what is the most optimal cost effective diameter of a hyperloop housing vacuum tube housing hyperloops that can ferry ALL cargo currently travelling by air and sea to and from the US and Europe? maximum 30 tonnes
Let's assume we are talking about transporting shipping containers, a ready unit of trade with well-established industry support via rail and road.
According to Joc.com, EU sold the USA 1.3 million TEU (Twenty-foot Equivalent Units, read: containers) and the USA sold 0.68M TEU back. So we'll use the higher number and add some headroom for growth, let's say to 2M containers per year.
However, trade is not consistent, and unlike ships, you can't just order a bigger one when it suits, so our tunnel will need to be able to accommodate peaks of utilisation, so we'll double up to 4M TUE per year.
Now another issue, this one of our own making: we have in one fell swoop cut the surface transit time from EU to USA from several weeks to just a few hours. There are of course already airfreight routes which can do something similar, but the added potential for trade in fresh goods, or lean manufacturing this new form of transport would open up is hard to fathom. Let's double again to 8M TUE per year. This is our minimum rate.
The original Hyperloop Alpha concept proposed peak rates of 2 pods per minute. We'll assume one pod = one container, in line with your 30T maximum rule. At peak rates then, a single lane could supply (365 days x 24 hours x 60 minutes x 2 TUE) = 1,051,200 TUE per year.
So unfortunately 1 lane just isn't going to cut it; we need 8 lanes per direction for 16 total.
Now, your question asks how big do we make the vacuum tube to fit all of these in, which I believe misses a vital point. The potential for damage should any single pod experience a problem is huge when dealing with 30T travelling at 1000km/hr. With 16 separate pod lanes your chances for an incident rise by about x4. Far better to have them separate from each other. It also allows them to be built one at a time and have a much lower volume evacuated if each individual lane is stand-alone.
So we need 16 tubes, each big enough to accommodate a pod capable of carrying a shipping container. A container is about 2.5m tall and wide, so a rounded pod capable of carrying one internally would need a minimum internal diameter of 3.53m, but we'll add some additional area for the pod walls, to make this around 4m. The original Hyperloop called for a 60% capsule/tube diameter ratio to allow for airflow compression, so the internal diameter of each tube would need to be around 6.7m.
So the answer is 16 separate tubes, each 6.7m in diameter.