# Maximum speed of falling objects?

#### Dinosaur

##### Rational Skeptic
Valued Senior Member
A recent TV program claimed that the maximum speed of a penny is between 35 and 65 miles per hour (56 to 104 km per hr). I guess that a penny does not fall edge first, or it would reach a higher speed.

I think that a falling human body reaches a maximum speed of about 125 MPH (200 km per hr).

How fast does a bullet fall? I have read about people being killed by bullets fired into the air and hitting a person when they fall.

Would a spherical steel ball bearing fall faster or slower than a bullet? I expect very small steel spheres to fall slower than large ones due to a larger area to mass ratio, but am not sure that medium size ones would fall slower than large ones.

Does anybody know how fast various objects fall?

A bowling ball and a walnut dropped from the same height would fall at the same speed. Although gravity has everything to do with mass, mass plays no part in determining which object falls faster. Both fall at the same rate, regardless of mass.

Technically, the only real top-speed of any falling object is the speed of light. When an object falls, it falls at a perpetuating accelerating rate. In free fall, you get faster and faster as you fall, no exception; be it a penny, bullet, person or grand piano.

Yes all of that is true but the air gets in the way limiting how fast objects can fall. I guess to reach the fastest speed object needs to act like a wing flying straight down to cutt through the air. Perhaps an ellipse would work better then a sphere.

Or maybe your could design somethat that would try accelerating as it fell like a fixed helicopter blade designed to fly down but passively powered by the natural act of falling and then spinning.

What a contest if would be to design an object to fall to the ground the fastest. I will be betting on the rock.

CTEBO: Like FNG2k4 said, all objects that fall through the air will eventually reach a maximum speed (called the 'terminal velocity') based on their mass and shape.

Dinosaur: I have also heard stories of people being injured or killed by falling bullets. The equations for calculating terminal velocity aren't very complicated. Maybe you could run them for a penny and a bullet and see how they compare?

Dinosaur said:
A recent TV program claimed that the maximum speed of a penny is between 35 and 65 miles per hour (56 to 104 km per hr). I guess that a penny does not fall edge first, or it would reach a higher speed.

Well the penny would go ~35 mph when dropped face down (and it stayed face down) and it would travel 65 mph if it stayed edge down.

How fast does a bullet fall?

All objects should fall at roughly the same acceleration (unless they aren't very dense like feathers) so the speed will depend (nonlinearly) on the maximum height from which the bullet came up to a certain height. Beyond that height the bullet will not get any faster (terminal velocity).

Would a spherical steel ball bearing fall faster or slower than a bullet?

I would imagine it travels slower than a bullet (if the bullet is travelling the right way) since the bullet is aerodynamically optimised for air travel. It has a very sharp front which minimised turbulence.

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 * Time<sup>2</sup> / 2

Acceleration = Approximately 32 Feet / Seconds<sup>2</sup> or 980 cm / seconds<sup>2</sup>

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.

It's really not that complicated. I recall having to calculate the terminal velocities of all sorts of things in my basic kinematics physics class, years ago. You can find the equations to do it here http://scienceworld.wolfram.com/physics/TerminalVelocity.html , although you'd have to look up the density for air at sea level, or wherever you want to do the calculation.

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.

Nasor said:
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.

Are you sure of what you say here? You can look at the link that you gave and see that the drag force depends not only on the cross-section of the objects but also on the shape of the object through the drag coefficient C_d.
The smaller the drag coefficient, the higher the final velocity. (with all other parameters remaining the same, including the cross-section).

Dinosaur, I don't know a where to find the info you are seeking, but the thread
reminded me of a program I once watched on the Science Channel, i believe.
It concerned a world record freefall jump from a high altitude balloon. I found a link to
the group that was to make the attempt, but am not sure if it has been completed
yet. The jump was to be from 130,000 ft. and velocities for the jumper were projected
to be much over Mach 1. I believe the record is Mach 1.7.
http://www.stratoquest.com/default.cfm?page=25

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.

Well if the maximum speed of a penny is higher than 65 mph as u say then they're wrong right? Simple as that! The max speed will be when it is edge down all the way. Probably not as remote as balancing a needle on its head but gets more remote the further it has to travel.
Even though you're ignoring the effects of the mass/density and shape, I would also expect a penny to fall faster than a body.
Yes there might be a very small horizontal component of velocity even without a wind but this is the least of our troubles concerning average or max speed.

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.

Well without a firepower behind it, the bullet is never going to fall with the muzzle velocity in an atmosphere. It is losing energy to the atmosphere all the time on the way up AND down.

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.

The bullet would have differential weight as well with most mass in the front to prevent deviations of the nose from pointing forwards all the time.

2Inquisitive:Unfortunately, the link you provided mentioned exceeding Mach 1 without specifying speed in MPH or km/hour. I think the speed of sound decreases with density, approaching zero in a vacuum. What is mach 1 at 130,000 feet? This is above 99% of the atmosphere. While it seems strange, I would expect a person falling from 130,000 feet to initially accelerate and then start slowing down at some point. I have no idea of what the maximum speed would be or where it would occur.

1100f: You seem to be on the ball, realizing that the drag coefficient is affected by the shape of the object, making cross sectional area and mass only part of the equation. I have heard it claimed that a smooth golf ball would travel about half the distance of a dimpled ball due to the effect of the dimples on the drag coefficient. This effect would also apply to a falling object.

Another issue is the effect of shape on orientation while an object is falling. Assuming still air, a sphere with the same mass and cross sectional area as the face of a penny would fall vertically. I would not expect the penny to fall vertically with one face down. Without actually experimenting I cannot be sure, but I would expect the penny to change orientation as it fell. I would also expect a horizontal component of velocity, and perhaps tumbling. I have no idea of how orientation would affect the vertical component of velocity. As the orientation changed, the cross sectional area and perhaps the drag coefficent would change. A horizontal componet of velocity would (I think) be at the expense of the vertical component.

As mentioned in a previous post, it has been claimed that a bullet fired into the air would be potentially lethal when it came down. Obviously atmospheric friction would slow it down. Would it be slowed enough to make it non-lethal? Small caliber weapons with a low muzzle velocity would surely be less dangerous than a heavier bullet with a high muzzle velocity. There have been stories about people being killed by a rifle or hand gun fired into the air. Are such stories merely myths?

current record jump in 1960 from 102,800 ft. reached a maximum speed of 614 mph,
"just under the speed of sound for his altitude." He opened his parachute at above
90,000 ft, but I don't know the exact altitude the speed was reached.
A excerpt from the Popular Science article linked to from the Stratoquest site:
"Twelve seconds later, her pace has picked up; the thin wind is howling and she's already descended 5,000 feet. Within another 15 seconds she's traveling nearly 700 mph, hits Mach and discovers how severe it really is. Another 10 seconds, and maximum speed: about 885 mph, Mach 1.3."
And yes, of course, a jumper's speed will slow as they move into denser air. At 20,000
ft. she will change to a horizontal, belly-flop position and slow to 150mph before releasing her parachute. I read Stratoquest is still trying to get enough sponsers
for the jump, which will cost over 6 million dollars for the specialized balloons and
equipment. A frenchman is planning a jump from the same altitude and there is a race
to see who can do it and survive. Very dangerous.
http://www.popsci.com/popsci/science/article/0,12543,409394,00.html

Dinosaur said:
2Inquisitive:Unfortunately, the link you provided mentioned exceeding Mach 1 without specifying speed in MPH or km/hour. I think the speed of sound decreases with density, approaching zero in a vacuum. What is mach 1 at 130,000 feet? This is above 99% of the atmosphere. While it seems strange, I would expect a person falling from 130,000 feet to initially accelerate and then start slowing down at some point. I have no idea of what the maximum speed would be or where it would occur.

1100f:Another issue is the effect of shape on orientation while an object is falling. Assuming still air, a sphere with the same mass and cross sectional area as the face of a penny would fall vertically. I would not expect the penny to fall vertically with one face down. Without actually experimenting I cannot be sure, but I would expect the penny to change orientation as it fell. I would also expect a horizontal component of velocity, and perhaps tumbling. I have no idea of how orientation would affect the vertical component of velocity. As the orientation changed, the cross sectional area and perhaps the drag coefficent would change. A horizontal componet of velocity would (I think) be at the expense of the vertical component.

As we've said before the chances are that the penny will not stay the same orientation. It will fall faster with less drag (smaller x-sectional area).

As mentioned in a previous post, it has been claimed that a bullet fired into the air would be potentially lethal when it came down. Obviously atmospheric friction would slow it down. Would it be slowed enough to make it non-lethal? Small caliber weapons with a low muzzle velocity would surely be less dangerous than a heavier bullet with a high muzzle velocity. There have been stories about people being killed by a rifle or hand gun fired into the air. Are such stories merely myths?[/

Well since I heard that a penny thrown off the Empire State Building would kill someone if it hit their head, I presume a shot fired into the air definitely would as it would travel higher than the building.

The TV show debunked the myth about a penny thrown from the Empire State building. Their mathematical analysis and some experiments showed that the penny would not do serious damage. It is too light and does not fall fast enough.

Either I missed part of the show or they did not analyze the bullet fired into the air and hitting somebody when it came down. I would guess that the bullet fired into the air could be lethal when it came down

I just worked it out. The velocity on impact of the penny would be 311 km/h which (even assuming zero air resistance and drag) is still a good deal less than half the muzzle velocity of a colt 45. It just might not kill u as u say!!!
Having said that, I think we can assume very little air resistance for a penny facing edge down most of the way.

There seems to be a lot of speculation about the lethality of a bullet fired into the air on it's return to earth.

"A bullet fired into the air can climb two miles and remain in flight for more than a minute. As it falls, the bullet reaches a velocity of 300 to 700 feet-per-second. A velocity of only 200 feet-per-second is sufficient to penetrate the human skull."

http://www.mcall.com/news/nationworld/all-gunfire0118,0,819915.story

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.

contrarian said:
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.

Well according to that report (and to my own calculations), a penny dropped off the Empire state building would penetrate the human skull!

contrarian said:
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.

I don't think density would have a very important effect on falling objects in air. Now in a liquid medium (especially a viscous one) there might be a large effect.

I think it'd most likely depend on how the drag force is correlated to the velocity of the moving object. If you just simplify things and say that the drag force is proportional to the velocity, then my best guess would be:

F = ma
mg - b * (dx/dt) = m * (dv/dt) (b is a constant)

And solve to see how velocity changes over time.

Of course, in real life, the drag force would certainly also depend on other factors. I think an engineer or at least an applied physics major would know this kind of thing pretty well.