Thunder foot is a popular youtuber known for relentlessly criticizing
creationists for their scientific illiteracy he is also a published
chemist whom to his credit has made valid contributions to scientific
research he has been praised many times on this channel
however he has also been criticized when he gets things wrong so far most of the
things he's gotten wrong have to do with politics or economics but that can no
longer be said
apparently his PhD in chemistry has not made an immune to the same quantitative
blunders he ridicules creationists for making another youtube user libertarian
list is an undergraduate chemistry student you may remember him from his
occasional guest appearances on the velocity podcast as well as from my
quickie on father's Law he's chimed in from time to time pointing out Thunder
fits over sites in one video response to Thunderfoot he demonstrated that a
particular energy estimate of thunder foots was off by a factor of six
thousand that's not a problem nobody's perfect and as long as you correct the
error there's no issue however Thunderfoot failed to do that recently
Thunderfoot started a series called Hyperloop busted where he criticizes
SpaceX's Hyperloop project Hyperloop is a plan for mass transit using trains and
pneumatic tubes under foot is criticized this is inefficient but sadly many of
his criticisms are invalid libertarian is suggested that we collaborate to
respond to his videos in this series and as always we're including all of the
sources in the description so you can check our work in the first video under
that attacks the safety of the Hyperloop by arguing that it would expose its
passengers to fatal accelerations in the event of a team failure this was just
one of the few demos I came up with what a vacuum for you might look like on a
tiny scale for the poor Schmucks actually in the Hyperloop now bear in
mind this is merely the acceleration that you can get off about 60
centimeters that's about 2 feet of tube the acceleration she would be delighted
to get in the event of failure on the Real Hyperloop or quite literally be
like being shot down a gun barrel hundred that attempts to demonstrate
this with the model test by placing a metal ball in a glass tube containing a
vacuum he breaks the tube
applying atmospheric pressure behind the ball accelerating it down the tube until
it breaks through the other end so this is what it looks like formed at 1,000
frames per second edition see this really quite a formidable acceleration
there and their mind this is a tiny diameter tube over a short distance
about half a meter if you had a chip on a two meter diameter tube as with the
Hyperloop over a significant distance it would quite literally be like being shot
down a gun barrel with no way of stopping there are many problems with
this test the biggest is the Thunderfoot incorrectly assumes that the
acceleration would be greater on the larger scale when in fact acceleration
would be much less Thunderfoot has made a basic error of physics
he's forgotten that when you scale up surface area becomes the square of the
multiplier while volume becomes the cube every physics student knows this as the
square cube la to demonstrate this let's consider a cylinder will say its radius
and its height r 1 meter the drag this cylinder will make when moving in a
straight line is the area of the circle that represents the cross-section which
is $OPERAND pi r square since our is one that's PI square meters the volume of
the cylinder is PI R squared H but again since its radius and height or both
1-meter that's PI cubic meters
now we need to find out the mass of the cylinder mass equals volume times
density know the volume so to compute the mess we need the density to work
with
let's just say that the density is one kilogram per cubic meter
we know that the volume is $OPERAND pi $OPERAND cubic meters so in this case
the mass is $OPERAND pi $OPERAND kilograms mass volume and cross section
are all pie
although of course they're in different units this will make it easier to see
what happens when we scale up so let's double its size
this will double both the radius and the height so both of those become 2 meters
are cross-sectional area is PI R squared and since our is now 2 meters the area
becomes 4 pie square meters area has increased by a factor of four but our
vows
volume is $OPERAND pi r squared eight and since our HR both two meters now
that means that the volume is $OPERAND pi x 4 square meters times 2 meters or
8pi cubic meters which means that since our density is still one kilogram per
cubic meter the mass of the largest cylinder is 8 pi kilograms in other
words we have eight times the mass for only four times the surface area which
means that the air pressure will be pushing on the cylinder with four times
the force but since the masses increased Eightfold acceleration will be lower not
greater as Thunderfoot claimed acceleration is force over mass so
although the force on the cylinder will be four times as big
since the masses eight times as big it will only yield half the acceleration
the more we scale it up the bigger the difference it makes
at ten times its original size the area becomes a hundred pi square meters but
the mass ends up being a thousand pie kilograms and so we only get one tenth
the acceleration Thunderfoot completely failed to account for this
so how far off is Thunderfoot what is the acceleration the Hyperloop
experience in such a scenario and how does it compare to a bullet being shot
out of a gun like he claims would be similar
first let's calculate the acceleration experienced by the Hyperloop pod the
abstract published by SpaceX sites a figure of four square meters for the
frontal area the passenger plus vehicle capsule and an overall mass of
twenty-six thousand kilograms when fully loaded with fuel passengers and luggage
in Thunderfoot scenario one atmosphere of pressure would be exerted on the back
of the pod this would result in an acceleration of only 15.6 meters per
second squared
this is less than what you feel riding a roller coaster and about half that
experience by a drag racer in fact it's just a bit less than 1.6 g not anywhere
close to what is experienced by fighter pilots so what's the acceleration of a
bullet
well bullets very in mass area and maximum pressure so there's no exact
figure but let's be as generous to Thunder for this we can
stay away from things like high-powered rifles and use a typical handgun will
look at the beretta 92fs a standard-issue US Army pistol it and its
variant the 92 FS are used by many police departments and militaries around
the world the ammo used by both the 92s and the 92fs is 9 x 19 millimeter
Parabellum which has an upward pressure limit of 240 1.3 to $OPERAND megapascals
a diameter of 9.1 millimeters and a massive 7.5 grams so a quick calculation
gives us over 2 million meters per second squared but we're talking about
guns this isn't the whole story
unlike a sudden increase in pressure a bullet is pushed by the continuous
burning of an accelerant our figure is the maximum acceleration experience but
being generous the Thunderfoot we're going to assume that he was being
analogous of the overall acceleration felt by a bullet as it travels down the
barrel to determine the acceleration of a bullet we need both the guns muzzle
velocity and its barrel length the equation is acceleration equals B
squared over 2 s where v is the muzzle velocity and s is the barrel length the
92s and the 92fs both have a muzzle velocity of 381 m/s and a hundred twenty
five-millimeter barrel length the bullets acceleration will therefore be
over 580,000 meters per second squared
this is over 37,000 times greater than the Hyperloop would accelerate in the
event of a tube failure Thunderfoot is off by five orders of magnitude not only
with this scenario be nowhere near bullet being fired from a gun the
acceleration level passengers with experience is not only survivable but
commonly experience with no ill effects whatsoever and that's just in his first
video a short one intended to introduce the series this doesn't bode well
so stay tuned I'm sure libertarianism and i will have more to say about this
series until then as always stay strong and be free
yeah