Port size vs performance

[Moonbogg]

Intuitively I want to make a port size the same diameter as the barrel for maximum flow. However, intuition often fails. HGDT predicted that performance would be basically the same with a 1" port vs a larger port for my last design, and sure enough, performance is just fine. It makes sense that the mass of the projectile becomes the limiting factor in velocity vs the size of the port, within reason of course.
I'm working on my next design and I have an 1 3/4" port, but I'm thinking 1 3/8" would be just as good in almost every scenario. The projectile would have to be very lightweight for a larger port size to really improve performance. At least that's what I'm thinking. How do you feel about port sizes matching the diameter of the barrel? Do you think it's necessary or beneficial? Using a smaller port size means using a smaller piston, which means the whole cannon is smaller and cheaper and lighter.

[jackssmirkingrevenge]

I think your reasoning is spot on.

Port size and opening time are what determine the rate at which pressure rises behind the projectile.

That rate of pressure increase is not linear vis a vis the port size so it reaches a point where the advantage of making it any bigger is minimal.

[mrfoo]

Quite. There's going to be a point of diminishing returns where, for a given design and geometry, going bigger will eventually slow the piston down.

There's a lot of benefit to be had, for a port that's smaller than the barrel, from profiling the edges of the port, both chamber side *and* barrel side.

[D_Hall]

The purist in me loves the idea of a port that is actually larger than the bore, with the breech tapering down such that flow into the bore is smoooooth and maximized.

But yeah, the realist in me realizes that for the vast majority of cases this is beyond overkill. Hmmm... Let's see if I can come up with a rule of thumb on the fly....

Sonic velocity of the working fluid... Assume air at 1100 K... SonicVelocity = sqrt(1.4*287*1100) = 604 m/s = 1982 ft/s.

Assuming constant density (not true, but I'm not going to do the long math!),... MaxProjectileVelocity / SonicVelocity = PortArea/BoreArea

Or.... PortDiam / Bore = sqrt(MaxProjectileVelocity / SonicVelocity).

Just to throw some numbers at it.... If I have a 2" bore and I want to go 900 ft/s, that impliles that.... PortDiam = 2 * sqrt(900/1982) = 1.348"

So a port larger than (say) 1-3/8" doesn't buy you much - if anything - on such a gun.

Granted, the above are just my thoughts on the matter. I've not tested any of it out. It's just a thought experiment.

[Moonbogg]

Fantastic replies. Thanks for the interesting thought experiment, D_Hall. That gives me something to mentally chew on. I feel 1 3/8" is where it will probably end up for this one. An interesting thing I noticed is that giant (2 5/8" dia) potatoes break apart at 4X and I'm wondering if the 1" port is basically putting too much stress on the center of the tater. Perhaps for a reason like that, a larger port would serve a purpose or maybe flaring the outlet of the port to make it larger in front of the projectile could help. It could also be that giant potatoes are just too fragile for higher pressures and you need a longer barrel to get them going faster. I'm using my existing piston cannon as a learning platform before making the next one. There is actually a lot to learn while on my quest for the ultimate spud gun.

[hectmarr]

Important thought experiment and clarifies in theory the same doubts that Moonbogg has.
It must be taken into account that larger diameters generally use larger dead spaces, but it depends on the geometry of the transfer, as mrfoo says.
The final gun, in my view, does not exist. The interesting thing is that the next one is better than the previous one in some respect.

[D_Hall]

Some more thoughts on the thought experiment.... It assumes constant density, but this is obviously incorrect. But what DOES density do? In the first moments after the valve opens, not much. Constant density probably isn't a bad approximation. But as the projectile accelerates we know that pressure is going to drop. Some of that is going to be accounted for via temperature drop, but I strongly suspect that overall density decreases with pressure. That is to say that I think pressure is dropping faster than temperature and the result of that is going to be reduced density. With a quasi-constant mass flow this strongly implies that the previously mentioned rule of thumb is - if anything - conservative.

[hectmarr]

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[ToasT]

Not that I have much to add to this, but It's threads like this that make me a fan of spudfiles.