Gyrojets are weapons that fire rocket propelled darts,they are lightweight, they have low recoil, are very silent, and at long ranges have extremely high velocity. They however are highly inaccurate, have high visibility, and do not get to full velocity until they are 60m from the muzzle of the rifle, and ammo is expensive. These have high potential because of the fact that they can reach velocities of 1750 mph with a tiny handheld weapon, the problem is they are poorly designed so if anyone has any ideas it would be helpful, because i want to have a hard sci-fi universe with these used as a sniper or even assault rifle weapon, and if needed also a pistol.
some form of flashless propellant;
maybe some type of rocket that instantly accelerates to full velocity just before it leaves the barrel; and
The primary issue with a gyrojet was the high expense of the ammunition and the length of time needed to reach lethal velocity (it is sometimes said you could hold your hand over the muzzle of a gyrojet to block the round and remain safe).
To solve problem two, you need to increase the energy of the rocket propellant and release it rapidly enough that the projectile is moving at considerable velocity as it leaves the muzzle of the weapon. The primary difference between rocket propellant and gunpowder or the propellants of modern firearms is rocket propellant burns (granted at a very fast rate) to generate the gasses and create the trust, while gunpowder and nitrocellulose or more modern propellants burn fast enough to be considered explosions. The propellant charge in a 9mm or .45 pistol round burns in a fraction of a second inside the cartridge, and the expanding gasses "push" the bullet out, while a gyrojet round is still burning as the bullet leaves the muzzle and downrange to burnout at @ 60m downrange.
Gyrojet rounds of various calibers
9mm Pistol ammunition
Now there is no reason you could not have a rocket like projectile using a high energy propellant that would burn out rapidly (even inside the barrel), and some of the exotic mixtures considered for caseless ammunition might perform well in this role. The problem is the massive change from solid to gas in a fraction of a second would require a very strong casing to hold everything together. In a conventional gun, this is called the chamber, and the barrel is also strong enough to deal with the rapidly expanding gasses propelling the bullet.
Conventional rifle barrel. Notice how large the chamber end is compared to the rest of the barrel
A gyrojet round would essentially be the chamber and the barrel in function, which would mean the round would be quite heavy and bulky (especially if you want to follow the gyrojet formula of a lightweight aluminum barrel). You may end up with rounds similar in size to shotgun rounds, making for a very large weapon.
M-26 shotgun. Your Gyrojet may end up looking like this
Problem one is actually rather simple to solve. Making products in bulk through assembly line production is a well known process, and making large production runs also ensures quality control as there are greater statistical samples to draw upon when examining the process. Gyrojet rounds were essentially hand produced in the 1960's, but making millions on an assembly line would rapidly drive the price down through economies of scale.
do not get to full velocity until they are 60m from the muzzle
you could start them with a traditional charge, like smokeless gunpowder(nitrocellulose). It would leave the barrel slower then typical round but still much faster then a gyrojet alone (see #2). For example, it's probably a large caliber and so you don't want so much of a charge that it has a big kick. Maybe something like 1/4 to 1/3 of the max speed. This is just one thought.
You could use a magnetic acceleration method, like a coil gun. Maybe they don't have good enough tech to make full on rail guns, but maybe enough to get up to the 1/3 to 1/4 speed. This would be my choice if the energy requirements can be met.
As others stated you could simply use a faster burning solid rocket fuel or even compressed air.
Depending on the tech level you could also add guidance to it. This could be laser guidance where it rides a laser pointer beam. It could be heat seeking, motion seeking, or whatever your tech allows
You could use a discarding sabot round. This would let you put fins on them, basically the sabot is just some lightweight hi-temp foam/plastic that makes the arrow/flechette shape fit into a cylinder. You could also put a spacer between the traditional charge and the gas exhaust ports, if they need protecting from the starter charge (see #1) if using that method, so per-ignition or damage to the round is not an issue.
Something like this (for the gunpowder starter charge version) but with internal fuel as well. So if you can imagine replacing the solid sabot core with a self propelled flechette.
ammo is expensive
This is relative. If the ammo is mass produced the cost would come down a lot. It would always be more then a traditional round (especially if it had guidance). But that is the nature of the beast, a smart bomb costs more then a dumb gravity bomb. It's just the way it is.
For a ideal sniper rifle
You may actually want a slower round. Speed is not the top priority. You really want to keep it subsonic. The problem with subsonic bullets is they are losing speed all the time so they have poor range and accuracy compared to high velocity bullets. They also have less penetration. But they have the advantage of being [more]silent as there is no sonic boom. Most people think that the majority of the noise from firing a gun comes from burning the powder charge when really a lot of it comes from breaking the sound barrier.
So an Ideal sniper weapon (in my mind), would be as follows.
Boost phase, magnetic acceleration initially gets it started. This is silent, as long as it's subsonic. Maybe it makes some humming noise but much less then a gunpowder charge. There is no smoke, no flash etc. Maybe some sensitive equipment could pick up the magnetic discharge or the energy spike, but whatever.
cruse phase, using internal propellant. This just need to maintain the speed, or accelerate it up to just below the sound barrier. You would also do bulk guidance in this phase to get it going in the general direction of the target.
terminal phase, the round would accelerate as much as it could in this phase breaking the sound barrier.
You could use a separate fuel that burns faster, or if you can imagine having multiple holes with independent chambers, like separate rocket motors then you could just ignite additional "rockets" to increase the thrust. For example it has 6 ports in the bottom and uses 2 for the cruse phase, then it sets them all off in the terminal phase.
This phase would only be able to do fine guidance because of the speed.
Ideally it would use a solid propellant that burns as clean an clear as possible. I really like the idea of having many very thin rocket chambers. Perhaps a few dozen of them, because then you could pulse the firing of them and have finer control. Essentially it would not need to use the "rockets" the whole time, only to maintain speed an course. the trick here is you cant turn off a solid rocket. You can burn 2 chambers on opposite sides for a split second for low thrust, wait and then burn one or two on the right if you need to turn to the left. Or ignite them all for a quick burst of speed. They would be high thrust but short duration.
By the time it does break the sound barrier it's already down range, making it hard to trace back to the shooter. The slow speed would let you do some crazy guidance, like 90 degree turns, also making it hard to trace back to the shooter. The terminal phase lets you ramp up the speed so you get the penetration ability of a high velocity round while not giving away your position. Of course the round itself could have explosives (shaped or otherwise) or poisons etc.
A machine gun
This would work almost like the sniper type/mode. The only difference here is you would essentially just eliminate the cruse phase. Mag acceleration here would help with the rate of fire and by removing heat (from propellant exhaust) from the gun barrel. The round is outside of the barrel when it's little rockets ignite.
I could imagine a coil gun with powerful magnets that you cycle. To fire the next round you just shove it out of the magazine into the first magnetic field with a physical pusher mechanism. Then you could fire as fast as you can cycle the fields and push new rounds in. This would probably need a good electricity source though, but it would me much less then a full on rail gun or laser. Sort of a composite weapon.
Last thing is because you lose the cruse phase only fine guidance would be possible at these speed. This would make the auto mode better at short range but less accurate, which is what one expects.
do not get to full velocity until they are 60m from the muzzle
Your new gun is an air gun which fires the rocket ammo using pressurized air. The rocket leaves the barrel at a speed comparable to a standard firearm and then accelerates from there. Air guns this powerful exist. https://www.airgundepot.com/airforce-texan.html
The gun has a battery to recharge the pressure tank, or it could be recharged manually with a pump.
Alternatively if you want to be more sci-fiey you could spin the rounds up to speed mechanically while in the gun and accelerate them out with a short railgun.
The gyro jets were made with 1960s tech. Modern craft (like drones or stealth planes) have computers which make many rapid corrections to compensate for inherent instability. As with the original gyro jets the new ammo has 4 rocket propellant ducts which impart spin. If the output of each duct could be decreased or increased according to the section of rotation (for example, reduce output between 3 o'clock and 4 o'clock) it would be possible for the projectile to steer.
One could have an internal accelerometer which used this method to correct for deviations from a straight line. If your tech is small enough you could have an onboard camera and have the ammo steer itself towards the target.
ammo is expensive
The above modifications do not help much with that. Instead of guided accurate ammo (as a sniper would use) an assault-type weapon could use the airgun base to start them fast and dumb standard gyrojet ammo - but many of them.