Debunking the Nuclear-Powered Manhole Cover

In 1957, a high-speed camera caught a cast iron cap moving at 66 kilometers per second. It was being accelerated by a nuclear explosion beneath it. Did the Pascal-B nuclear weapons test actually make a manhole cover the first man-made object in space? Noted Nuclear Zaddy Kyle Hill finally does the math to determine what happened to this infamous object. We can stop making videos about this now. Thanks.

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[kylehill]

**Thanks for watching!** So many smart comments! You love to see it. Let's address them:

I knew (and said in the video) going in that everything was going to be a slightly better back-of-the-envelope. In terms of a first approximation that you might find in a primary or secondary physics class, I'm fine with it. I know that the atmosphere is only so high, I know that hypervelocity makes a difference, I know that heating takes time, I know the shape factor might not perfectly apply. Like I said, first approximation -- I don't have a supercomputer for millisecond-by-millisecond analysis.

Further thoughts:

Drag is proportional to the SQUARE of the velocity. So some of you saying drag is less at hyper velocity are not thinking about this. Observe how “slow bullets” move through water and hyper velocity bullets are more or less destroyed on impact (yes water is 1000x more dense I know, but the velocity increases the drag that much).

Think about the boundary conditions I set. We made it so there would have to be “at least this much energy.” There is, and so having it be 5-10x more energy than “required” means there is room for a fudge factor.

If you have problems with the approximation, do let me know. Otherwise, if there's a more capable physicist, take what I did one step further!

[espeterson]

There are some problems with all of the math. Three things: We assume that the cap was moving through the atmosphere perfectly flat; not sideface or tumbling. Second, the fluid dynamics of re-entry are not static. There is "peak heating", and as the cap moved upwards in the atmosphere, it would encounter VERY progressively thinner air. So, if we assume that the peak heating occurred fairly quickly, in the denser parts of the atmosphere (which is a safe assumption), then there is a plethora of unknown data values after it reaches peak heating. Thirdly, hypersonic atmospheric interaction on a shape like the cap isn't a known value, and there is too much assumption made on that; meteors explode at lower speeds precisely BECAUSE they are traveling at a lower speed.

All this to say, it is most probably accurate to assume that the cap did not make it to space. However, there is a LOT more math that needs to be done to be actually conclusive. Also, before its likely vaporization, it most certainly was the fastest man-made object ever created.

[LlywellynOBrien]

You made one critical error in your calculations. You seem to have assumed that your audience wouldn't angrily math, but boy howdy are they down here angrily mathing.

[theCodyReeder]

I have an old video where I detonated some explosives inside a thick wall steel cylinder with a flat copper disk capping the end. I found that the disk forged into a pointy shape much like an explosively forged projectile.
Which definitely would help but I figured not enough.

[the_fat_electrician]

Ay lol 😂
Lemme know when we’re teaming up to recreate it!

[bestsnowboarderuknow]

I wrote a paper on this when studying for my PhD in Aeronautics at Stanford. Even if the blast turned it into a more aerodynamic shape with a drag coefficient of 0.50 (YouTuber Cody's Lab had suggested this a decade ago and it prompted me to write the paper), I showed it would have burnt up before reaching space at 150, 000 mph or whatever it was I calculated the speed at. Cody's Lab believes it could have reached space. I believe his video on it is still up.

[doubldave]

So it didn’t make space… but the high speed video still confirms it was temporarily the highest velocity man made object ever...

[dumsparce]

Kyle: I did the math
comments: yeah, about that...

[TrainsandRockets]

Few points:
1) That cover might flip and go sideways due to drag and stability.
2) Meteors are more porous and loosely packed than Iron plate.
3) Moving faster means taking much less time, to what if it before melting completely it exits the lower and denser atmosphere and then goes into orbit as a semi-solid hot lava?
4) The equation considers many coefficients, and the difference in energy is only 8 times. What if the coefficients slightly vary and there isn't enough energy available to melt?

Food for thought. I request some scientists to perform an experiment again with better cameras and better trackers.

[ericsmith]

Kyle, you made a mistake in the velocity numbers. The heating equation is based on the change of velocity. You assumed the entire velocity was lost when you used 0 for Vo and 66 for Ve. You showed that the cover had enough kinetic energy to vaporize...but only if it stayed in the atmosphere enough to drag down to zero V. This baked the answer to your question into your equation to answer that same question.

You need to figure the atmosphere exit velocity based on the drag estimate and gravity. After this point the cover is in space with no more heating. Was this delta V enough to vaporize?

[FartingSpider]

I love how Kyle probably made this video because he was tired of people talking about this but, now, because of his math errors, people are talking about it more than before. And now he probably has to make another video on this subject fixing his broken math.

Are you happy now, Kyle?

[festerallday]

The problem with the math is the assumption that reentry is just the inverse of exit. The iron disk would be traveling at a negative acceleration and would be experiencing less atmosphere as it rises. Not accelerating as the atmosphere density increases. The forces on the iron would be constantly decreasing and it's chances of survival increasing with every meter of altitude

[gabe]

A few variables worth considering:

1) The cap likely was not moving through the atmosphere perfectly flat, but likely tumbled. Coins falling through air end up tumbling and traveling (mostly) at least partly edge-on. This absolutely changes the aerodynamics and the drag considerations

2) The cap is not similar to a meteor because it was traveling UP through the atmosphere, instead of DOWN through the atmosphere. Atmospheric density drops off very quickly the further up you travel. at 150, 000mph, it would have exited the troposphere entirely in about 0.16 seconds (we can round to 0.20 for easy math and to account for some slowing down due to drag, though getting an accurate number on that is an entirely different calculation), which would have put it past 80% of the atmosphere in about the time it takes to blink

3) The cap is also not similar to a meteor because, to our knowledge, it shot straight upwards. Most meteors travel through the atmosphere at an angle, many of them a pretty low angle, so the sheer amount of atmosphere they encounter is substantially higher than an object traveling straight up or down through the atmosphere

4) Transfer of heat is not instantaneous. Even for an object moving very fast and generating a ton of friction, the heat transfer still takes time. The leading idea behind the cap making it to space is that, while it was certainly going fast enough to burn up, it simply left the atmosphere too fast to substantially heat up. Again, it left the troposphere in a fifth of a second, and every mile that it traveled, the atmospheric density lessened exponentially

[percent]

I'm willing to be wrong but a part of me believes this can't be accurate for two reasons:
1. The equation assume air density is increasing, which is not the case here
2. The equation doesn't account for time spent within atmosphere (thus ignores conductivity).

The second point may not matter in this context if the material is deteriorating ablatively, which is no doubt happening to at least some degree, but it worries me that time isn't even a factor in the equation. Perhaps I just don't understand thermodynamics all that well :)

[Dominic_Berry]

There's a major mistake in this calculation that invalidates the result. The ratio eta = C_H/C_D given in the paper is intended to be the fraction of the kinetic energy that is transferred as heat to the vehicle, and so can be no larger than one. In the numbers used at 9:37 it is given as 24.1/1.28, which is far too large. If you assume the maximum allowed value of one, which is ALL kinetic energy transferred to the vehicle, then it is 2*10^12, which is too LOW an energy for vaporisation.
Edit: There's an even worse error on the left side of the equation, where the number they got is too large by a factor of nearly 1000. That means the kinetic energy is far more than enough for vaporisation. The velocity is not really a reliable estimate, but even if it was just escape velocity then the energy would be more than enough for vaporisation.

[FartingSpider]

The thumbnail: "I did the math!"
The comments: "You did the math... wrong!"

[midbcmidbc]

The air drag would have been nuts. The lid would have been flipping like a coin and moving in a direction that wasn't straight up. If it wasn't vaporized a chunk of it might still be sitting somewhere

[michaelgoldberg]

The surface of the manhole cover deminishes as it gets vaporized, and so does it's velocity
The math is incomplete

[VoidHxnter]

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[Jaysonengineering]

I dont think that a manhole cover several [edit: inches] thick would have instantly vaporized over .8 seconds. Your formula accounts for it spending its *entire flight down to a velocity of zero* in a gradually thickening atmosphere, not escaping into frictionless space in less than a second.