Re: Does exhaust hitting the ground help a rocket take off?

To some extent, the student is indirectly correct. [added by MadSci Admin: I teach, also, and I would not give credit to the student's answer even though, as you will read below, some small launching force may occur when the rocket is very close to the ground. But to launch it into space? No, no credit!]

When a rocket is on the launch pad, the rocket exhaust is directed into a fire pit beneath the launch pad. The pressure will build in the fire pit as the hot gases of the exhaust fill it. Most of that pressure and the hot gases are transmitted away from the launch pad via a trench leading out the side of the launch pad. However, there is an opening at the top of the launch pad for the rocket nozzles. Pressure can be transmitted up through the opening(s) to the rocket. Because there is a pressure pushing upwards, the pressure from the exhaust interacting with the ground does provide a measurable additional boost while the rocket is very close to the ground. The pressure rapidly drops once the rocket leaves the launch pad and is probably very near zero by the time it reaches an altitude of a few meters.

How much additional force could the pressure produce?

The Saturn V is the most powerful US rocket ever launched. It is 10.1 meters in diameter at the base of the first stage. If the geometry is grossly simplified to a simple cylinder, the surface area of the base of the rocket would be about 80 square meters. I cannot find the pressure in the fire pit, but an overpressure wave of 7 kN/m^2 (1 psi) will snap off a telephone pole, so I will use that as an upper limit because we know the rocket is not damaged by the pressure. Such a pressure wave would exert a total force of 5,500 kN on the bottom of the simplified rocket. In comparison, the five F-1 engines develop a total force of 33,400 kN at sea level. Therefore the pressure that would not damage the rocket is less than 7 N/m^2 (about 1 psi) which would generate a force equal to less than 1.5% of the rocket engine thrust.

So the exhaust striking the ground does not directly add a force to the rocket to propel it, but the pressure the exhaust generates beneath the rocket through its interactions with the ground and launch pad structure can produce additional upwards forces at the time of launch. Once the rocket leaves the launch pad and that pressure is no longer generated, the additional forces are no longer acting on the rocket.