A thinner wall costs more energy. Quantum limits require a wall near the Planck length.
Each dot is an amount of energy on a logarithmic scale, so one tick is a factor of 1018. Warp figures are negative energy, shown by size.
It solves Miguel Alcubierre's 1994 spacetime for the tanh-walled bubble in his paper. Energy is integrated numerically across the wall, as measured by observers at rest outside the bubble.
The integrator matches the closed-form result to within 0.001% and a separate volume integral to within 0.002%. Using Pfenning and Ford's stepped wall, the same equations give 6.9 × 1062 kg for their 100 m case, against their published 6.2 × 1062 kg. The tanh wall needs two-thirds of the stepped-wall figure.
The quantum limit is an order-of-magnitude bound. The steering and horizon checks are published qualitative results, applied here as a simple test of whether speed exceeds c. Spin-up and stopping are not modelled.