Maybe someone ought try answering the OP; I’m bored, so…
It seems he’d like to know at which point in the barrel the bullet goes supersonic - at least that’s what I’m assuming he wants to know. I’ll start by calculating the time the bullet takes to exit the barrel from the time it is fired. Since the final velocity is 2560 fps, and we know the starting velocity is 0, the average velocity is 2560 / 2 or 1280 fps. Since the barrel is 26 3/8" or 2.198 feet long, it takes the bullet 2.198 / 1280 or .00171 seconds to emerge. Now I can calculate the acceleration. Acceleration equals the change in velocity divided by time. The change in velocity is 2560 fps - 0 fps, or 2560 fps. 2560 / .00171 = 1,497,076 ft/s[sup]2[/sup] or 46,783.6 G. Wow! Now that we know this, it’s a simple matter to calculate how far along the barrel the bullet reaches the speed of sound, which for purposes of this excercise, we’ll take to be that at 20 [sup]o[/sup]C at sea level - 1127.3 fps. At 1,497,076 ft/s[sup]2[/sup] it takes the bullet 1127.3 / 1,497,076 or .000753 seconds. Taking the average velocity of 1127.3 / 2 = 563.65 fps, we can now say that the bullet travels .424 feet in that time. So, there you have it. The bullet reaches the speed of sound when it has travelled about 19% of the length of the barrel.
See, I told you I was bored. There’s also probably a much easier way to work this out, but you’re on your own, there.
This is interesting. But I wonder, how much would hypersonic forces affect a bullet? It sounds like these things would be most critical in a large, complicated object, e.g. military aircraft, space vehicles, or chucking pianos with trebuchets. With a small mass, simple object like a bullet, would hypersonic forces have an effect, assuming you could fire one that fast?
(Although I’m pretty sure the OP meant to say “supersonic” instead…)
Doesn’t that assume that the accelleration to the average velocity and then deceleration is a perfect bell curve? I keep thinking that since an explosion accellerates the bullet it wouldn’t work to use the average velocity. Then again, I just stayed up all night and right about now nothing makes much sense.
Yes, but it was only meant to be a first-order approximation. If anyone wants to refine the calculation for the acceleration curve of an explosion, go right ahead.
Agreed, but since we’re fighting ignorance here, why not be accurate? Scruloose posted something in the format of a definition (but without a cite) which was not accurate. If you want to say Mach 5 is a good rule of thumb, that’s great. If you say, as he did, that Mach 5 is a specific defining characteristic of hypersonic flow, that’s just wrong.
The important thing is understanding why we even give it another name. If it just meant a speed greater than Mach 5 (or any other boundary), there’d be no point in having a different name for that regime. Hypersonic is named because hypersonic flows behave very differently than supersonic flows. They’re not just faster, there’s a lot more going on.
Probably not. Hypersonic effects are very important for vehicles with pesky protrusions like wings because you get shock-shock interactions (such as where the oblique shock from the nose hits the bow shock on an engine canopy) and shock-vehicle interactions (such as the shock from the nose hitting a wing). The forces involved in these interactions can eliminate those protrusions and make your fancy vehicle look like a bullet in short order. Since a bullet is a nice slender body, you don’t have to worry about shock interactions even when the shock layers get very thin as they do in hypersonic flow.
On the other hand, the high temperatures and chemical reactions the boundary layer of a hypersonic flow might cause significant ablation so you lose mass from the bullet. The bullet might also soften, deform, and ultimately fracture because of the temperatures and forces of a high-speed flow.
There may be a lot of other issues. I recall that some railgun researchers had significant problems even with simple projectiles, but I think most of these were due to acceleration rather than top speed, so the forces on the bullet required to get it to hypersonic speeds might be a bigger issue than the hypersonic effects once acceleration was complete.
As noted above, that definition is wrong. I’d refer you to specific texts in the field such as “Hypersonic and High Temperature Gas Dynamics” by John Anderson. This book includes the old-quy quote I referred to as the front plate to chapter one. It does include a note that Mach 5 is a good rule of thumb, but spends the bulk of chapter one defining what hypersonic really means. The important point is that Mach 5 does not define hypersonic flow but that a Mach 5 flow is more likely than not to also be hypersonic.
This one has been debunked repeatedly. Cecil got it flat wrong. Hydrostatic shock isn’t even close to the top wounding mechanism in a bullet wound. The primary wounding mechanism is the permanent wound channel - The volume of the body that is torn and disrupted by the physical passing of the bullet as it rips and crushes its way through the tissue, plus the volume torn and disrupted by secondary missiles such as bone and bullet fragments. The second most important wounding mechanism is shock. The third mechanism is sepsis. Prolonged bleeding due to an untreated wound is next. Finally (and far away the least of the bunch), you get to the temporary wound channel - the tissue stretched aside by a hydrostatic pressure wave. The problem with the temporary wound channel is that it is temporary - No opened major blood vessels, no destroyed organs. That is, no destroyed organs unless you hit a relatively solid organ like the liver or a kidney, in which case the organ might be stretched beyond their elastic limit. The other special case is in a cranial hit, where the pressure wave contained within the skull may be enough to cause a rupture. Or maybe not.
Quite often the determining factor in whether or not a particular wound is fatal is the mental state of the victim - Aggressive, angry, drugged, or really determined victims have often survived wounds that might have otherwise killed them.
This topic often comes up in discussions about “stopping power” of a gun or bullet. The most interesting thing that I have read is that a major reason people fall down when they get shot is that they think that they are supposed to! The brain says “I have been shot in my torso! Oh no! I guess I am dead! May as well fall down.”
(Note that this rational does not follow to someone who gets their leg shot off.)