Gun-loving India 'god-woman' shoots wedding guests

[Seth]

The main reason that smaller bullets are unlikely to cause harm is down to the way that surface area increases with size. As things get bigger the weight increases far faster than the surface area. So if you had two perfect spheres of lead of different sizes, and dropped them from a height, the big one would fall faster because the drag would be less in relation to it's mass.

Interesting claim. I'm a bit uncertain of your conclusion though. You say smaller bullets (spheres) are less likely to cause harm because they are of lesser weight, but then you say that its due to the surface area of the larger bullet (sphere) impeding its acceleration due to gravity as a function of aerodynamic drag.

Since we know that both spheres are accelerated by gravity at exactly the same rate; 32 fps2, regardless of their mass, according to Galileo and as confirmed by experiments on the moon with dropping a hammer and a feather at the same time in a vacuum and seeing them strike the ground at the same time, it would seem to me that the small sphere would fall faster because of it's smaller aerodynamic profile and the larger sphere would fall more slowly (though only marginally so) because of its large aerodynamic profile.

Did you err, or am I missing something in your argument?

[Hermit]

The main reason that smaller bullets are unlikely to cause harm is down to the way that surface area increases with size. As things get bigger the weight increases far faster than the surface area. So if you had two perfect spheres of lead of different sizes, and dropped them from a height, the big one would fall faster because the drag would be less in relation to it's mass.

Interesting claim. I'm a bit uncertain of your conclusion though. You say smaller bullets (spheres) are less likely to cause harm because they are of lesser weight, but then you say that its due to the surface area of the larger bullet (sphere) impeding its acceleration due to gravity as a function of aerodynamic drag.

Since we know that both spheres are accelerated by gravity at exactly the same rate; 32 fps2, regardless of their mass, according to Galileo and as confirmed by experiments on the moon with dropping a hammer and a feather at the same time in a vacuum and seeing them strike the ground at the same time, it would seem to me that the small sphere would fall faster because of it's smaller aerodynamic profile and the larger sphere would fall more slowly (though only marginally so) because of its large aerodynamic profile.

Did you err, or am I missing something in your argument?

I think mm is saying that the effect of wind resistance varies in line with the ratio between mass and surface area. If the surface area per grain is greater in small calibre bullets than large ones he'd be right.

[JimC]

The main reason that smaller bullets are unlikely to cause harm is down to the way that surface area increases with size. As things get bigger the weight increases far faster than the surface area. So if you had two perfect spheres of lead of different sizes, and dropped them from a height, the big one would fall faster because the drag would be less in relation to it's mass.

Interesting claim. I'm a bit uncertain of your conclusion though. You say smaller bullets (spheres) are less likely to cause harm because they are of lesser weight, but then you say that its due to the surface area of the larger bullet (sphere) impeding its acceleration due to gravity as a function of aerodynamic drag.

Since we know that both spheres are accelerated by gravity at exactly the same rate; 32 fps2, regardless of their mass, according to Galileo and as confirmed by experiments on the moon with dropping a hammer and a feather at the same time in a vacuum and seeing them strike the ground at the same time, it would seem to me that the small sphere would fall faster because of it's smaller aerodynamic profile and the larger sphere would fall more slowly (though only marginally so) because of its large aerodynamic profile.

Did you err, or am I missing something in your argument?

MM was correct. If air resistance did not occur, objects of any mass or shape would accelerate downwards at the same rate (9.8 m/s/s). However, given air resistance, smaller objects are disproportionately affected by air resistance, so that their terminal velocity is lower. The reason is that their weight force is proportional to the cube of their radius, whereas their cross-sectional area is only proportional to the square of the radius. The same would apply to the less dense of 2 identically shaped and sized objects. Further complications arise, of course, if the 2 objects are different shapes, or if one is tumbling and the other is not.

[Feck]

I'd still take a bet that it wasn't a 'falling bullet'.

[mistermack]

To simplify it, consider two cubes. One has 1ft sides, the other has 2ft sides.
The one with 1ft sides has a surface area of 6 sq ft, and volume of 1 cu ft. Ratio 6:1
The one with 2ft sides has a surface are of 24 sq ft and volume of 8 cuf ft. Ratio 3:1

[JimC]

I have constructed an Excel spreadsheet which calculates the terminal velocity of any spherical object of given radius and density. I am such a fucking nerd...

[Feck]

Bullets are not spherical (this century )

[JimC]

Bullets are not spherical (this century )

If falling without tumbling, then the difference in terminal velocity to a musket ball with the same mass and density would be relatively small.

[Seth]

The main reason that smaller bullets are unlikely to cause harm is down to the way that surface area increases with size. As things get bigger the weight increases far faster than the surface area. So if you had two perfect spheres of lead of different sizes, and dropped them from a height, the big one would fall faster because the drag would be less in relation to it's mass.

Interesting claim. I'm a bit uncertain of your conclusion though. You say smaller bullets (spheres) are less likely to cause harm because they are of lesser weight, but then you say that its due to the surface area of the larger bullet (sphere) impeding its acceleration due to gravity as a function of aerodynamic drag.

Since we know that both spheres are accelerated by gravity at exactly the same rate; 32 fps2, regardless of their mass, according to Galileo and as confirmed by experiments on the moon with dropping a hammer and a feather at the same time in a vacuum and seeing them strike the ground at the same time, it would seem to me that the small sphere would fall faster because of it's smaller aerodynamic profile and the larger sphere would fall more slowly (though only marginally so) because of its large aerodynamic profile.

Did you err, or am I missing something in your argument?

MM was correct. If air resistance did not occur, objects of any mass or shape would accelerate downwards at the same rate (9.8 m/s/s). However, given air resistance, smaller objects are disproportionately affected by air resistance, so that their terminal velocity is lower. The reason is that their weight force is proportional to the cube of their radius, whereas their cross-sectional area is only proportional to the square of the radius. The same would apply to the less dense of 2 identically shaped and sized objects. Further complications arise, of course, if the 2 objects are different shapes, or if one is tumbling and the other is not.

Yes, I see that you are correct after reviewing my college aerodynamics texts, not that I understand Reynolds numbers or drag calculations at all anymore. Drag increases with the square of the velocity, which is all I really needed to know as a pilot. I concede the point.

[Seth]

I have constructed an Excel spreadsheet which calculates the terminal velocity of any spherical object of given radius and density. I am such a fucking nerd...

Let's see it!

[Seth]

I'd still take a bet that it wasn't a 'falling bullet'.

I think you're right. After reading the article it looks like she and her guards were just waving the guns about and firing. She's been charged with murder.

[JimC]

I have constructed an Excel spreadsheet which calculates the terminal velocity of any spherical object of given radius and density. I am such a fucking nerd...

Let's see it!

I would if I knew how to attach an Excel file to a post, or even a picture of one. Brian might tell me how...

[Seth]

Bullets are not spherical (this century )

If falling without tumbling, then the difference in terminal velocity to a musket ball with the same mass and density would be relatively small.

Well, maybe. A sphere is not a very efficient projectile.

The ballistic coefficient of a round ball weighing 750 grains with a diameter of 0.50 in is 0.276.

The ballistic coefficient of a 50 Cal .510 750 gr A-MAX bullet is 1.050.

A higher BC means less drag.

Therefore, a 750 grain sphere will reach a lower terminal velocity than a 50 Cal .510 750 gr A-MAX bullet will if it falls nose-down.

I don't have my ballistics calculator handy at the moment. Perhaps JimC can run the nerdy numbers.

[Seth]

I have constructed an Excel spreadsheet which calculates the terminal velocity of any spherical object of given radius and density. I am such a fucking nerd...

Let's see it!

I would if I knew how to attach an Excel file to a post, or even a picture of one. Brian might tell me how...

print it out as a PDF and attach it as an image.

[JimC]

I'll give it a go when I have some time...