Perhaps we should have read it as an omen that the MagSafe 2 adapter for older, original MagSafe connectors was listed as discontinued on the Apple Store in the U.S. and Canada last week. It’s back in stock this week, but MagSafe’s future in new Mac laptops is uncertain with the revelation of the single-port MacBook. With just a USB-C connection for power, data, and display, MagSafe may be on its way to sing with the choir invisible.
That’s a shame because Apple has retrained people of all ages, and perhaps some animals, to not worry about Mac laptop power cables. Go ahead! Stand on it, trip over it, yank it—the force of the smallest effort pulls it free.
…the surface area of two magnetically attracted halves determines the number of magnetic flux lines and therefore the holding force between them because the holding force is proportional to the contact area between the two magnetically attracted halves…
What they said.
A USB Type C (or USB-C) cable has no such advantage. It has two distinct differences: first, a USB-C male end, such as the tip of a cable, is plugged into a port, very much like larger and deeper Type A and Type B USB connections.
Second, while MagSafe was optimized to help with “non-axial” force—any direction except straight out—the USB-C style plug and jack suffer the worst from that. As astrophysicist Katie Mack said, “The genius of the MagSafe connector is that if you apply a force in any other direction it breaks the magnetic seal very easily, and then there’s virtually no force required to remove the connector entirely.”
But how likely is a cord-tripper to yank a new MacBook off a surface versus the USB-C cable coming out first? My calculations, vetted by Mack and a variety of engineers, show it’s almost certain the MacBook will move a bit or a lot unless all your stars perfectly align.
Hold on! Some math’s coming, but it’s worth it.
There’s a disturbance in the force
The USB Implementors Forum specifies precisely how much force should be required to pull a USB-C cable free, measured in newtons (N), which is the force required to accelerate one kilogram (kg) of mass at 1 meter per second squared (1m/s2). Because an object under acceleration continuously increases its velocity, an object travelling at rest that is moved at 1m/s2 traverses 0.5m (1.6 feet) in the first second, 2m by the second second, and 4.5m by the third second.
The USB group says a fresh connector should require 8N to 20N of extraction force. After 10,000 connection cycles, no fewer than 6N should be required. (To compare with something you’re already familiar with, USB Type A connectors sold as parts typically note a minimum 10N force for extraction.)
The MacBook exerts a pull of its own, just sitting there. We start with its mass, 2.03 lbs (0.92 kg), which would require a force of about 0.9N to accelerate it to 1m/s2. But we also have gravity in our world, and a so-called normal force must be calculated. Let’s assume the MacBook is on a level surface. The earth exerts a pull of roughly 10m/s2 at the surface. We multiply that by 0.92 kg to get our force in newtons, or approximately 9N. (Aerospace engineer Bradley Grzesiak cautioned me to avoid too many decimal places: earth’s gravity varies enough around the globe.)
But we have to factor in friction. Assume the rubber-footed MacBook—it has four feet, just like a MacBook Air—is on a wood table. A standard friction coefficient for rubber on wood, the closest comparison I could find, is 0.70 for static friction (sometimes called stiction), or friction at a standstill. Dr. Drang—the nom de Internet of a consulting engineer who writes exceedingly clever things about science, software, and engineering—suggested via email that 0.70 is optimistic for many surfaces, and 0.40 more reasonable.
Now we multiply the coefficient of 0.70 to get roughly 6N, or 0.40 to get about 4N. If the laptop is on a slick metal or glass table, the coefficient could be 0.20, or 2N or so. Consider gravity: this range of 2N to 6N is about 20 to 60 percent of one earth gravity. Not so much!
However, Grzesiak pointed me to a 1942 National Bureau of Standards (now NIST) testing report on rubber (see above) that looked with more detail into the initial point of overcoming static friction at various rates of initial acceleration. The higher the acceleration from zero velocity, the larger the coefficient.
A jerk from a cable could accelerate a laptop so rapidly that the initial coefficient factor of rubber on a glass table could be as high as 5—meaning you’d need force on the order of five earth gravities (50N) to get the MacBook moving. But recall that force involves mass and acceleration: an abrupt yank by a heavy weight (like a human’s leg intersecting with a cable) could briefly produce force on that order of magnitude!
After the laptop has overcome static friction, kinetic friction comes into play, dramatically reducing the force necessary to keep it in motion and accelerate it further.
A smashing good outcome
We have a lot of idealized and estimated starting conditions, so we can perform our thought experiments now. (I asked Apple for input, but didn’t hear back.)
Let’s take the case in which someone performs the most perfect pratfall such that the direction of force is absolutely and perfectly opposite the USB-C jack, so that there is no shear in any other orientation that we need to consider.
In that scenario, we know you need to apply an initial force of between 2N and 50N depending on materials and assumptions to cause the MacBook to reach an acceleration rate of the magical 1m/s2, but then less force thereafter. Since we need to pull at 8N to 20N to remove the connector, this is clearly ambiguous. Will the plug have pulled out of the jack by the time static friction has been overcome?
And there’s a wrinkle. If you accelerate faster, you exercise greater force. That is, take 1 kilogram to 2m/s2, and the force is 2N. Thus, take the action noted above of someone’s leg intersecting with the cable, and assume the mass of the leg involved in the force is 10kg. That’s a tenfold multiplier against any acceleration produced.
The cable’s tip and socket are supposed to measure just 6mm. Assuming the USB extraction force’s upper end, 20N, is the static friction and 8N is the kinetic friction, it’s possible that the cable pops free in a fraction of a second before the laptop moves much, if at all.
Dr. Drang explained to me further:
What happens to the MacBook when you pull on the cable has less to do with the force you apply than the rapidity with which you apply it. If you pull on the cable with constant speed, or with any acceleration less than 4.8 m/s2, the connector will never come out, and you’ll dump the MacBook on the floor. If you pull on the cable with an acceleration greater than 17.8 m/s2, the connector will come out and you’ll heave a sigh of relief.
Because the USB Implementors Forum describes a wide range in the spec, until and if Apple’s specific USB-C adapter is tested across multiple computers for extraction force, it’s impossible to know the necessary acceleration.
Let’s also look at cases with shear, where the cord is tripped over or yanked at any angle or orientation. Mack noted, “Pulling out the cable cleanly would be very difficult to do by accident. If you’re pulling at any angle other than straight on, it’s quite difficult, as the force is now directed in a direction that would increase friction a lot.”
Dr. Drang and Mack both said that if the laptop was free enough to be dragged off a surface, that shear could be reduced by the laptop rotating first to a less oblique horizontal angle. However, there’s still the matter of the angle from the MacBook to the point on the cable where force is being applied. That’s likely vertical, a drop from the plug’s slot to the floor where someone’s foot or leg catches on the cable.
Greg Koenig, an industrial designer in Portland, Oregon, and a principal at Luma Labs, examined Apple’s logic board images and other photos of the MacBook at my request. He noted that the USB-C female connector isn’t part of the main logic board, unlike connectors on previous MacBooks. This isolates damage, if any were to occur.
Koenig says the port’s design doesn’t expose any portion of the sheet metal beyond the aluminum case. With enough oblique force, the cable’s metal head will be pinioned against the MacBook’s frame, not putting stress directly on the port. If the laptop is loose on a surface, pulling obliquely on the cable will almost certainly bring the laptop with it more reliably than in our “perfectly straight-out” thought experiment.
However, if the laptop is secured in some fashion—even if you’re holding it tightly in your hands—the cable’s male plug end is probably the weak point, and it would be torn off, said Koenig, leaving its shell in the USB-C port, potentially without causing any harm to the MacBook. The metal shell could then be removed carefully.
Trip the lightweight fantastic
At some level, I’m trying to reverse engineer Apple’s thinking around design and testing, both in its larger engineering participation in shaping USB-C, and in its particular implementation. All the calculations and exercises above have certainly been performed a thousand times in simulation and prototyping internally, shaping the development of the socket, logic board, external cables, and more.
In the end, it’s not really enough. Mac laptops are going to go crashing to the ground in vastly greater quantities than they have over the last several years. I’ve heard it said since Monday morning that MagSafe was the single best hardware feature Apple invented for its laptops, and I’m hard pressed to deny that—although extra-long battery life is nice, too.
Clearly, MagSafe was better and experts agree. I recommend retraining your toddlers now.
(Thanks also to Ramez Naam for schooling me in some of the physics and spitballing ideas.)
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