Hyperloop: Height difference

The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. The Hyperloop will need to change elevation as the pod travels. Imagine you are designing a tunnel for the Hyperloop that has to drop in elevation by some height $h$ over a horizontal distance of a kilometer. In other words the tunnel will be horizontal at $x=0~\mbox{m}$ and at height $h$ , then begin to drop in elevation until $x=1000~\mbox{m}$ , at which point the tunnel is horizontal again but at height $0$ .

You decide to make the shape of the tunnel a cubic spline. One thing you need to ensure for safety is that the pod always remains on the bottom of the tunnel supported by the air cushion - smashing into the ceiling of the tunnel is not a good thing. What is the maximum value of $h$ in meters that can be safely accommodated by such a tunnel?

• The pod travels at a constant $300~\mbox{m/s}$ through the tunnel.
• Model the pod as a point mass.
• In the Hyperloop design there is very little space between the pod and the tunnel.
• The acceleration of gravity is $-9.8~\mbox{m/s}^2$ .