# Simple Math and Physics Behind Elon Musk Breakthroughs

Elon Musks Boring company wants to do just three things to get to approximately an order of magnitude improvement, and beyond that.

1. Cut the tunnel diameter by a factor of two or more. So a single road lane tunnel according to regulations has to be 26 feet, maybe 28 feet in diameter to allow for crashes and emergency vehicles and sufficient ventilation for combustion engine cars. But if you shrink that diameter to what we’re attempting, which is 12 feet, which is plenty to get an electric skate through, you drop the diameter by a factor of two and the cross-sectional area by a factor of four, and the tunneling cost scales with the cross-sectional area. So that’s roughly a half-order of magnitude improvement right there.

2. Tunneling machines currently tunnel for half the time, then they stop, and then the rest of the time is putting in reinforcements for the tunnel wall. So if you design the machine instead to do continuous tunneling and reinforcing, that will give you a factor of two improvement. Combine that and that’s a factor of eight.

3. Tunneling machines are far from being at their power or thermal limits, so you can jack up the power to the machine substantially. I think you can get at least a factor of two, maybe a factor of four or five improvement on top of that.

So Elon think there’s a fairly straightforward series of steps to get somewhere in excess of an order of magnitude improvement in the cost per mile.

Elon Musk reduced Tesla factory to a different equation: output = volume x density x velocity.

Need to bring down the cost of batteries? Fill as much of the factory’s volume possible with equipment.
* Instead of using 3% of the volumetric space, Tesla plans to use at least 30% to get more production per unit of space.

Need to produce 500,000 cars per year rather than the 50,000 Tesla has managed so far?
* Speed up the assembly line by a factor of seven from its typical 0.2 meters per second to 1.5 meters per second. Then build factories as a series of mini facilities, each one iterating on the design of the last so incremental improvements can be rolled out to Tesla’s battery, solar panel, and car plants.

The Tesla team believes there are three variables it can control to build a cheaper battery that will outperform its competitors:
1. materials
2. labor
3. factory design.

Every decision at the Gigafactory is intended to maximize at least one of them.

The Gigafactory is being built as a series of mini facilities, each one iterating on the design of the last. Although the first phase of the Gigafactory is not yet complete, construction is already underway on the next (the factory’s exterior walls are removable). The first phase is more than double the capacity of a similar sized factory in Asia, said Yoshihiko Yamada, executive vice president of Panasonic, who was on-site working with Tesla’s engineers. Tesla plans to repeat this process numerous times. Today’s Gigafactory occupies just 14% of the planned area.

The design of the car is difficult to optimize.
Factory improvement can yield an order of magnitude more results.
The usage of cars can be optimized by an order of magnitude by making the sharable and self driving.