Alignment, obstacles, centrifugal forces

Alignment on a normal pipeline is controlled by the forces acting against pipe direction changes (water wants to continue moving straight compared to the curved alignment).

For a high-speed system, the limiting factor is centripetal force, measured as the square of the velocity divided by the radius of curvature.

If we are to maintain a maximum centripetal force of 9.8 m/s^2 (1 g), at full speed (900 m/s), the required radius will be 900*900/9.8 = 82,653 meters, or 51 miles.

If the pipeline is laid in 20-foot lengths, the allowable deflection per pipe joint is arctan(20 ft/51 miles), or 0.004 degrees. Obviously, that kind of precision can't be laid, especially under field conditions. Therefore, there must be some allowable deflection within the carrier pipe itself.

With a 1-meter diameter material canister, inside a 1.5 m carrier pipe, let's assume that there is an allowable 0.1 m of allowable movement within the pipe. For a 5-meter long canister, a 0.1 m deflection allows for a "forgiveness angle" of arctan(0.1/5), or 1.14%. That kind of accuracy is more than manageable --- sanitary sewers are normally laid with a precision of +/- 0.1%.

That leaves us back to an average allowable deflection of 0.004 degrees, with some short-term "wiggle room". Over a 20-mile linear stretch, a curvature of up to 1 mile can be achieved. Therefore, major obstacles can be avoided with proper alignment.

Since velocities need to be fairly constant, sudden changes in altitude will require power input, and should therefore be avoided. Microtunneling technology should be applied wherever possible through elevation changes, rather than going up and down terrain changes.

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