Using lower stage as reaction mass

Question

As I was thinking about the process of stage separation, I realized the empty stage dropped, often many tons, is usually separated quite gently, moving at sluggish couple of m/s or less away from the upper stage. The immediate thought was "What a waste! Even ejected at moderate speed, so much mass could provide a lot of delta-V!"

Then I began thinking on how this could be done from engineering point of view and besides some totally impractical ideas, came up blank. But c'mon, there are people smarter than me and surely I'm not the first who thought of this.

So - were there any projects (realized or not) to gain extra boost from the process of separation - by ejecting the dropped stage as a reaction mass, with a considerable force?

Answer 1

The additional speed you can gain from this is too small to be of any use. Here is why:

First of all, the stage and payload is not designed to withstand acceleration larger than few g, e.g. 5g. That means, ejection of the first stage must take place over an extended amount of time. Let's assume a time of 1s - at 5 g this gives an additional 50 m/s to the second stage - not too much.

Now, let's see if at least this is feasible: The empty Falcon9 first stage seems to have a mass of about 30 tons, while the full second stage including payload amounts to about 120 tons, four times more. That is, if we want to accelerate our second stage with 5 g, we need to accelerate the first stage at 20 g - much more than it is built to withstand.

Additionally, during our second of acceleration the distance between both stages increases to 125 meters - and we need to keep a mechanical connection between both, e.g. with a spring that is able to withstand the immense force needed for acceleration.

At the same time, all masses involved in this need to weigh less than one ton - that's about the amount of fuel we can save. The conclusion can only be that it is rather impossible to make use of the first stage or any other large part of the vehicle as reaction mass. Ejecting burned fuel on the other hand works very well as we can use comparably tiny amounts at a time and accelerate it to high speed.

Answer 2

The fuel-efficiency of a rocket (the delta-V you get from a given amount of fuel) is directly proportional to the speed that you give to the reaction mass when you eject it. It's true that you've got a lot of mass there, but I suspect that the fuel needed to eject it could be better used to accelerate its own exhaust gases to a much higher speed (almost 4.5km/sec for hydrogen-burning engines, for example), providing maybe a couple of extra seconds of thrust from the main engines, than by accelerating that much larger mass to a much smaller speed.

So if we imagine you've got a 30-ton empty stage and you can push it away at 5m/s (as others have commented, you don't have long to push, and you don't want to jolt your ship too hard), that would give roughly the same impulse as pushing 30kg of rocket exhaust away at 5km/s. So if the mass of the ejection fuel, plus the mass of whatever mechanism actually does the pushing (pistons?) comes to more than 30kg, it's a losing proposition.