The fastest Travel from A to B
Travelling with normal distributed velocity?
Differentiation gives the acceleration curve?
Integration of the velocity bell curve gives the total distance?
from -T/2 to T/2 integrate vmaxe^-(4t/T)^2
brings us in time T along a distance of the integral by reaching a peak velocity of v in the middle of the distance.
from -144 to 144 integrate 75*e^-(t/72)^2 dt
for example brings us in 288 seconds along a distance of the integral about 10 km by reaching a peak velocity of 75 m/s = 270 km/h in the middle of the distance.
What now must be the highest velocity vmax for travelling a given distance in a distinct time?
What is the peak acceleration for this travel and which acceleration is bearable for all humans?
In a tube with diameter 18 y we could pack 2 to 7 tubes with 6 m diameter, which can be used for the railway and or other purposes. At least the middle tube could be used as emergency access and shelter.