May 30, 2024

During Tesla’s Cybertruck reveal on 23rd November 2019, the truck’s windows failed Elon on an on stage live smash test. Here’s what I think might have gone wrong.

Last week, Elon Musk unveiled the long awaited Tesla’s electric pickup truck. This Cybertruck’s event is one of the few pieces of technology in 2019 that didn’t leak, which to me is pretty impressive. But Tesla is pretty good at building suspense and excitement and the shattering all expectations with the release of their completely unforeseen awesome piece of design and tech.

With a futuristic stainless steel exoskeleton, Tesla’s massive Cybertruck has rendered fans and critics polarized: either they completely hate it or love it. I belong to the later; I love the elegant futuristic Batmobile-DeLorian simple design and think that people who think the contrary are a bunch of idiots. The truck’s sharply angled body and an overall wedge shape has been an approach to futuristic, sci-fi and aerodynamic design. What’s most impressive about this truck is its specs: starting at $39,900 grand for a single motor rear – drive with adaptive suspension achieving 0-60 in 6.5 seconds and a triple motor all in -wheel drive option at $69,900 achieving 0-60 in less than 2.9 seconds. Additionally, it has a 500 plus mile range and a 14,000 lb towing capacity.

The recent unveiling was one of the most showy events Elon and his team have ever done. There were lazers, fire, props and a lot of excited Tesla gearheads. In case you weren’t present at the event or didn’t see the launch demo video on YouTube, Elon wanted to demonstrate the strength and ruggedness. Elon called Tesla’s chief designer Franz von Holzhausen and asked him to hit a normal truck door with a sledge hammer. Obviously, it made a dent. But when he banged the hammer on the Tesla Cybertruck door … Not a scratch!! This showed that Tesla’s Cybertruck is the perfect car if you are being chased by people with sledgehammers.

That was the impervious steel exoskeleton but what about the windows? Musk claimed that the windows are made with Tesla’s new armored glass. To test this glass, a steel ball was dropped on a regular car glass and it cracked from a height of around 1 meter. The same ball was dropped onto the Tesla Armored Glass from about 3 meters and the ball bounced off. Then the ball was dropped from a higher height and still no crack. So Elon invited Franz again to throw the ball on the glass of the Cybertruck at display. Franz threw the ball and the window smashed. Awkward. “Well maybe that was a little too hard”, said Elon to Franz and so he threw the ball softly at the rear passenger window. The glass again cracked. More awkward.

Musk broke the awkward moment by commenting, “at least it didn’t go through.” And then the rest of the presentation was carried out in front of a broken windowed Cybertruck. I admire Elon Musk’s confidence and cool.

So I thought to use physics and solve the mystery of the broken glass fiasco.

Classifying the Collision

The main difference between the dropping of the ball and the throwing of the ball is the difference in impulse (change in momentum) of the steel ball on the glass on collision. This impact can be evaluated by either calculating momentum (p = mv) or kinetic energy (K = 1/2 mv2). For analyzing this broken glass fiasco, I am going to use momentum.

Momentum of Drop

Momentum is defined as a mass in motion and is the product of an object’s mass and velocity. So to calculate the momentum of the ball right before collision, we need to know the mass of the ball and it’s velocity right before the collision. Tesla wasn’t that helpful in releasing the specs of the ball and the height of drop they used to test.

So first let’s calculate the mass.

After a lot of research, I found that the most common steel ball used for durability and shattering tests is a # inch diameter chrome steel ball which weighs 1804.7 g. But for making the calculations easier, I will consider the weight of the ball as 1.8 Kg.

Now we need to calculate the velocity.

The balls from a height of about 3 meters with initial velocity 0 m/s. As the ball was dropped, the acceleration of the ball is only dependent on the gravity, g = 9.8 m/s2 and due to the small height the effect of air resistance is negligible. So to calculate the speed we can use the formula

v2 = u2 + 2as

where v is the velocity of the ball before collision, u is the initial velocity, a is the acceleration due to gravity and s is the displacement. Substituting all the values:

v2 = 2*9.8*3 = 58.8

v = 7.6681158051 m/s

The velocity of the steel ball before collision is around 7.67 m/s.

Now we have the mass and the velocity, so the momentum is

p = mv

p = 1.8*7.67

p = 13.8 kg m/s

Momentum of Throw

To calculate the momentum of the throw, we need to take into consideration few assumptions.

  • The speed of the ball increases with constant acceleration.
  • Franz moved the ball from rest to final speed v for a distance roughly about a meter.
  • Looking at the slow mo video released by Elon Musk which assuming was shot at 240 frames per second and it is played at 24 fps, the video is playing 10 times slower than real time.
  • Excluding the wind up time when measuring the time of throw by Franz.

So calculating the time: In the slow mo (shown below) it almost takes 3 seconds for Franz to throw the ball. So in real time it would have taken him less than 0.3 seconds.

So to calculate the speed we need to equate average velocity with change in distance over time:

(u + v) / 2 = x / t

v = (2x / t) – u

where v is the final speed, u is the initial speed (0 m/s), x is the change in distance (1 m) and t is the time (0.3 s)

v = 2 / 0.3 = 6.67 m/s

Therefore the momentum is:

p = 1.8*6.67

K = 12 kg m/s

The momentum of the ball thrown is almost the same as the ball dropped. So theoretically, the ball shouldn’t have broken the window.

Why the window broke?

The window still broke, so what went wrong? That day, Musk provided an explanation on the broken glass fiasco on twitter:

This explanation seems completely plausible as shown by a backstage slow motion video Elon tweeted showing Franz throwing the ball at the glass and the ball bouncing off. But I think there is also a different reason for the glass cracking up which has to do with its mounting and impulse.

Imagine throwing an egg on the curtains and on a wall. On contact the egg will break when it collides with the wall and no the curtains. This is because the curtain moves for a greater distance with the egg increasing the contact time and so decreasing the force excreted as when impulse is constant, force and time are inversely proportional:

I = p f – pi = Ft

This is what happened with the window. In both the cases of the trick window and the freely mounted window, the change in momentum is the same 12 kg m/s and 13.8 kg m/s respectively. The difference is that the truck window is firmly mounted whereas the glass on which the ball was dropped was just kept on a stand, giving the window room to move. So when the ball collided with the truck window, it displaced very little (like the wall) – stopping distance was shorter – and so the contact time was less and force was more. The freely mounted glass displayed more when the ball collided – stopping distance was larger – and so the contact time was more and hence the force was less. So more the distance the glass moves, less the force and less the probability of the window breaking.

How should Elon and his team at Tesla fix this problem: They could add tiny shock absorbers or springs on the truck armored glass window to decrease the force experience. But I guess it would spoil the look.

Anyways, I loved the Tesla Cybertruck. It’s one of the most rugged pick up truck on market and has specs similar to a sports car and looks amazing.

Sources

  • Drop height data: Chappell, Bill. “Elon Musk Unveils Tesla’s Cybertruck, With A Polarizing Wedge Shape.” NPR, NPR, 22 Nov. 2019, www.npr.org/2019/11/22/782052992/elon-musk-unveils-teslas-cybertruck-with-a-polarizing-wedge-shape.
  • Steel ball weight data: Media, Axia. “3 Inch Diameter Grade 100 Hardened 52100 Chrome Steel Balls.” 3 Inch Diameter Grade 100 Hardened 52100 Chrome Steel Balls 52100 Chrome Steel Balls – Bearing King, www.bearing-king.co.uk/bearing/3-inch-grade-100-52100-chrome-steel-balls/17261.

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