Would a bullet made from ice be capable of killing somebody at 100 metres before melting? As an author I would like to use this in a science fiction novel.
The short answer is probably no.
It would either shatter because of the amount of force the weapon puts on it or melt because of the heat (in case of a "regular" combustion gun). The former has more chance of happening, before the ice even has the time to start melting.
The only way to shoot it without shattering it nor melting it, at least using weapons available to us, would be to use compressed air weapons, but it would need to be significantly powered down to prevent the bullet from shattering, so it would probably not be powerful enough to cause damage.
The force needed to break through one square inch of ice is roughly 400 pounds on average. The bullet you're trying to fire is probably 9mm, but let's just calculate as though it was about one square inch (although it's actually quite smaller than that): those 400 pounds equal roughly 1800N.
The force that comes out of a 9mm gun is approximately 383 ft-lbs, which equals to 520 newtons per metre. That amount is about 52000N per centimetre. One inch is about 2 and a half centimeters, so that means it's more about 20'800N per inch. As you can see, it's a lot more than what it takes to break ice.
As for the "wall" towards which something has to be pushed in order to break it, the air will fulfill the role: the atmospheric pressure is about 15 pounds per square inch: it doesn't seem like a lot, but in the time it takes the bullet to "win" this force and gain momentum, it gets shattered by the enormous amount of energy produced by the weapon.
I'll go with Yes. But it depends how far into the future your setting is and how close your shooter needs to be and how big the gun can be.
Sea level on a normal day, speed of sound is 340.29 metres per second or 1125.33 feet / second. The projectile has to deal with the sonic shock wave. So max speed is 80% of speed of sound. 270m/s or 900fps means it reaches the target at 100m in 1/3 of a second. http://www.pyramydair.com/article/Velocity_and_Pellets_April_2003/2 for discussion of high speed air rifle and pellets
Ice Bullet size/shape
I'd guess it should be streamlined enough to not tumble or fracture, wide enough to do damage on impact. Somewhere between John Dallman's 1g NATO sized round and 10g (2-teaspoon) hailstone musket shot. I'm favouring 10g of ice in a ball or pellet shape.
A 10g lead pellet is 10 times denser (.2 teaspoons), or for the same volume weighs 10 times more (2 teaspoons of lead is 100g).
Stock high velocity air rifles can fire a 15.5 grain (1g) lead pellet supersonic. So 20grain at 270m/s is tough but doable right now in lead. Ice is bigger but a custom rig should be able to launch 10g of ice at 270m/s.
Rail Gun/Coil Gun (Gauss Rifle)
A small rail gun may be the way to go. The ice slug is electromagnetically accelerated to 270m/s in 1.2 metres of gun barrel. The ice slug could sit in/on a sled of gold (or superconductive) foil or mesh, or a more robust structure that somehow separates from the ice slug after firing. This is a discarding sabot round.
The sled cannot just hit the end of the rifle and stop as the kinetic energy would be unmanageable.
The sled should not hit the target as that would be like firing a bullet.
Superconductive foil or mesh could peel off the slug in the atmosphere. If it were a mesh it can unravel along the path to the target and break up.
An alternative to a sled would be to make the ice slug out of a electrically conductive salt solution. But how salty and would the wound have traces of that? Normal Saline is 9g per 1L of water w/v. So not enough for really good conductivity.
An evaporating conductive shell may also work but seems even more complicated. In this case the projectile is even more of a discarding sabot round.
Salt would lower the freezing temperature of the ice slightly.
There are definitely some issues around the phase shift of the ice slug to liquid/vapour especially under pressure and acceleration. But 10g ice electromagnetically accelerated to 270m/s is probably doable with a little science fiction engineering in the rail gun.
I don't think the brittleness of ice is a problem at 10g over 100m. But in case I'm wrong a 50g-100g initial payload should leave sufficient mass to be lethal.
@DonaldHobson suggested a coil gun as an alternative to the rail gun.
For clarity, my answer allows for a slug made of ice and a weapon that does not use gunpowder or similar chemical accelerant. The ice bullet fractures/melts in a gunpowder weapon.
Sadly, this trick is well-known to science fiction readers. It is a minor variation of one in Alfred Bester's The Demolished Man, which every SF writer should read. Bester was a huge influence on William Gibson, among many other writers.
In the Demolished Man, the replacement bullet was a gelatine capsule of water, which worked at very close range. The capsule burst immediately the gun was fired, and the target was killed by the powerful jet of water. I'm not sure how plausible this is as ballistics, but it was good enough for story purposes.
An ice bullet will melt immediately the gun is fired, and a water jet won't hold together for 100 metres, so I'm afraid your exact scenario isn't workable. If you can describe exactly what you're trying to accomplish, we may be able to help more.
My instinct as a gun guy who knows a fair amount about low velocity weapons is that it would definitely not be practical as a 100m weapon. It might even be impossible to kill someone at that range. My feeling is that a gun shooting a lethal ice projectile might work at extremely close ranges. A lot of questions remain to be answered via experimentation.
From a purely internal ballistics standpoint, it should be fairly easy to launch a projectile at a dangerous speed so long as the accelerative force is sufficiently low to avoid breaking apart the ice projectile. You'd honestly have to experiment with different powders and charges to see what worked best. Unfortunately, the ultimate velocity from the barrel might end up being quite low, or the required barrel length to reach a decent velocity might be very long (ie using a very slow powder and a long barrel to get something decent). I would definitely opt for putting the projectile inside a shot cup of some sort because ice is brittle and generally unsuitable for sealing against the rifling of a barrel.
Melting isn't a serious risk because even a very low velocity firearm that burns gunpowder will eject the bullet from the barrel within a couple of milliseconds at most. Water has very high specific heat and requires lots of energy to melt ice. This isn't a serious concern IMO.
As far as 100m accuracy goes, remember that ice is 1/12th the density of lead, so expect wind drift and velocity loss to be cripplingly bad. Perhaps far too bad for 100m accuracy. Remember that many handguns and smoothbore slug guns struggle to remain accurate at this range using lead projectiles at much higher velocities than we are attempting here.
I would guess that being hit by even a blunt icicle at 300-500fps would at least be unpleasant but terminal ballistics is another completely unanswered question as far as ice projectiles go. The low density of ice vs metal makes (1/12th the density of lead) means that it will lose energy quickly in the air but even more quickly once it hits a human body, let alone a clothed human body. It is very possible that even a solid hit from an ice projectile would just produce a severe bruise or a superficial wound rather than the deep penetrating wounds associated with shotgun/handgun slugs. Also, keep in mind that a 300-500fps ice slug might have lost quite a bit of velocity by the time it gets to 100m, so it might be almost impossible to kill someone with it.