A question about ballistics

[thetexan]

According to wikipedia a battleship 16" gun fires a 2700 lb shell at a muzzle velocity 2690 fps with a range of up to 24 miles.
A high power rifle bullet at that muzzle velocity can only be expected to travel 1-2 miles. Why the discrepancy?

If both objects leave the muzzle at 2960 fps they both are free flying at the point they leave the muzzle. Everything I thought I had learned about rate of fall is that two objects of different mass fall at the same rate...in other words...are effected by gravity the same way. Both projectiles have the same initial velocity, and are effected by gravity the same way...why the difference in distance?

tex

 

[RUber]

I think the principle difference is the angle of launch. Artillery in general will use a higher angle to maximize range. Very few marksmen will ever point their rifles up 30 degrees from horizontal and hope to hit a distant target.

 

[nuclear_chris]

The actual distance a projectile (bullet, cannonball, etc) travels will depend on the angle at which it is fired. As long as the gravitational forces do not change, mass has no play into determining where and in what time the projectile lands. It can be shown that in order to maximize the distance, you fire at 45 degrees relative to the horizontal.

The question I would ask to avoid confusion is what angles were the bullet and the shell fired at?

 

[berkeman]

Even angling the rifle barrel up, you won't get more than a few miles of bullet travel.

The main difference is in the mass of the artillery round versus the bullet. It loses velocity to air resistance much more slowly, so it can travel much farther.

 

[nuclear_chris]

Air resistance will play a role in how far the projectile lands, however, if it did have a significant effect, I would think the bigger cannon ball would be impacted more than the smaller bullet (assuming that there shapes are similar).

I don't recall that air resistance has a significant effect in projectile motion, but I'm not completely sure.

 

[jbriggs444]

Air resistance will play a role in how far the projectile lands, however, if it did have a significant effect, I would think the bigger cannon ball would be impacted more than the smaller bullet (assuming that there shapes are similar).

I don't recall that air resistance has a significant effect in projectile motion, but I'm not completely sure.

Berkeman has it right. Air resistance has a very significant effect on projectile motion. The rearward acceleration of a bullet due to air resistance is typically much larger than its downward acceleration due to gravity.

A larger cannon ball (actually more cylindrical than ball-shaped) has more surface area (scales as roughly as diameter squared). But it also has more mass (scales roughly as diameter cubed). More mass per unit area means less effect from aerodynamic drag.

 

[jim mcnamara]

Answer to OP: the mass of the projectile is very important in exterior ballistics.

https://en.wikipedia.org/wiki/Ballistic_coefficient - this is exterior ballistics.

The ballistic coefficient of given projectile measures how well the projectile resists drag. The drag on projectiles is so important that there are defined standard atmospheres for testing flat trajectories, less than 20 degrees from horizontal, assumed to keep air pressure constant:
“Army Standard Metro Conditions" is 29.53 inches of mercury at a temperature of 59 degrees F. with a relative humidty of 78 percent.
The ICAO Standard atmosphere is a temperature of 59 degrees F. at 29.92 inches of mercury, with 0% RH.
When you run ballistics programs the POC software usually assumes one of these for base tables.

Mass is a major factor. Air density is also a major player since drag from air molecules is what slows projectiles diffently depending on ballistic coefficient.
Obvoiusly gravity is constant for every project, so we want to see why some go further than others.

There are several methods to calculate this.(See link).

The reason for high angle trajectory testing and modeling: For artillery rounds, the US Army used flat trajectory methods historically and then used methods where the projectile goes through differing air densities as the projectile goes up and down through the atmosphere. Some large guns fire projectiles out near the upper bound of the atmosphere( defined as 100000 ft) when fired at high angles. So accounting for change in air density is really important.

 

[thetexan]

Ok...muzzle angle for both is 45 degrees. Muzzle velocity 2960 fps for both. The 16 inch shell weighs 2900 lbs, the rifle bullet 180 grains. Why will the big she'll go much farther?

 

[Mark44]

Ok...muzzle angle for both is 45 degrees. Muzzle velocity 2960 fps for both. The 16 inch shell weighs 2900 lbs, the rifle bullet 180 grains. Why will the big she'll go much farther?

Your question is answered in posts #4, 6, and 7. Please read those replies.

 

[berkeman]

Why will the big she'll go much farther?

"She'll be coming 'round the mountain..."

https://en.wikipedia.org/wiki/She'll_Be_Coming_'Round_the_Mountain

 

[Dr. Courtney]

There are right and wrong answers above.

The right answer has to do with the ratio of drag force to projectile mass.

A bullet with a ballistic coefficient of 0.400 will lose half its energy (30% of velocity) in about 400 yards at sea level. Rifle bullet ballistic coefficients vary from 0.300 to 0.800.

 

[jim mcnamara]

Rifle BC's are typically less than 1.0. 16" Naval guns have a BC of ~14.9. BC measures how much resistance to drag. More resistance to drag == greater distance travelled. That is why.