The world’s fastest manhole cover?

Tuesday, xkcd’s What-If mentioned the story of a manhole cover that may have gone into space before Sputnik:

A brief story:

The official record for fastest manmade object is the Helios 2 probe, which reached about 70 km/s in a close swing around the Sun. But it’s possible the actual holder of that title is a two-ton metal manhole cover.

The cover sat atop a shaft at an underground nuclear test site operated by Los Alamos as part of Operation Plumbbob. When the one-kiloton nuke went off below, the facility effectively became a nuclear potato cannon, giving the cap a gigantic kick. A high-speed camera trained on the lid caught only one frame of it moving upward before it vanished—which means it was moving at a minimum of 66 km/s. The cap was never found.

66 km/s is about six times escape velocity, but contrary to the linked blog’s speculation, it’s unlikely the cap ever reached space. Newton’s impact depth approximation suggests that it was either destroyed completely by impact with the air or slowed and fell back to Earth.

This remark includes a link to a post about the test on “Notes from the Technology Underground.”  A comment on that post takes some of the fun out of it:

It probably never left the atmosphere. As Newton found, a projectile penetration into a medium is proportional to their relative densities, times projectile bodylength, quite irrespective of projectile velocity.

Here we have steel projectile (8 g/cm3), thrust into air (0.001 g/cm3), meaning that the projectile will only travel 8000 times its bodylength into the atmosphere.

If it was 4 foot across, weighted 2 tons (I think I saw that figure somewhere else), and was roughly circular, this works out to thickness of 22 cm. So face up, it coul travel 1 760 meters high. If it somehow turned to its side and stayed in that position, it could travel 4 feet (120 cm) * 8 000 = 9 600 m high. Even this best case scenario is short from leaving the atmosphere. Thinning of air as you get higher is obviously not considered, but I don’t expect it would change the results much.

It gets even less exciting when we look at these old remarks on “Above Top Secret,” based on discussions with Dr Robert Brownlee, the principal investigator behind the test in question (known officially as Pascal-B):

For an authentic account of this incident by Dr. Robert Brownlee himself, this web site is pleased to host:Learning to Contain Underground Nuclear Explosions.

As Dr. Brownlee explains, the figure of “a velocity six times that needed to escape Earth’s gravity” refers to the results of a simulation, that may not of been a good model of the actual test conditions (the actual yield for example, was unknown even if all other parameters were correct). No measurement of the actual plate velocity was made.

If the description of the plate is accurate – 4 feet wide, 4 inches thick and made of steel – then it would weigh about 900 kg (a lower weight is possible if the dimensions are inaccurate or if it was not of uniform thickness). A velocity of 6 times Earth’s escape velocity (67 km/sec, since escape velocity is 11.2 km/sec) would give the plate a kinetic energy 60% larger than the total energy released by the explosion. This is clearly impossible.

Brownlee explained to this author, by email, that the concrete plug placed in close proximity to the bomb was vaporized by the explosion. Thus the propulsion of the plate could be considered to be due to the energy imparted by this expanding vaporized material, rather like the propellant of a gun. From the descriptions available of the plug a mass of at least 3000 kg can be estimated, and if half the bomb’s energy were deposited in it then it would have an energy density of 50 times that of normal gun propellant. From the physics of high velocity guns, it can be estimated that velocities produced by the gas expanding up the long shaft could propel and object to velocities exceeding Earth’s escape velocity, perhaps as much as twice escape velocity.

If by some chance the metal that had made up the manhole cover did escape from the atmosphere (and after all, the atmosphere is thin enough that after less than two seconds going straight up at the hypothetical speed of 66 km/second the blob of molten iron that once made up the manhole cover would be in a near vacuum,) interesting things might have happened.  If it had fallen straight down, for instance, it would have bounced off the atmosphere back into space.  Perhaps it might have repeated that process several times, growing ever hotter.  With each bounce some iron vapor would have been flung down into the atmosphere, some flung outward into space.  Perhaps the bit of the blob that finally crashed into the ocean would have been quite small.

Probably nothing of the sort happened; probably the whole blob dissipated before leaving the atmosphere.  But one does wonder where the metal ended up…

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