"[According to the Boring Company FAQ,] The current standard for a one-lane tunnel is approximately 28 feet. By placing vehicles on a stabilized electric skate, the diameter can be reduced to less than 14 feet. Reducing the diameter in half reduces tunneling costs by 3-4 times.
"This claim is contradicted in professional literature. Studies of particle accelerator tunnels as well as rail tunnels that look at different diameters find that reducing the diameter in half reduces costs by a factor of two and not three or four."
That's actually quite surprising. I would have thought that changing the diameter would have no effect whatsoever on the price of boring a tunnel, to a first order of approximation. Almost none of the variables involved are dependent on the diameter of the tunnel.
Musk seems to think that costs for tunneling are proportional to the square of the diameter (i.e., proportional to cross-section). If you assume that the cost is dominated by the amount of spoil you need to excavate, that makes sense. But that's not the domination of the cost.
A tunnel bore is relatively cheap. Musk cites the costs of $1 billion/mi. subways, but that is a very malicious bait-and-switch. The tunneling cost for those subways come out to around $100-150M per track-mile of tunnel, and I suspect that includes the standard tunnel accoutrements: drainage, airflow, lighting, etc. Much of those accoutrements are invariant to the tunnel diameter, to a first approximation.
Tunnel-boring itself has some costs, but most of those don't scale as fast as cross-sectional area. Cutting head replacements and the ultimate spoil disposal are the only things I can think of that do. The TBM itself, and the tunnel shielding are going to scale linearly with circumference. Things like the power systems, spoil recovery, or manpower costs for manning the TBM are going to pretty much be invariant with size (assuming the size is generally the same magnitude).
All totaled, you'd expect the costs to scale somewhere around linearly with diameter/radius.
Well the area of a circular tunnel is proportial to the square of the diameter. Perhaps a lower area allows the bore to tunnel faster? That kinda makes sense, but I have no idea how much the area of a circle relates to tunnel boring in reality, if at all.
The tunnel boring machine would likely cost much more, for a larger tunnel, but it's fixed relative to the length and a capital expenditure, much of which can be recovered or re-used. The amount of material moved would be proportional to the area of the tunnel, but I can't see that as a major cost factor. A larger machine would need more lining material, and more workers...
"[According to the Boring Company FAQ,] The current standard for a one-lane tunnel is approximately 28 feet. By placing vehicles on a stabilized electric skate, the diameter can be reduced to less than 14 feet. Reducing the diameter in half reduces tunneling costs by 3-4 times.
"This claim is contradicted in professional literature. Studies of particle accelerator tunnels as well as rail tunnels that look at different diameters find that reducing the diameter in half reduces costs by a factor of two and not three or four."
That's actually quite surprising. I would have thought that changing the diameter would have no effect whatsoever on the price of boring a tunnel, to a first order of approximation. Almost none of the variables involved are dependent on the diameter of the tunnel.