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Comment by rich_sasha | Hacker News Reader

Smaller projectiles lose more energy to air drag.

Doubly so when you consider the supersonic barrier.

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.

> It barely changes from 0mph through 300mph

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.

Just in case you misunderstood the parent post -- your Cd as a cyclist is pretty much constant around your normal cycling speeds. Your total air drag goes up with the square of velocity, that's for sure, but if you went transsonic on your bike, your Cd would ALSO increase dramatically on top of the already brutal velocity-squared multiplier.

It’s almost worse, because you’re working against this quadratic force, at a rate proportional to speed. So power output, the usual limiting factor for a cyclist, scales like 3rd power of speed.

Fair enough ... I really did not get that :-)

You mean objects with lower surface area to mass ratio, AKA objects with lower density. If he wants some high-density objects to throw I think there are stores in the US that sell small, dense metal objects he could use.

Mass is not a factor in drag equations.

https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...

Velocity-squared is the factor in drag.

But very much in inertia, which is acting against the drag, trying to sustain its initial velocity.

https://en.wikipedia.org/wiki/Ballistic_coefficient

Density is important when comparing two spheres of the same mass.

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.

That's density of air, not of the object.

https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...

I wonder if you could do something like this[0] on the projectile to reduce drag:

"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...

The laser in the study is moving with the projectile, so I guess even for $2000 you won’t be able to have a 30 km altitude, Mach 6 flying object with perfectly controlled laser launched from a trebuchet.

I'm talking about a projectile that has the laser capabilities in itself (i.e the electromagnetic slug is emitting the femtosecond laser pulses after it is launched), not launched via a laser (it could be launched however, but I was assuming later on the comment that both the rail gun and the slug itself will need to be charged up).

Yes, it's 'moving with the projectile'. How does that make it easier?

I never said how easy it would be only that there is a difference between a payload that is launched via a laser and a payload that has laser capabilities in it (yes, 'moving with the projectile', like i was talking about from the beginning where you assumed otherwise).

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).

Try to read my comment, I never 'assumed otherwise', the difficulty of having the laser as payload is exactly my point.

> so I guess even for $2000 you won’t be able to have a 30 km altitude,

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...

Also try to read my other comment, the difficulty is precisely my point.

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.

> flying object with perfectly controlled laser launched from a trebuchet

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...

The frontal area of two spheres of the same mass will be determined by the sphere's density, and that drives the air resistance.

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?

> Cd = D/(rAV^2/2) where A is frontal area.

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.

It absolutely is, and will then drive differences in reference area, thus affecting the drag of the object.

"Appears to be"?

They explicitly said so.

Twice.

You’re missing nothing, you’re correct.

Only when they are flying to normal atmosphere..

One can use a laser + charge to pre-boil the flight-path into a plasma channel. Sort of like cavitation, but with gasses.

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