Exhaustive Projectile Analysis

[CommissarCold]

Good afternoon.

As part of a personal hobby, I've been trying to design a relatively small projectile that can travel at 'bullet speed' (say, a .22 caliber bullet fired from an appropriately sized gun).

I understand that the overwhelming majority of mass-produced bullets today come in a small variety of bullet lengths and diameters, and tend to be conical in shape. I also understand that the smaller an object gets, the more viscous air is relative to it as it travels. Finally, I understand bullets lose a small amount of their material as they travel, which could result in smaller bullets disintegrating before reaching their target if they were shot with the intent of going at the same speed and distance of larger bullets.

Suppose, for the sake of argument, that I had a high quality metal or plastic 3d printer and wanted to make a projectile roughly as large as a bee stinger, and that I intended to launch that projectile to travel the same speed and distance as an average .22 caliber bullet.

Are there any resources out there that provide novel equations and published experiments from others with similar ambitions to guide me in the right direction towards narrowing down a list of materials and shapes that would successfully result in such a projectile?

Thanks.

 

[berkeman]

Summary:: TL;DNR - How small can a projectile get while still being able to travel at the speed and range of, say, a .22 bullet; and, what materials and projectile shapes could make this a reality

Good afternoon.

As part of a personal hobby, I've been trying to design a relatively small projectile that can travel at 'bullet speed' (say, a .22 caliber bullet fired from an appropriately sized gun).

I understand that the overwhelming majority of mass-produced bullets today come in a small variety of bullet lengths and diameters, and tend to be conical in shape. I also understand that the smaller an object gets, the more viscous air is relative to it as it travels. Finally, I understand bullets lose a small amount of their material as they travel, which could result in smaller bullets disintegrating before reaching their target if they were shot with the intent of going at the same speed and distance of larger bullets.

Suppose, for the sake of argument, that I had a high quality metal or plastic 3d printer and wanted to make a projectile roughly as large as a bee stinger, and that I intended to launch that projectile to travel the same speed and distance as an average .22 caliber bullet.

Are there any resources out there that provide novel equations and published experiments from others with similar ambitions to guide me in the right direction towards narrowing down a list of materials and shapes that would successfully result in such a projectile?

Thanks.

Hmm, hard question. The problem with a lighter projectile is that it loses more energy to wind resistance compared to a heavier projectile, given the same initial velocity. Lighter bullets tend to have higher muzzle velocities (compare a .270 to a 30-06, for example), but they tend to lose velocity faster than the heavier bullets.

So a first cut at your question would be to reduce air drag as much as possible. That means a very slim shape, which is harder to manage as a gun round.

 

[jrmichler]

Are there any resources out there that provide novel equations and published experiments from others with similar ambitions to guide me in the right direction towards narrowing down a list of materials and shapes that would successfully result in such a projectile?

Start with search term exterior ballistics. Then study the effect of ballistic coefficient on retained velocity.

Small diameter bullets have challenges. It is a good idea to learn from those who have experimented with them. There are a number of 17 caliber wildcat cartridges. Search term 17 caliber centerfire will find information. You can also get a copy of Cartridges of the World by Barnes. Barnes discusses a 14 caliber made from a necked down 222 Remington cartridge, and mentions some 12 caliber experiments. That's in my 8th Edition, the newer editions may have more information.

I understand bullets lose a small amount of their material as they travel, which could result in smaller bullets disintegrating before reaching their target if they were shot with the intent of going at the same speed and distance of larger bullets.

No. Bullets do not lose material traveling through the air. Lead bullets at high velocities will leave some lead on the inside of the gun barrel, but not from traveling through the air.

 

[jim mcnamara]

Get a copy of the Speer reloading manual. There are other titles. It provides lots of basics, without advanced math.
Almost too short an answer: I think what you a want to consider are larger caliber projectiles with multiple ogives, and a boat tail. This is what long range target shooters prefer. And it will entail reloading and testing. You may also want to look at getting a chronograph - used to measure muzzle velocity.

 

[berkeman]

Paging @Dr. Courtney

 

[Dr. Courtney]

There are several practical challenges as the projectile gets smaller:

1. Bullets are spin stabilized - little gyroscopes. The spin keeps them point forward in flight. Bullets that resist air drag really well are long and skinny. But smaller and smaller calibers have larger length to diameter ratios so they need to be spun faster and faster to maintain stability. Small defects in shape and mass distribution are a practical limitation when you spin them faster and faster. These effects make it hard to make 22 caliber (5.56 mm) projectiles as aerodynamic as 30 caliber (7.62 mm), and are also a reason why 50 cal bullets have advantages at longer range.

At some point, it may be advantageous to use a fin stabilized design rather than a spin stabilized design. But that quickly increases your manufacturing and production costs for both the consumable projectiles and for the launcher.

2. Manufacturing smaller things with the same relative precision is challenging. A 0.0001" tolerance in a 22 caliber projectile is 1 part in 2200. An 11 caliber projectile needs a 0.00005" tolerance to have the same relative precision in both the bullet and the barrel. A 2 caliber projectile needs a 0.00001" tolerance. That level of precision is much more difficult and expensive. If projectiles and their launchers are made with lower relative precision, the projectiles tend to "wobble" in flight which significantly increases the drag.

 

[Vanadium 50]

Suppose, for the sake of argument, that I had a high quality metal or plastic 3d printer

Manufacturing smaller things with the same relative precision is challenging. A 0.0001" tolerance

0.0001" is 2.54 microns. An Ultimaker S5, a pretty good 3D printer costing $6000, can do 50 microns. You can get a printer that has a better resolution and/or smaller feature size, but it will cost a lot more, and when it can achieve its best performance will be a far more complicated business.

There exist CNC lathes with micron tolerances. They are not cheap. Operating them is not cheap either.

I would rethink whether 3D printing is the way to go.