Ballistic Bridges

Over the last couple weeks, Marika and I were on a road-trip to Florida for a little relaxation between jobs. Along the way, we crossed several drawbridges, and Marika wondered (theoretically, I hope): How fast do you need to drive to jump an open drawbridge?

To be clear, this is the type of bridge I'm talking about:

via Wikipedia

It turns out, everywhere except the US, this is called a bascule bridge, while the term drawbridge is reserved for the medieval type.

If we assume the car leaves the bridge with a certain angle and velocity, and we ignore air resistance, we can use the equations for ballistic motion:

where g is the acceleration due to gravity, and vx, vy are the x- and y-components of velocity. We don't really care about the time, so we can combine these by setting up some coordinates:

The equation for the path becomes

The minimum velocity then is

Of course, this is just the velocity we leave the ramp with. As the tilt increases, it's harder to climb the bridge, so we need additional velocity:

To get an idea of how fast this actually is, we can take some numbers from one of the most famous bascule bridges, Tower Bridge in London:

At 45°, the total speed required is around 80 mph, which may not be out of reach of our little Ford Focus, but I haven't accounted for air resistance, or the rotation of the car as it moves through the air. Maybe if the University of Florida accepts my postdoc application we can get some experimental data!