Well, this might be supersonic but doubt it would throw heavy boulders at fortresses anytime soon to be useful as a siege weapon.
50g @ 460m/s = 5290J
25kg @ 50m/s = 31250J
that is to say, the small but fast projectile is 1/6th the energy but only 1/500th the mass
edit: formatting
edit2: a 300g projectile at 460m/s would have approx the same energy as a the 25kg boulder at 50 m/s. at point blank range anyway.
You can't take their mockery anymore, so you set about fixing your projectile.
The pebble lost much of its energy in flight - drag is a huge issue with any distance to target. You make a projectile in the shape of a rod. This has the effect of decreasing the cross-sectional area of the projectile relative to its mass, minimizing drag losses. There's a limit to the length:width ratio, however- go too skinny and it'll deform under firing forces.
The projectile's length also allows it to burrow deeper into the rock -- when material at the tip breaks off on impact, it's got the rest of the shaft behind it, just as mad.
To pack the most punch into your projectile, you craft it from tungsten (then known as Wolfram). In order to keep it from yawing in flight, you add some rigid vanes at the back. It looks like a small, superheavy arrow.
Now you have the issue wherein it doesn't fit well into your cannon anymore. No mind -- you set it in a cup of sorts that seals the barrel. Wait, where did you get a cannon? This is the year 1217 AD...???
Congratulations: you have constructed an armor-piercing fin-stabilized discarding sabot munition (APFSDS). You load it into your M256A1 120mm smoothbore cannon. You peer through the sights.... now where were those sac à merde?
(Frankly I don't know if this makes much sense from the physics standpoint, but it's what I read in passing.)
At that energy level you have significant damage from spalling from anything the projectile passes through, the superheated metal the projectile actually passes through is launched everywhere, there's the shockwave of the projectile, etc.
That's easily enough to be anti-personnel, incendiary, and obliterate electronics and cables and pipes and hoses. And have lots and lots of penetration, which on a ballistic arc could mean exiting below the waterline, and I imagine something traveling at supersonic speeds hitting water probably does some pretty impressive things.
If you send one of those projectiles through a magazine, missile battery, or fuel bunker - a lot of people are going to have a very, very bad day.
For kinetic systems, the projectile-target interaction is critical. A flimsier target actually needs an impact to be spread over a larger area. Think of a pellet shot through tissue as opposed to, say, a blast of sand or salt.
There are some analogues with subatomic particles and fast/slow neutrons (slow neutrons are far more effective at sustaining nuclear reactions, as they effectively "stick around" where they're more likely to interact with other nuclei for a longer period of time, and the apparent cross-section of the target nuclei appear larger).
https://www.radioactivity.eu.com/site/pages/Slow_Fast_Neutro...
Solid shot goes through the ship, perhaps injuring anyone in the way. Solid shot hitting the structure of the ship on its way through creates massive, dangerous splinters.
https://kurage.files.wordpress.com/2018/03/hocker-isbsa-14-p...
One reason to use larger projectiles is to deliver similar amounts of energy without having to fight things like that.
https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...
Velocity-squared is the factor in drag.
https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...
Where frontal volume is determined by mass and density for a sphere.
So, two speheres with the same mass, but different densities will have different drag forces.
https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...
"It is reported that femtosecond-duration laser pulse can be deployed to reduce drag for blunt-body vehicle in high-Mach flow field of air by generating laser plasma and shockwave. The interaction of plasma shockwave induced by femtosecond-duration laser pulse and bow shock over the head of the blunt-body vehicle is investigated numerically in the flow field of 30 km apart from the surface of the earth at Mach number of 5 and the mechanism of deploying the femtosecond laser plasma to reduce the drag of the vehicle is analyzed. The Navier-Stokes equations are exploited to compute the drag reduction for different femtosecond laser energies. The present numerical experiment proves that the femtosecond laser pulse has a better drag reduction effect than the nanosecond laser pulse under the same condition. When the femtosecond laser energy is 0.06 mJ, the femtosecond laser plasma can reduce the drag by 98%. And the higher the energy of femtosecond laser pulse, the higher the drag reduction ratio and the longer the time of low drag. Deploying three femtosecond laser energy point to reduce the drag of hypersonic vehicle is much more obviously. This energy-deposition mode can improve the optimum drag reduction ratio and save the laser energy."
Probably out of the scope for a $200 build, but maybe in the scope of a $2000, $20000, or $200000 build?
I also wonder if iterating on the above, combined with a concentrated solar power plant of arbitrary sized solar field that could provide enough energy for a railgun to launch payload with femtosecond laser plasma capabilities out of earths gravity well?
Maybe, we could escape from the Goddard age eventually lol
[0] https://www.researchgate.net/publication/282709902_Exploring...
But for one, the energy source would have to be on board the payload to power the laser (localized around the payload), and for the other (that I was not talking about) the laser is not on the payload and as the payload travels further away from the launch site, you would use an non linear increasing amount of energy and follow the path of the payload (ionizing air not only around the payload continuously but along the path where the payload no longer is, which would require more energy than needed).
Does seem like it references some difficultly-ness
> flying object with perfectly controlled laser launched from a trebuchet
Does seem like it 'assumes otherwise' to (or its at least ambiguous to me and would be less so if there was a perhaps some separation between the laser and launched, but maybe that's a bit nit picky)
> The laser in the study is moving with the projectile,
And would be even more difficult than such (at least going by how much energy would be required).
But regardless, I'm not sure that 30 km altitude and first achieving mach 5 is a major constraint beyond that is probably not achievable at the $2000 price point (or its not clear to me that it is from the paper) and would be something that could be worked around with more iterations of what level of ionization of surrounding air around a projectile with a given density would give the desired amount of drag reduction (perhaps zeptosecond[0] pulses would work even better than femtosecond ones that were compared against nanosecond, or achieve similar results with lower mach number and higher density of air being ionized around the payload).
[0] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.11...
I don't see how 'laser in the study is moving with the projectile' is in any way, form, or shape ambiguous.
And the $2000 price point is not from the paper but from your own post.
Is what I considered to be ambiguous because it wasn't clear to me that you were assuming the system would be either 'laser launched' or 'launched by a from a trebuchet' with the laser part only applying to the object, regardless of your mention of:
> The laser in the study is moving with the projectile,
Your comments after that made it clear that we are both on the same page regarding the laser part is referring to the payload.
The difficulty being your point is not that interesting to me when i made the post, but the possibility of being able to send something into LEO while minimizing drag effects on the payload to something negligible along the flight path of the payload.
The $2000 came from the cost of the trebuchet system, I'm more interested in at what price point would a system be possible (Ideally below the cost of hypersonic missiles [0] now that I assume use something like this) with a rail gun kind of system.
[0] https://www.scmp.com/news/china/science/article/3142581/chin...
If frontal area didn't matter to drag, wouldn't all spheres would have the same drag coefficient?
From that page:
Cd = D/(rAV^2/2) where A is frontal area.
What am I missing?
You're citing a page that uses the word "density" differently than you do.
"D" is density-of-the-air. The density you're talking about appears to be the density-of-the-sphere.
They explicitly said so.
Twice.
Air drag is proportional to the drag-coefficient * velocity^2. So doubling your speed quadruples the drag.
Except... the drag-coefficient itself is a complex curve over velocity. It barely changes from 0mph through 300mph, but once you reach transonic and supersonic speeds, the drag-coefficient skyrockets.
As a result: 250mph is more than 4x more efficient than 500mph from a drag perspective (4x predicted from Drag equation, but in practice might be 8x or more). This is mostly a problem for airplane efficiency and fuel consumption, but I'm sure it applies to war-machines and projectiles too.
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But modern airplanes fly at very high heights, so the air is thinner, reducing drag, but requiring a pressurized cabin lest everyone gets hypoxia.
Tell that to cyclists :-) You can barely go above 25 km/h (~15 mph) without feeling like you are just pedaling to overcome the drag.
Reducing the Cd on a bike, ie going recumbent and putting a aerodynamic shell on it, ie switching to a velomobile allows you to go 40 km/h (~25 mph) with relative ease.
One can use a laser + charge to pre-boil the flight-path into a plasma channel. Sort of like cavitation, but with gasses.
nm