1.5" vs. 2"

[Solar]

How many of you guys are using 1.5" (40mm) vs. 2" barrels?

[Pete Zaria]

I have both but end up using the 1.5" more. Tighter fit with most vegetables and common projectiles I find. I use the 2" for caulk tubes and other things but I'd say the 1.5" sees 2x as much use.

Peace,
Pete Zaria.

[Blitz]

I have a 1.5" barrel, but I seldomly use it compared to a 2" one.

i think this answer will vary between people based on what kind of ammo they have most readily available to them.

[SpudBlaster15]

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[jimmy101]

...Not to mention the fact that given identical lengths, a 1.5" barrel will produce faster projectile speeds, more range, and more impact energy density (more damage) than a 2" barrel.

I'm not sure all of those statements are correct.

A smaller projectile will have a "faster projectile speed" but will not necessarily have greater range or more impact energy.

A larger barrel has greater surface area and more force is applied to the projectile at a given pressure. Comparing a 2" barrel with a 1.5" barrel would give 16/9 times more force applied to the projectile in the larger barrel.

The mass of the projectile goes up with the diameter of the barrel, roughly as the square of the barrel diameter. So a spud from a 2" barrel is about 16/9 times more massive than from a 1.5" barrel.

Lets see, the force on the projectile can be written as;
Force = PA = ma
Where P is pressure, A barrel cross sectional area, m is the mass of the spud and a the acceleration. Rearranging gives the accelerations as;
a=PA/m

We know that the area (A) goes up as the square of the barrel radius and the mass (m) goes up by about the same amount. So, to a first approximation, the acceleration (a) of a spud in a barrel is independent of the diameter of the barrel. (Remember, we are comparing a 1.5" and 2" barrel with everything else held constant.)

Since the two barrel give the same acceleration then the muzzle velocities are the same when the spud exits the barrel.

The kinetic energy of the spud is (1/2)mv². Since the muzzle velocities are the same for the two barrels the v² is the same. The difference is that the spud from the 2" barrel is 16/9 times more massive than from the 1.5" barrel. So, there is 16/9 times more kinetic energy in the 2" spud than in the 1.5" spud.

One thing I've left off is the difference in friction between the two barrels. The larger barrel will have a larger contact area with the spud than the small one. The contact area scales as the circumference of the barrel. A 2" barrel has 2/1.5 times more contact area than the 1.5" barrel. Hence, 2/1.5 more friction. (I've assumed that the spud length is independent of the barrel diameter which is only approximately true.) The small increase (33%) in friction partially offsets the greater mass (the mass had a 78% increase) of the 2" slug.

The net result is that the 2" slug has more kinetic energy than the 1.5 inch slug.

[SpudBlaster15]

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[Freefall]

Jimmy101, you say:

A smaller projectile will have a "faster projectile speed" but will not necessarily have greater range or more impact energy.

but then go on to say:

Since the two barrel give the same acceleration then the muzzle velocities are the same when the spud exits the barrel.

Both statements cannot be simultaneously true.

You also state:

We know that the area (A) goes up as the square of the barrel radius and the mass (m) goes up by about the same amount.

This is only true if the projectiles are of equal thickness. Typically, projectiles scale in thickness along with diameter.
So:
As diameter doubles, area quadruples, but volume (and thus mass) goes up by a factor of eight. 4x area acting on 8x mass = half acceleration and thus half velocity at a given point.

energy = mv^2

Since we have increased the mass by a factor of eight but cut the velocity in half, we've doubled the projectile energy at any given point in the barrel. (8)*(.5)^2 = 2

Now, for a given chamber with ideally sized barrels, the thin barrel will be longer than the fat barrel, such that the energy difference will not be so great. Typically, the thin barrel will have higher losses, leaving the fat barrel producing slightly higher energy levels.


Just pick a barrel that suits your needs and your available ammo. Do you want to lob big heavy projectiles, or do you want high muzzle velocity and a flatter trajectory?

[jimmy101]

No, the smaller round will not do "more damage to the target".
The smaller round will do more damage to a smaller area of the target. The total damage will be less with the smaller round.

Case in point, an armor piercing round. An APR is designed to give maximum damage to the smallest possible area to increase the chances of penetrating the armor. The actual damage to what is behind the armor is done by injecting more energy through the small hole made by the round and not by the actual damage to the armor.

[SpudBlaster15]

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[schmanman]

I use 2", works great for me, and I seem to find more stuff that fits in 2" than 1.5 inch.

3 and 4 inch are another story....

[jasonsmithmyer]

I have only made cannons with either a 3/4 inch barrel or a 2.5 inch barrel because they are common sizes for easy to get ammo. i.e. paintballs and tennis balls.

I've never shot a potatoe out of a gun

[jimmy101]

Also, because of the extra frontal area of the 2" round, it will lose energy to drag at a greater rate than the 1.5" round after leaving the barrel. At a certain range, the non proportional rates of deceleration would mean that the smaller round would actually have more kinetic energy.

Are you sure about that? I thought the affect of air drag was dependent on the sectional density of the round. The sectional density of a 1.5" and 2" diameter round should be the same. They should decelerate such that their kineitc energies drop off at the same rate. Their ranges, at the same launch angle, should be very similar.

Another way to look at it...
The drag (a force) is proportional to the area. The deceleration caused by the drag is;
a=F/m
The larger round has more drag (increases deceleration) but also has more mass (decreases deceleration).

Arne't most rifle rounds designed for extreme ranges fairly large? Is it possble to build a 0.22 that has an affective range of a couple thousand yards?

[Blitz]

I use 2", works great for me, and I seem to find more stuff that fits in 2" than 1.5 inch.

3 and 4 inch are another story....

Definitely true for the top statement. But I have lots of access to 3" ammo; water bottles fit very nicely! And I have lots of cans for 4", but I don't have a chamber powerful enough to fire those kinds of projectiles right now. doh

[judgment_arms]

...Arne't most rifle rounds designed for extreme ranges fairly large? Is it possble to build a 0.22 that has an affective range of a couple thousand yards?

Not unless the round was made out of something denser then lead, it’s all about mass, the heavier the projectile the farther it will go. Wad up a 3X3 inch piece of paper and throw it then wad up a piece of aluminum foil the same size and throw it. Which goes farther?

Also with the 2.00cal barrel you’ll have a higher flow coefficient. Fire a 1oz projectile out of a 1.50cal barrel and then fire a 1oz projectile out of a 2.00cal (run a simulation in the GGDT only changing barrel diameter.) the 2.00cal barrel will yield a high velocity.

[jimmy101]

Jimmy101, you say:

A smaller projectile will have a "faster projectile speed" but will not necessarily have greater range or more impact energy.

but then go on to say:

Since the two barrel give the same acceleration then the muzzle velocities are the same when the spud exits the barrel.

Both statements cannot be simultaneously true.
Freefall bitch slaps me back to reality. Yep, I started with SpudBlaster15's statement which is not true.

You also state:

We know that the area (A) goes up as the square of the barrel radius and the mass (m) goes up by about the same amount.

This is only true if the projectiles are of equal thickness. Typically, projectiles scale in thickness along with diameter.

By thickness you mean length right? If so, then it is true that the projectiles are of equal thickness. For spud guns the length of the round is independent of the diameter of the barrel. So you might think that the volume (and mass) of a spud projectile would scale as r³ but that is not the case. The volume and mass scale (usually) for a spud round as r². So Typically, projectiles scale in thickness along with diameter is not true with most spud gun rounds. I can't imagine a spud gunner changing the length of their spud ammo when they move from a 1.5" to 2" barrel.

So:
As diameter doubles, area quadruples, but volume (and thus mass) goes up by a factor of eight. 4x area acting on 8x mass = half acceleration and thus half velocity at a given point.


So I don't think the above is correct. The relative mass of a typical spud round cut in a 2" versus a 1.5" barrel is much closer to;
2²/1.5²=16/9=1.78
than it is to
2³/1.5³=64/27=2.37.
This is one of the curriosities about spud rounds. You don't typically use a longer round in a larger diameter barrel.