Smooth bore as far as I know. Even tank cannons are mostly smooth-bore these days.

The problem with those graphs is that they are not optimizing propellant quantity for each barrel length. Adding an axis for quantity of propellant shows that you get diminishing returns to increasing barrel length and propellant, but there is a limit to how much you can increase both without increasing the barrel's thickness (as well as the firing mechanism's strength).

You also have to remember that a gun will require > Mach 25 to get to orbit, and air acts differently at that kind of speed (, and once past ~Mach 3).

Thanks for the insight - I guess it doesn't scale!

Is there a reason the space gun would be at a 45 degree angle and not pointed vertically? I know the reason rocket launches happen as close to the equator as possible, but they still go straight upwards...

Rockets only go up for a little while; most of the propellant is used to build up speed in the 'horizontal direction'. There have been some arguments that a strictly vertically-firing rocket would be best for going outside of Earth orbit, but the current strategy for all launches is to go up until outside the thickest part of the atmosphere, then go horizontal, to build up to orbital velocity.

After reading about the end of of Project HARP - it seems like they intended to use the gun to fire a rocket, and after a certain altitude the engine would ignite to get into space.

Yes, and in the years since HARP, there have been a few rocket-assisted projectiles developed (though none which have been intended for space launch).[1]

I should also mention that unless the projectile was fired at or above escape velocity (intended to leave the Earth's gravity well), it would require some onboard propulsion to 'circularize' its orbit (and avoid crashing back into the Earth on its first time around).

[1] https://en.wikipedia.org/wiki/Rocket-assisted_projectile

Rifling improves accuracy at the cost of speed (and thus range). That's great for traditional guns, where you care more about effective range (i.e. a reasonable chance of hitting your target) than how far away you can send the bullet; but orbit is a big target and space gun projectiles would have their own rockets to guide them, so there'd be no benefit to rifling there.

(As nickff points out, modern tank cannons are generally smoothbore; the current fashion for armor-piercing is solid kinetic darts that need to go very, very fast to punch through their target, and rely on stabilizing fins for accuracy.)

Biggest problem of rifling is that the "lands" wear down quickly. For a pistol it's probably good thing that it wears down before it has time to break in other ways. For tank gun, you can use some other, more accurate way to keep track of shots fired.

Probably second biggest down sides of rifling is that it weakens the barrel. How much depends a lot on how the rifling is done. But anyhow this has to be compensated with thicker/stronger barrel.

But that gets problematic at extreme pressures. You wan't to use pressure vessel steel, because such steels 1. have good fatigue strength and 2. they tend to send around little less shrapnel when they fail. Problem is that such steels are typically low alloy steels with somewhat low yield strengths. So you would like to make thicker barrel, but the problem here is that you quickly hit diminishing returns. There is usually very little point making barrel thicker if the outer diameter is twice the inner diameter. (Except if you need more rigidity to improve accuracy. But that's whole another subject.)

Anyhow, the brits still use rifled tank gun.