Edinburgh-Newcastle is 193.4km (194)

The estimate is around $3-$6 million per km that's between £2-£6 million in GBP.

We could do 2 routes, a coastal route or through the land. If we go through the land it will cost more as we will end up hitting hills. This will increase the cost between 10-15 million dollars per km.

My view would take the coastal route to cut costs, this is only if we are allowed to build around the coast.

The lowest cost would be £388 million and the highest estimate would be 1 billion one hundred and sixty-four.
We would need 2 stations 1 in Edinburgh and 1 in Newcastle for the high-speed rail. We need a price on each capsule to carry as many passengers per hour.
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As you can see with images above the land is hilly in some areas especially at Rothbury and Barrow Burn, you can bypass hill area by going between Rothbury and Great Tosson.
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This is the main hilly area that will put the cost up massively.
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This would be the best route to take to save costs. This will cost between £388 million/ 1 Billion one hundred and sixty-four