard estimates of 125 MPH as the maximum for a human body, but do not know what assumptions are made about being tucked up or spread eagled. The clothing (if any) would make some difference.

The falling penny is a very difficult problem. The lower estimate of 35MPH and the higher estimate of 65MPH are not the difference between falling flat or edge down. It is due to different assumptions about how the penny changes orientation as it falls. Falling exactly edge down is a theoretical possibility like the possibility of balancing a needle on its point. Edge down, I would expect a penny to fall faster than a human body. Note that a penny would not fall straight down. When it was at a angle with the veritical, it would have a horizontal component of velocity. It might tumble.

The TV program was debunking a myth about a penny tossed from a high building and killing somebody when it hit them in the head. It said nothing about a bullet fired upwards and hitting somebody when it descended. In a vacuum, it would impact at muzzle velocity if fired straight up, but I have no idea about the atmospheric effects.

I am not sure how a bullet would fall. I suspect that it would fall nose first after the first few hundred feet, but am not sure about this.

I was hoping that some body here knew formulae or a URL leading to some real information.

So that is in-fact is correct would the constance acceleration of 2g's be twice the speed, or is there a compounding factor involved?

 

[Dinosaur]

JesseLeigh: Water would act much like concrete if you fell from 90-100 feet Belly Flop style. Water would not act like concrete if your entry is like a diver doing a Swan dive or using the entry you describe with toes pointed.

Falling from 90-100 feet onto concrete would likely be fatal no matter how you were oriented. Falling onto a lawn, you might be better off with a spread eagle landing. I suspect that landing face up is better than face down. This might be better than landing feet first & trying to use leg muscles to decelerate more slowly.

 

[Sci-guy]

In an ideal enviornment there is no maximum velocity of an object because on earth the gravitational acceloration is 9.81 m/s2, but when accounting for the air resistance that an object would encounter you must observe the object geometric shape. It all depends on how areodynamic the object is.

I heard the same sorty on television of a bullet after being fired in the air that landed and injured someone. They tested these accounts on mythbusters, you might want to watch the episode, it was a good one! Well not really because they all are good episodes.

 

[Tom13054]

I am a retired Police Officer when we went to the range to shoot there was a test area behind the hill of another shooting range. Now I know this is only a ricochet so the bullet did not go as high up but on occasion we would get hit with a falling bullet it didn't kill but it sure hurt a lot. The speed of the ammo used was 950 ft a second at the muzzle.

I may be totally off base here, but wouldn't the density of the object be a major factor, as well. I keep thinking of Archimedes Principle.

 

[three-brane]

I would think the density of the object would have alot to do with it. i am thinking of how the mass of an object curves space. your mass curves space. not nearly as much as the earths mass. and the suns mass is even more so, right. your thinking "no shit".
well the mass of a collapsed star where it warps space to the point of tearing it. not even light escapes and it is traveling at the speed of light.
the mass of a photon.
my point is your falling into the curve of the space around the earth. if you were the mass of a star and the size of you, your density would be so great the earth would be actually falling into you. yet you could argue you fell to the earth.
so i say yes density would matter.

 

[freziggity]

The max falling speed of anything is directly relative to the mass/density of the objects and the gravitational field of the test environment. On earth, gravity accelerates an object 9.8meters per second per second. On jupiter it is 9.8 per second per second times 2.5 Since Jupiter has 2.5 times earth's gravity. Other than that, friction will diminish the rate of fall for any object, but in a vacuum, everything falls at the same rate of speed. Cool question.

 

[Pinwheel]

You can try chucking darts off the top of a skyscraper.

 

[Syzygys]

Alright people, just a few observations and facts:

1. It is a well documented FACT that bullets fired into the air can kill people. Happens quite often actually. To reach the highest speed at arrival, it is better to fire the gun at an angle, so the bullet would keep its spin, instead of tumbling down.

2. There should be a dropping height limit, somewhere where the air starts to get thin. Those record parachute jumps shouldn't count because they started in the thin air area, thus they had the advantage of speeding up before reaching normal air. Thus it is not really a drop.

3. Shape is everything in this matter, and bullets tumble coming down. Now we could talk about the penny coming down on its edge if we make it spin, before the drop. My guess is that the fastest shape is the raindrop shape, a spherical shape with a tail. That has the lowest natural air resistance ratio...

 

[Syzygys]

Interestingly, it doesn't matter what shape a falling object has; only the cross-section is needed for calculating terminal velocity. A pointy object would have the same terminal velocity as a flat object, so long as they had the same cross-sections pointing toward the ground and were of the same mass.

This is incredible silly missconception. Because of the airdrag, shape is everything in falling....

You are saying that a rocket-shape and a parachute would fall with the same speed assuming everything else (weight and cross-section) being the same...

 

[iceaura]

In an ideal enviornment there is no maximum velocity of an object

There is, of an object accelerating only by gravity toward the earth.

The pull of the gravity gets smaller as the distance from the ground gets larger, and decreases faster than the distance increases - so eventually, falling from much higher up doesn't add much to the final speed.

My guess is that the fastest shape is the raindrop shape, a spherical shape with a tail. That has the lowest natural air resistance ratio...

Arrows fall faster than raindrops - and I doubt raindrops have a tail when they are falling.

 

[D H]

I would think the density of the object would have alot to do with it. i am thinking of how the mass of an object curves space. your mass curves space.

True, but completely irrelevant to the problem at hand. The Schwarzschild radius of a feather is about 10[sup]-30[/sup] meters; for a Nimitz class aircraft carrier the Schwarzschild radius is about 10[sup]-19[/sup] meters. General relativity is not relevant to this discussion.

An object's density, shape and even surface texture are important because the object is falling through the atmosphere. Atmospheric drag builds with velocity. At low Reynolds numbers drag is proportional to velocity. Once turbulent flow kicks in the drag force grows with the square of velocity. As a falling object gains speed the drag force will grow to be equal to gravitational force. This velocity where drag force is equal to gravitational force is called the object's terminal velocity stops accelerating at this point, called terminal velocity.

 

[Syzygys]

Arrows fall faster than raindrops - and I doubt raindrops have a tail when they are falling.

Have you actually tried it?

What's your point by the way?

1. Arrows are NOT natural.
2. There is more to it, like density and cross-section.

Anyhow you are just proving that shape does count...

 

[three-brane]

True, but completely irrelevant to the problem at hand. The Schwarzschild radius of a feather is about 10[sup]-30[/sup] meters; for a Nimitz class aircraft carrier the Schwarzschild radius is about 10[sup]-19[/sup] meters. General relativity is not relevant to this discussion.

An object's density, shape and even surface texture are important because the object is falling through the atmosphere. Atmospheric drag builds with velocity. At low Reynolds numbers drag is proportional to velocity. Once turbulent flow kicks in the drag force grows with the square of velocity. As a falling object gains speed the drag force will grow to be equal to gravitational force. This velocity where drag force is equal to gravitational force is called the object's terminal velocity stops accelerating at this point, called terminal velocity.

but if there was two objects of similar size and shape, the difference one has twice the density, they would still have the same terminal velocity?

 

[Syzygys]

but if there was two objects of similar size and shape, the difference one has twice the density, they would still have the same terminal velocity?

Nope. A bowling ball has a bigger TV then a same sized ball made of styrofoam.

"Terminal velocity varies directly with the ratio of weight to drag. More drag means a lower terminal velocity, while increased weight means a higher terminal velocity."

 

[D H]

but if there was two objects of similar size and shape, the difference one has twice the density, they would still have the same terminal velocity?

Of course not. That has nothing to do with relativity, however (the point you were trying to make in post #27). It has everything to do with atmospheric drag.

 

[iceaura]

Have you actually tried it?

yes.

Arrows are less dense than water, should fall more slowly on that criterion alone. If shot straight up, watched carefully straight down, they will overtake even fairly large raindrops after just a couple of hundred feet of free fall, at most. Mist and the like just floats.

Of course shape matters. But falling things, even liquids, do not automatically assume the best shape or orientation for maximum speed. Leaves from trees don't, for example. Air is complicated stuff to push through.

 

[D H]

My guess is that the fastest shape is the raindrop shape, a spherical shape with a tail. That has the lowest natural air resistance ratio...

That is a misconception. From http://www.newton.dep.anl.gov/askasci/gen01/gen01429.htm

If the drop is larger like a raindrop in free-fall, it has a domed top and a semi-flattened bottom because as it falls it must push the air out of its way. That "upward" push of the air being displaced causes the falling drop to have a rather flattened bottom.

Contrary to popular misconception, a free-falling raindrop is not shaped like a teardrop -- round on the bottom and pointy on top.​

Using the equivalence relationship "1 picture=1000 words," here are 3091 words on the shape of a raindrop.

 

[Syzygys]

>a free-falling raindrop is not shaped like a teardrop

I guess I misspoke. One of the best aerodynamic is the teardrop, at least that is what carmakers are trying to copy when they want to make a small airresistence car...

I guess the rain is too soft and it bends, thus kind of parachuting itself. But making it from hard material, a teardrop would come down pretty much with the fastest speed possible...

See the shape on the top: