Trajectory question

[nvbirdman]

I'm sure this has been asked MANY times before, but would a .320 round ball at 1200fps have the same trajectory as a .535 round ball at 1200fps?
No reason to be asking, just started thinking about it today.

 

[Musketeer]

I'm no ballistician, but I believe that a larger projectile always has a higher (more pronounced) trajectory. :thumbsup:

 

[musketman]

I'm sure this has been asked MANY times before, but would a .320 round ball at 1200fps have the same trajectory as a .535 round ball at 1200fps?

If they're both sighted in for, say 50 yards, then their impact trajectory will be at the same spot, zero at 50 yards... In that since, the answer would be yes...

However, the .535 roundball has a larger diameter and more mass, so it will have different characteristics than the .320 rb...

For instance, the heavier ball will not be effected by the wind as mush as the lighter one, also the smaller RB will take less powder to achieve the same velocity as the bigger projectile...

Thus, their trajectories will differ due to their mass and air resistance, not gravity...

Gravity effects all things the same, so they will both have the same "PULL" on them downwards...

Remember the gravity experiment?
A .320 round ball and my Ex-Wife dropped at the same time from the same distance will hit at the exact same time, only the roundball won't cause the cement to crack...

 

[robinghewitt]

I think the bigger ball will hit higher. Tiny balls from shotguns are quickly spent, cannonballs go much further.

There seems to be an advantage in being big.

 

[Ohio Joe]

I don't have any info on the .320 RB, but I can substitute it with the .350 -vs- .535 RB from the Lyman Black Powder Book I have.

.350 RB at 1200 fps will drop 3.81 inches at 50 yards...

.535 RB at 1200 fps will drop 3.54 inches at 50 yards...

This according to Lyman... I believe the trajectory would be as "Musketman" said, the same. The heavier .535 ball would be as "Squire Robin" said.

However, to get the two to strike at the same point of impact you would have to aim higher with the .350 RB.

Confussing isn't it. You would think if you aimed higher with the lighter ball that the trajectory would have to change at least a minimum of 0.27, but it doesn't. Your rear sight adjustment would and your line of sight becomes equal to your point of impact with both rounds.

I hope that made sense??? I think I just confussed myself??? :what: :hmm:

 

[waksupi]

I would think that the higher mass of the heavier round ball would take over in the trajectory department at longer ranges. The smaller ball, having less mass, would slow faster from wind resistance. Good physics question.

 

[Chickenfax]

Did somebody say physics????
I think the key to most of this is inertia. The heavier projectile has more inertia than the lighter projectile, hence air resistance will affect the lighter projectile more than the heavier one causing the lighter projectile to slow more than the heavier one, hence experiencing more bullet drop at the same muzzle velocity, hence this being a runon sentence and all.
As far as wind causing deflection... I don't think it would have much of an impact to one ball being deflected more than the other. Due to the fact that the larger ball having more inertia (more difficult for the wind to exert force upon) and the larger ball has more surface area. I would imagine these results would cancel each other out so that each ball would experience the same amount of deflection. Now, experimentally, I have seen a 50 caliber ball deflect in a moderate wind at 100 yards up to 8 +/- 1 inches.
ok, I am confused now too.

I'd also imagine somewhere in the mix, you'd have to consider terminal velocities as well.

:results:

 

[Stumpkiller]

I think the key to most of this is inertia. The heavier projectile has more inertia than the lighter projectile, hence air resistance will affect the lighter projectile more than the heavier one causing the lighter projectile to slow more than the heavier one, hence experiencing more bullet drop at the same muzzle velocity, hence this being a runon sentence and all.

Air resistance can be isolated from inerita. Inertia is a body's resistance to movement, and usually refers to a stationary object. (An object at rest tends to stay at rest). Since it is moving at 1,200 fps, inertia has been overcome. I think you meant momentum.

In the original question: 1,200fps for both a .32 and a .54 rifle. The .53 ball has almost five times the mass of the .310, so it starts with five times the energy since you've given them the same speed. Being that much more massive, it "bucks" the wind better and holds the energy (and trajectory) better. The wind resistance (side deflection from a breeze as well as frontal air resistance) is a factor of surface area, and a .310 ball has 1/3 the surface area, while having only 1/5 the mass, so it is less wind resistant that the .53.

Round projactiles behave differently than conicals. You get into all kinds of ballistic coefficients and sectional densities and it gets complicated. Since these are identically shaped: bigger = better.

And then there is the gyroscopic effect of the rotating ball resisting a lateral change it the linear force vector of it's straight path further resisting a change due to the unequal forces on it's surface caused by a side-wind. My brain hurts.

 

[Chickenfax]

Just to clarify.

Newton's first law of motion states that "An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This tendency to resist changes in their state of motion is described as inertia.

The force that slows the projectile is air resistance so I don't see how air resistance can be isolated from inertia. Also, inertia don't care if yer goin' half the speed of light, course Aunt May's cookies might turn out a little more cooked than usual...
There are many factors to consider with ballistics which is why it can get confusing. I was only dabbling in one of the possibilities. Don't forget that the rotation of the Earth contributes to a coriolis effect.

 

[Stumpkiller]

. . . so I don't see how air resistance can be isolated from inertia.

An object experiencing inertia is motionless. A bullet is a barrel obstruction or a chewing hazard at those points. Ain't no air resistance at all if it is not moving through the air. It's the in between we're worrying about. As soon as it moves it has no inertia and then has momentum. Look up "Inert."

And pass one of Aunt MAy's cookies before you run off for that dyctinoairy.

 

[Stumpkiller]

Upon further review, the Undersecretary of Ballistics of the Muzzleloading Forum has determined that I was wrong and "Inertia" does in fact apply to moving objects; that is, the property of a moving object to resist change is still inerta.

Not to be confused with equilibrium or stasis. (What do I know about Mass, I'm Methodist).

Point goes to Chickenfax.

Back to: "Something goes "Bang" and something else falls over."

 

[Chickenfax]

:huh: Undersecretary??? :huh:
I'm just tryin' to make it to Active Member....

But alas, this gives me an idea for a personal project. I'll go dig out my phisiks books and write down a treatise on bullet trajectory. It has always been an huge interest for me anyway. The main reason I've been in shooting. If anyone is interested, I'll post it here in the general forum.

And, I'd like to donate the point back to you Stumpy for the Moose Milk. Love it!

:redthumb:

 

This is amazing!

Some of you guys are actually nearly smart!

Now I know! My students were always sleeping through History class because they were resting up for physics!! And all of this time I thought it was just my teaching!

:results:

 

[Zonie]

For anyone interested, I ran the numbers thru a little Roundball ballistics program and came up with these answers.
They just prove that everyone who posted above is right.

This is for a .32 and .54 ball with a muzzle velocity of 1200 FPS. Both guns are sighted in for 50 yards.
It starts at 50 yards so the balls have lost some velocity. D=drop V=velocity
.32 roundball:
50 YARDS D=0 V=901
70 YARDS D=-2.8 V=828
90 YARDS D=-8.2 V=759
100 YARDS D=-11.9 V=727
120 yards D=-22.5 V=664
140 yards D=-37.4 V=605

.54 roundball:
50 YARDS D=0.0 V=991
70 YARDS D=-2.0 V=936
90 YARDS D=-5.9 V=887
100 YARDS D=-8.6 V=864
120 YARDS D=-15.7 V=822
140 YARDS D=-25.1 V=781

For hunters using a .54 cal roundball sighted in at 75 yards with a muzzle velocity of 1975 FPS. E=Ft/Lb Energy

50 YARDS D=+1 V=1397 E=1029
75 YARDS D=0 V=1203 E=758
100 YARDS D=-2.6 V=1073 E=607
120 YARDS D=-6.7 V=1007 E=535
140 YARDS D=-12.4 V=951 E=477