Between 5.7 and 9mm?

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I am interested in a cartridge imaginary or possibly one that already exists which falls in-between 5.7x28 and 9mm par. What I mean by that is a cartridge which utilizes a slightly smaller diameter bullet and casing to increase velocity and magazine capacity, and that has a greater overall length than 9mm to maintain some performance lost by shrinking diameter.

The motivation for the cartridge comes from the trend over the last 40 years for cartridges to favor smaller, higher velocity rounds (part of the motivation of the 5.7 in the first place) and the desire for highly effective "personal defense weapons". This push was in its heyday in the 90's during the development of weapons like the FN P90 and the HK MP7. There was, and still is a departure away from "sub machine guns" to "personal defense weapon" these are both loosely defined terms but generally it means a smaller diameter, body armor defeating cartridge with good performance in short suppressed weapons. This also includes the wave of SBR AR-15 derivatives which demonstrate this trend as well. Generally speaking, it seems that we are more interested in penetration and speed of delivering rounds, than we are in "knock down power" (see the fall of 45 acp in popularity).

9mm has really found a sweet spot in today's combat thinking, and I am not sure if it will stay as popular as it has over the last 100 years, but I definitely see one area where a new cartridge could fill a perceived gap.

I imagine the PDW cartridge as having a smaller base diameter than 9mm, longer length (but short enough to fit in a pistol grip), give at least 1500 fps, and able to hold a bullet weight at least 70 gr. This would land us somewhere around the following dimensions:

Base Diameter: about 0.35
Bullet Diameter: about 0.307
OAL: about 1.20"

During my research I came across a couple cartridges which actually come close to this, .30 cabine, 7,62 Tokarev, .22 TCM, and . this group while quite diverse does give the performance I am interested in. What I am imagining is either a necked up .22 TCM, a shortened .30 carbine, or a shrunken 7,62 Tokarev. Side note, I imagine that the case would be slightly shouldered, I think you would get better performance out of that than a straight walled case.

Someone let me know if this concept makes any sense or if it even matters, I am sure there is a reason why there seems to be such a large gap between the velocity and mag cap. of 5.7x28 and the effectiveness of 9mm despite its shortcomings.

To clarify I am a gun enthusiast and a mechanical engineer. This is strictly a side interest to me and my knowledge on these subjects is mostly superficial. I am posting just out of a technical or historical interest, and do not intend to make any objective statements about the performance of cartridges.
 
I actually am familiar with the 7.5 F, however I determined that the overall length was too great and the base too wide. It's nearly 1.4 inches long, which I think could negatively impact pistol ergonomics, and it also has a base diameter of 0.425 which gives you less capacity that 9mm. The size constraints I laid out are really the only part that make this interesting, there are MANY cartridges that are close to that range but not many within it.
 
A 30 Luger (7.65X21 Parabellum) would be close to what you're looking for. It shoots a 93 grain bullet to 1200 fps. Maybe run it with slightly higher pressure to get a 70 grain bullet at your desired speed. The base diameter is a little big, but if you're looking for something that already exists, that's what you have to work with.

https://en.wikipedia.org/wiki/7.65×21mm_Parabellum
 
So something along the size of a 556 case cut down to optimal length and necked down to 264, 277, or 284. Add a slight taper to aid in center feeding out of the magazine and give more OAL in the magazine at the cost of a little extra width in the grip, negated by the reduction in case base diameter.

556 base diameter = 9.58mm
9mm base diameter = 9.93mm

Just using two cases I happen to have in front of me at the desk.
 
I've had the same interest lately, I've been thinking of a 7.62x25 Tok necked down to .277 or .357 SIG necked down to .284.

Those would be really cool to see numbers on too, but .357 being based on the 10mm auto has a wider base diameter than 9mm and 7.62 Tok is just barely less, and I think having an increased magazine capacity is one of the big selling points for what I am imagining. I often hear people complain about how ineffective non-AP 5.7x28 rounds are for man-stopping, yet people still love it enough for Ruger to make a new gun for it. I think that comes down to the awesome capacity you get, I arrived at my base diameter from trying to balance mag cap with energy.
 
Your 1.20" length is odd, It's between the 9mm and a 38 Super, which means it won't fit in a 9mm-length frame and is a bit short in a 38 Super frame.
 
So something along the size of a 556 case cut down to optimal length and necked down to 264, 277, or 284. Add a slight taper to aid in center feeding out of the magazine and give more OAL in the magazine at the cost of a little extra width in the grip, negated by the reduction in case base diameter.

556 base diameter = 9.58mm
9mm base diameter = 9.93mm

Just using two cases I happen to have in front of me at the desk.

This Is exactly the process i was thinking about if I were to use existing brass, this is how the 22 TCM is made, but I think you could compete more with 9mm, .40 S&W, ect. by using some 7mm caliber bullet like .308. Based on what I am hearing it sounds like I want a "30 TCM"
 
I just found this from the creator of the 22TCM mentioning the .30 Carbine:

“Since Armscor is also a large manufacturer of ammunition, (most people don’t realize that) I had a huge amount of resources at hand. I originally started out smaller with a .30 Carbine case and a 9mm-platform pistol. This netted the performance similar to a 5.7×28, which a lot of you are familiar with. Although this was good, I wanted more out of the cartridge so I ended up working with a .223 Rem case. The key to the cartridge is our proprietary bullet design. This short truncated head allows for maximum case length, thus more powder and a bigger BANG! So, the cartridge case in all practical sense is a short .223 Rem.”

Based on this I think that the 22 TCM is probably just right and a 30 TCM or other similar cartridge doesn't gain you much over it.
 
Those would be really cool to see numbers on too, but .357 being based on the 10mm auto has a wider base diameter than 9mm and 7.62 Tok is just barely less, and I think having an increased magazine capacity is one of the big selling points for what I am imagining. I often hear people complain about how ineffective non-AP 5.7x28 rounds are for man-stopping, yet people still love it enough for Ruger to make a new gun for it. I think that comes down to the awesome capacity you get, I arrived at my base diameter from trying to balance mag cap with energy.
I see what you mean, my thinking was geared more towards a carbine with a 10-16 inch barrel rather than a handgun.
 
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