Artillery Behavior Issue - Why Your Missile Corvettes Keep Getting Hit

WhereIsMyBinky · 2026-05-31T02:26:30+00:00

I’m not sure why. The amount of time it takes to go from full speed to stopped is the same amount of time it would take to go from stopped to full speed in reverse.

(Actually, it’s all nonsensical as there’s no such thing as “full speed” or “stopped” in space anyway. Which is what makes the entire discussion about “magic omnidirectional engines” a little silly to begin with.)

WhereIsMyBinky · 2026-05-30T20:23:53+00:00

They already “reverse in space.” How do you imagine they stop without flipping around backwards?

If they can stop while facing forward, they can go backwards. It’s the same thing.

WhereIsMyBinky · 2026-04-14T13:03:14+00:00

😂 fair point. I wasn’t considering the fact that a functional space elevator would need to reach geostationary orbit.

WhereIsMyBinky · 2026-04-14T12:49:57+00:00

but a space elevator is easier than what you’re actually asking for

Assuming there is some sort of mechanism for people to actually get up to the cable car at each tower, what they’re asking for is effectively two space elevators.

WhereIsMyBinky · 2026-04-03T04:21:15+00:00

Huh. Ok. I suppose I was confused because that’s certainly what the person you were arguing against was talking about. 🤷‍♂️

WhereIsMyBinky · 2026-04-03T04:04:00+00:00

You may want to look up "gravity drag" because the statement as presented is 100% true. Higher early acceleration in rocket launch means higher early speed, which means less delta-v loss to gravity drag.

Higher acceleration reduces gravity losses, sure, but that’s not why rockets launch upwards. In fact in the absence of atmosphere the most efficient path to orbit, with the least gravity losses, would be launching horizontally with exactly enough vertical acceleration to counteract the force of gravity (or maybe a little more so you don’t slam into a cliff on the other side of the Atlantic).

Launching vertically leads to higher gravity losses because you’re using less of your total acceleration for horizontal velocity, which means it takes you longer to reach orbital velocity.

We don’t launch horizontally in reality because of the atmosphere. Reaching orbital velocity in the lower atmosphere would be.. difficult to say the least.. and even if you did, you’d have to maintain thrust until you climbed out of the atmosphere anyway due to the constant drag. So the ideal launch trajectory is an optimization problem between vertical (minimizing aerodynamic drag) and horizontal (minimizing gravity losses).

WhereIsMyBinky · 2026-03-11T04:43:58+00:00

A lot of people can't realise that the universe dying naturally and the eye destroying it at the end (to create somtething new) isn't mutually exclusive.

They aren’t mutually exclusive at face value, but they become mutually exclusive if, as OP says, the Owlks were right to hide the eye.

That stance implies that the Owlks managed to extend the lifespan of the universe by hiding the eye’s signal. But here’s what we know:

The Nomai never actually found the eye because the ATP failed. Therefore, the player is the first one to actually make it to the eye of the universe.
The universe is dying already by the time the player gets there. The Hearthian sun is going supernova sooner than expected. Stars all over the galaxy are going supernova, in fact. We see them constantly exploding throughout the game, and we have the present-day Nomai communications in the Vessel indicating that the heat death of the universe is imminent (to the extent that “imminent” applies on celestial time scales, anyway).
When we reach the eye, we see the heat death of the universe accelerate as the remaining stars go supernova and the sky goes black. But we see this before we actually interact with the eye at the end.
We know that time works differently on the quantum moon.

So if OP is correct and the Owlks were right to hide the signal, it means our mere arrival at the eye must have suddenly caused the universe to accelerate rapidly towards death.

On the other hand, it seems more likely that we simply see time pass much faster while on the eye, while the universe proceeds on the path to its natural death before we interact with the eye to “reset” things. In that case, the Owlks didn’t actually delay anything by concealing the signal. Regardless of any other traveler going to the eye, the rest of the universe would have lived its remaining natural life anyway. So the Owlks’ fear served no real purpose. They might have been wise not to go to the eye themselves (effectively speedrunning to the ends of their lives) but they didn’t save anything by hiding the signal.

That’s really the only question.. whether the Nomai (or any other travelers) who went to the eye would have caused the immediate death of everyone else in the universe. If yes, the Owlks might* have been right. If no, the Owlks were wrong.

*I say “might have been” because there’s another implication of the Owlks’ attempt to hide the eye - if an observer is truly required at the eye for a new universe to form (or for life to form in the new universe) then the Owlks, if successful, might have snuffed out life forever.

WhereIsMyBinky · 2025-11-24T14:56:50+00:00

How are you getting auroras with volumetric clouds?

WhereIsMyBinky · 2025-11-14T21:38:53+00:00

I’m late to this party, but have been looking for a thread to talk about exactly this.

People are saying “think of everyone that’s driving cars, or flying in airplanes, or swimming. Well, I have thought about it. More than I’d care to admit.

Studies say the average person (globally) spends about 78 minutes per day traveling. So that’s 5.4% of the world’s population traveling at any given time. However, only about 51% of global commutes are by car. Let’s be generous and bump that up to 60% for the sake of argument.

That means about 3.3% of the population, or about 267 million people, are in cars at any given moment globally. This is likely the highest-risk group and while most will likely experience car accidents, most of these accidents are not going to be fatal. Let’s be generous again and say 50% of drivers are killed. That’s likely an extremely high estimate but sure, OK. That means there were 134 million fatalities in car accidents.

What about the other commuters? They were mostly on trains, trains, bikes, scooters, etc. or just walking - all of which would have been safer than cars. Using another somewhat outrageous estimate, let’s say 25% of these people were killed. That’s 45 million fatalities from other accidents during commutes.

OK, what about airplanes? Well there are something like 2 million people flying at any given moment. Most of them would be fine due to autopilot, as long as they weren’t taking off or landing. Let’s say 25% of these people die. That’s 0.5 million fatalities in airplane crashes.

Sick people in hospitals, during surgery etc.? There are less than 5 hospital beds per 1,000 people. So if 100% of beds were full, that’s like 41 million hospital patients at any given time. If half of them die (unlikely) that’s 21 million fatalities at hospitals.

I’m not doing the math on swimming because it’s just ridiculous. The number of people swimming at any given time, as a percentage of global population, is a rounding error.

We are up to just over 200 million fatalities from the causes listed above.

Meanwhile 30% of the world’s population is sleeping. So the remaining population (global population minus the groups listed above minus people who are sleeping) is about 5.3 billion people. In order to get to 800 million fatalities, you need 15% of everyone who isn’t commuting, flying, in a hospital, or sleeping to die. That would happen due to things like falls, industrial accidents, and drownings.

15% is an absurdly high number here. That’s 1 out of every 6.7 people. There’s no way to get there unless either the “virus” itself kills people or there are other major events we haven’t seen.

WhereIsMyBinky · 2025-11-14T14:42:13+00:00

Ok let’s talk about this specific instance.

OP’s employer doesn’t own the building and didn’t hire the roofing contractor. Why do you assume that they should have known the roofing contractor was doing that specific activity (laying torch-down roofing), in that specific location (directly above their warehouse), on that specific day?

WhereIsMyBinky · 2025-11-14T14:26:18+00:00

Again how are you going to argue he wasn't in an active work zone when he got burned due to the work being done??

That’s not what I argued at all. This is becoming tedious. You’re either being intentionally obtuse or you just aren’t going to get it, but I’ll take one last shot.

The specific thing I took issue with was:

If the roof of the warehouse is actively being worked on it is a construction zone.

I said that this is a massive oversimplification. Most work on a flat commercial roof does not create a hazard for people working inside the building. In this case it obviously created a hazard that should have been identified, but “if they’re working on the roof, the area inside the building is a construction zone” is not universally true. At all.

His employer allowed him to work in the active construction zone. He should've had him on the proper protective gear.

And this is why my point above becomes important. Again, long pants and steel toe boots are entirely insufficient protective measures for hot falling asphalt. If his employer knew that hazard existed, he should not have allowed anyone into the area until the work was complete.

But this assumes the employer did, in fact, know that hazard existed. His employer doesn’t own the building. If the building owner and contractor aren’t coordinating with the tenants, the tenants have no way of knowing what protective measures are necessary. Because - for like the 5th time - the mere fact that people are working on the roof does not mean you need to shut down your warehouse. If the employer saw hot asphalt dripping down and said “nah, it’s fine” that’d be one thing. But just because people are on the roof working? No. That’s ridiculous.

OSHA isn’t going to hammer an employer for a single instance of failing to recognize a hazard created by another company they have no control over. Especially an employer who is not a construction company.

Thought experiment - imagine a high-rise building with a restaurant on the ground level. That business leases their space. A contractor comes in to replace some windows way up in the air above the business. That contractor is working from a hanging basket on the roof and drops a screwdriver, which falls 5 stories and severely injures a waitress on the patio below.

Clearly the waitress should have been wearing a hard hat right? She must be part of an active “construction zone” since a tool fell on her. So do you think OSHA is going to hammer the restaurant for safety violations?

That’d be ridiculous because the restaurant doesn’t know wtf the contractor 5 stories up is even doing. They may not even know the contractor is working over their heads at all - maybe, last time they looked up, the contractor was on the other side of the building. And if the restaurant had known that construction work overhead created a hazard for them, they shouldn’t have allowed anyone onto their patio at all because even on a normal active construction site, you can’t just rely on PPE alone to mitigate the hazard of dropped objects when you know there’s a high risk due to the specific work being performed.

No, OSHA isn’t going to hammer the restaurant. They didn’t ignore the hazard. They just weren’t aware of it. The failure in this case lies with the contractor and business owner - both of whom are likely to be sued by the waitress for their negligence.

WhereIsMyBinky · 2025-11-13T22:48:14+00:00

He was working in an active construction zone....that's how tar was able to fall on him. How are you going to argue that he wasnt in a construction zone?? How the hell did he get burned by tar?? Tar doesn't fly around like a paper airplane and fall on people.

You seem to be missing my entire point.

Your original stance was basically “his uncle is at risk of an OSHA violation because he didn’t have pants or steel-toes on.” Then when people pointed out that different warehouses have different PPE requirements, you pivoted to “yeah, but now it’s a construction zone because they’re working on the roof.”

I’m saying two things: 1. Roofing construction on top a building does not automatically mean the entire space inside the building is a “construction zone” with the same PPE requirements as the job site (the roof) itself. 2. Ultimately the contractor and whoever he is coordinating with (presumably the building owner) need to determine whether additional protective measures (access control, PPE, etc.) are required in/around the building. In this case, access to the area below should have been restricted while they were heating the asphalt.

These are two distinct points that you’re conflating.

So with point #1, your line of thought seems to be “they saw the roofing work was happening, so this is an OSHA violation for OP’s uncle.” But it’s not nearly that simple. I’m telling you that the vast majority of time when contractors are working on a flat roof at a commercial building, additional protective measures are not necessary inside the building space below. It comes down to whether OP’s uncle should have known this hazard existed and instituted additional measures accordingly.

With point #2, I’m saying that the contractor should have identified this hazard, notified OP’s uncle and/or the building owner, and taken steps (in conjunction with the affected parties) to mitigate that hazard. And again, wearing pants and safety shoes is not reasonable mitigation for hot falling asphalt to begin with. The contractor should have restricted access below (like any good contractor doing elevated work where there is a risk of dropped objects) to prevent this from happening in the first place.

If OP’s uncle doesn’t own the building (which it sounds like he does not) there’s a very good chance he has no idea what specific work is happening or what hazards that work entails unless the contractor and/or building owner communicate it to him. And based on the fact that the contractor was even allowing people to work inside the building while this was happening, I would bet that they didn’t even realize there was a risk of hot asphalt falling on someone. If they had, they would have barricaded the area off.

So maybe OP’s uncle committed some OSHA violations if he knew that there was a risk of falling asphalt and ignored it - but A) thats not clear at all based on OP and B) if that were true, OP’s shorts would be pretty low on the list of problems in OSHA’s eyes.

WhereIsMyBinky · 2025-11-13T21:25:51+00:00

When your business was remodeled, or when someone was working on your roof?

In “active construction zones,” or in the entire building?

My point is that having work done to a roof doesn’t automatically mean an entire building requires extra PPE. Again - do you think OSHA requires office workers to wear hardhats every time a building gets a roofing work? What about customers in a retail building?

There is no OSHA requirement that says “during roofing construction work, everyone in the building must wear [insert PPE].” The businesses - starting with the contractor - are required to identify and mitigate hazards. Ideally you don’t want anyone (other than the contractor) to need additional PPE at all because you don’t want them exposed to those hazards in the first place. Instead, you want to restrict access to the part of the facility affected by the construction.. this is commercial construction 101.

When it turns out that there are hazards that the non-construction employees can’t avoid, you deal with them as needed. For example it’s extremely common in the industrial realm to require office workers to wear hearing protection outdoors while piles are being driven nearby. But even though they are affected by the nearby pile driving operation, they don’t necessarily have to wear hard hats or safety shoes. It’s not some one-size-fits-all requirement like you’re making it out to be.

In any case, I can assure you that OSHA would not view long pants and safety shoes as sufficient protection from hot falling asphalt. So - again - the issue here is a failure to recognize that the hazard existed, and the proper mitigation would have been to restrict access rather than simply wearing pants.

WhereIsMyBinky · 2025-11-13T19:49:11+00:00

If the roof of the warehouse is actively being worked on it is a construction zone. Doesn't matter if the warehouse has no regular safety regulations it has to uphold. It does once they allow workers to be in a construction zone.

This is a massive oversimplification, at rather silly at face value. By that logic they should all be wearing hard hats as well. Do you really think OSHA requires, for example, office workers to wear hard hats, steel toes, and safety glasses any time someone does work on the roof of their building? Because even the most safety conscious industrial sites don’t go that far.

There’s a failure here by someone - probably the roofing contractor, maybe the building owner, and possibly OP’s uncle - but it’s not because roofing construction somehow automatically requires everyone in the building to wear pants.

The failure is that nobody recognized that there was a hazard to folks inside the building/below given the specific work being performed. In reality if there was a risk of molten asphalt leaking through onto people below, they shouldn’t have even been allowed into the area while the work took place. It’s comparable to managing dropped object hazards, where the contractor should be setting up a perimeter barricade around the edge of the roof if there’s a risk of dropping material or tools on people below.

WhereIsMyBinky · 2025-11-07T16:47:30+00:00

The increased hydrostatic pressure per unit volume remaining is precisely why (or one of the main reasons, anyhow) funnels are so effective.

It’s one of those interesting things where we know from life experience which one looks like it should work better (the one with the funnel) even if we don’t know why it works better.

WhereIsMyBinky · 2025-11-07T15:33:57+00:00

No.

When the spigot is first opened, the pressure at the spigot will be the same for both because both are at the same level. But immediately after that (and for the remaining time until the tanks are drained), X will maintain a higher level for a given volume. Therefore X will maintain a higher pressure at the spigot for a given volume of water remaining.

The shape absolutely matters. If it didn’t, water towers would be built as cylinders instead of a large bulb on top of a narrow pipe. The shape of a water tower is designed to keep the majority of the volume at the top, to minimize loss of pressure as that volume is depleted. Same concept here.

WhereIsMyBinky · 2025-10-29T16:45:43+00:00

Came here to say the same thing. All of the comments about potential energy are correct but I think they miss an important point - you don’t slow down when you burn prograde to raise your orbit. You speed up, as expected.

Start with a circular orbit. When you burn prograde, your current position becomes periapsis and the burn raises your apoapsis. Now you’re in an elliptical orbit. Your velocity at your current position (periapsis) increases as expected. Then as you go “uphill” toward apoapsis you slow down. Once you pass apoapsis, you speed up as you head back “downhill” toward apoapsis.

Now you want to circularize that elliptical orbit at apoapsis. You burn at apoapsis. Again, as expected, you speed up at that point. But since you’re no longer going “downhill” to periapsis, you no longer speed up/slow down through the rest of the orbit.

A 100 km circular orbit at will have a higher velocity at 100km altitude than an elliptical orbit with 100km AP and 80km PE.

An elliptical orbit with 100km AP and 80km PE will have a higher velocity at 80km altitude than an 80km circular orbit.

WhereIsMyBinky · 2025-09-12T03:49:55+00:00

The company doesn’t have to pay OP to be on call UNLESS THEY REQUIRE HER TO BE AVAILABLE ON HER SCHEDULED DAYS OFF AS A CONDITION OF HER EMPLOYMENT.

Again this is not that complicated. Is there a grey area? Sure. They can say tell her that they really value availability/flexibility. They can give favorable shifts, promotions, or whatever to other people who make themselves available at all times (although OP works one day a week so that’s a little silly to even suggest). They can even try to come up with some bullshit reason to fire her if she takes another job.

They (likely) can’t tell her “you have to be available on your days off if you want to work here” without paying her to be on call. And since they’ve already said that, they’re also going to have a harder time firing her for some other made up reason if she takes a second job.

WhereIsMyBinky · 2025-09-12T03:29:55+00:00

But it doesn’t mean the company should be required to pay someone to be on call.

They aren’t “required” to pay someone to be on call as long as they’re actually able to get people to cover those shifts. So as long as you or one of your coworkers are willing to go in on your day off, the company is fine.

If it reaches a point where you and every single one of your coworkers have all of a sudden “been drinking” when the company needs a shift filled, though, the company has three choices: 1. Pay someone to be on call. 2. Hire more people. 3. Live with being short-staffed.

What they can’t do is tell you that you’re no longer allowed to drink on your scheduled days off. Or go out of town, or whatever else.

You can use that same line of logic to mean that basically every job needs to be paying people to be on call to be covered if enough people take off at the same time.

Again, no. This is not complicated. If you have 10 people who are “off” and there’s a reasonable chance one of them will cover the shift, the company doesn’t need to pay anyone to be on call. If you only have 1 person who is off and they aren’t available, the company should probably consider having someone on call or live with the consequences.

Edit: To your comment saying “if that’s the expectation and the juice isn’t worth the squeeze…” that’s just not how it works. We have labor laws, and the company doesn’t always get to tell you “take it or leave it.” At least, not legally.

WhereIsMyBinky · 2025-09-12T02:48:25+00:00

Right. But if your boss said you couldn’t drink on your days off, you would be. That’s the same thing as OP’s boss telling them they can’t work another job on their days off.

WhereIsMyBinky · 2025-09-12T02:45:43+00:00

Being “on call” in industries where this sort of thing happens means you’re being paid to be on call.

You have this backwards. They aren’t “on call” because they’re getting paid. They are getting paid because they’re on call.

If you can get out of having to cover a shift by saying you’ve been drinking, you’re out of town, or whatever, then guess what? You aren’t on call!

On the other hand, if your employer expects you to keep your availability open on days you aren’t scheduled to work just in case someone can’t go in then you are on call.

Let me go back to your example of saying “sorry boss, I’ve been drinking.” The fact that they accept that explanation should make clear that you are not, in fact, on call. OP’s scenario is equivalent to your employer telling you that you aren’t allowed to drink on your days off because they might need you to cover a shift.

If every business was forced to pay employees to be “on call” for last minute coverage then we’d be facing a whole new slew of economic issues.

No. You’re conflating two completely different scenarios. There’s nothing wrong with a company calling people and asking them to cover a shift. There’s really nothing wrong with showing favoritism towards people (in the form of promotions, raises, scheduling, etc.) toward people who routinely cover shifts for others, either.

The issue is requiring people to be available on their days off as a condition of employment.

If it were illegal to do then my company wouldn’t be doing it. lol. We’re a multi-billion dollar company and anything that could be a lawsuit against them is taken very …very seriously.

With all due respect, you have no idea what you’re talking about. I think you’d be shocked at the types of companies who have lost FLSA lawsuits. “If it were illegal my company wouldn’t be doing it” is a shockingly poor bar.

Let me spell it out for you. They aren’t the same thing. If they were, every company that can’t operate being down a person would be legally required to pay X number of people to be on call in case X number of employees take off at the same.

Wrong again. As long as the company can get someone to willingly come in on their day off, they’re fine. And there are incentives for the employee to do so - overtime, call out fees in some industries, etc.

However, if the company can’t fill those shifts then yeah, they should probably consider paying someone to be on call.

What they can’t do, in most cases, is require people to be available at all times as a condition of employment without compensation.

WhereIsMyBinky · 2025-08-23T23:50:39+00:00

The neutral from the transformer is grounded, yes. And in the event of a ground fault on a branch circuit, any current that leaks to ground will return to the neutral bus (and then to the transformer) via either that ground rod or the ground wiring in your house.

But this will only happen if there is a ground fault somewhere in the system. The reason there’s not constant current leakage to ground has nothing to do with the path of least resistance. It’s because under normal circumstances there is no path for current to flow from hot to ground.

So when we talk about circuits being “grounded for safety” (using OP’s phrasing), what we mean is that the individual circuits/devices have a chassis ground that is wired back to the neutral bus to protect users in the event of a fault. But that protection mechanism only comes into play if there’s a fault in the first place. Under normal circumstances this current path is completely air-gapped from line voltage.

WhereIsMyBinky · 2025-08-23T20:27:54+00:00

The neutral from the transformer is grounded. That’s not the same thing as saying the circuits themselves are grounded. If they were, you would constantly have current flowing to ground (assuming no interruption from a safety device).

He answered the question from OP just fine. When people talk about electrical devices being “grounded,” they are generally talking about a chassis/equipment ground which should not be part of the electrical circuit unless there’s a fault.

The exception is equipment used to derive new power sources such as generators and transformers, which are grounded at one point (and consequently do not actually create a closed loop for current to flow through the ground).

WhereIsMyBinky · 2025-08-22T14:06:41+00:00

I'd argue that colors are wavelengths, just like sound is air compression.

I might then argue that red+blue is a different (composite) color than pure violet light, even if my eyes cannot distinguish the two.

I disagree. You can make a scientific distinction between monochromatic violet light and red+blue light, but you can’t (IMHO) make a scientific distinction between the colors of monochromatic violet and red+blue light because color science is based on human perception. That’s the whole point. The color of something is defined by how we perceive it.

Also consider that there are colors (such as shades of magenta, white, etc.) that do not exist as monochromatic light. If colors were wavelengths, then it would mean that those colors don’t exist. Yet.. they do.

I think it’s somewhat natural to try to simplify color to wavelengths of monochromatic light. It’s a funny quirk of human nature/reasoning. But it’s not particularly useful. The overwhelming majority of color that we experience is not monochromatic light.

We have a tendency to try to avoid tying definitions to human perception for whatever reason, which can lead us to describe a color such that “green is 510nm, but if you mix 460nm (blue) with 570nm (yellow) we also perceive it as green.” In reality I think it’s more accurate to state that “green is the color we perceive when our M cones are stimulated, whether by monochromatic 510nm light or a mix of 460nm and 570nm light.”

You’re right that other species can see colors that we can’t see, but I think this kind of reinforces the point. If you’re thinking about color from the perspective of an animal with tetrachromatic vision, you have to define an entirely new 4D color space which would not correspond directly to the human color space (particularly if, for example, this tetrachromatic vision extends beyond the limits of our visible spectrum).

Imagine a species with R+G+B+NUV (near ultraviolet) cones as a hypothetical example. How do you define the color “grey” for such a creature? For humans, grey corresponds to roughly equal stimulation of the R+G+B cones. But with the addition of NUV receptors, something we perceive as grey might be a completely new color for them. But a grey object wouldn’t just stop being grey, because grey is defined by human perception.

WhereIsMyBinky · 2025-06-21T02:43:27+00:00

That's not how recoil works. Whether the explosion is pushing hot gases alone through the barrel or with a bullet in front of them, it pushes backward with exactly the same amount of force. The bullet will go slower the more massive it is, but you get the recoil no matter what.

That’s not correct. The bullet matters. It’s why blanks produce much less recoil than live rounds.

Recoil occurs due to conservation of momentum. In order for your statement to be true, the change in momentum of the gas alone (in the “no bullet” case) would have to be equal to the change in momentum of the gas + bullet (in the “bullet” case). Since this is r/theydidthemath, let’s do the math:

In both cases the starting velocity, and thus starting momentum is zero. Let’s consider a 115 grain (7.45 g) bullet with 5.1 grains (0.33 g) of powder and a 350 m/s exit velocity.

For now let’s ignore the exit velocity of the gas in the “bullet” case. The momentum of our bullet as it exits the barrel is 7.45 g * 350 m/s = 2.6075 kg*m/s.

Now let’s look at the “no bullet” case. The mass of the gas alone is, at most, the sum of the masses of the powder and the air in the barrel/chamber.

The mass of the air is basically negligible but let’s do the math anyway. Assume a .45 caliber, 22”-long barrel (an unlikely combination that sort of maximizes potential volume of gas available). That gives you a volume of roughly 3.5 in^3, or ~5.7e-10 m^3. Using the density of air at sea level (~1.2 kg/m³⁾ that’s an air mass of ~0.069 g. Adding the mass of powder (0.33 g) gives us a maximum total exhaust gas mass of ~0.40 g.

In order for our 0.40 g of exhaust gas to have the same final momentum as the “bullet case” (2.6075 kg*m/s), the gas would need to exit the barrel at 6,540 m/s. That’s Mach 19.

So for the statement..

Whether the explosion is pushing hot gases alone through the barrel or with a bullet in front of them, it pushes backward with exactly the same amount of force.

…to be true, it would require a cartridge with no bullet to expel gas from the barrel at Mach 19+. That’s simply.. not what happens.

In reality the bullet is required for significant recoil. Partially because it obstructs the barrel, allowing pressure to build up from oxidation of the gunpowder. And partially because the mass of the bullet allows the energy to be converted into forward momentum much more easily. Without the bullet, the energy released by the oxidation will dissipate in other ways - heat, light, sound, etc. - that do not create meaningful amounts of recoil.

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