I have significant doubts that any oxidizer weight savings from using an air-breathing engine for the first few tens of thousands of feet (before the air gets too thin to support an air-breathing engine) is worth the added complexity. What you are talking about doing results in making a two-stage rocket into a three-stage rocket where the first stage is used for less than a minute.
Not to mention, ramjets and scramjets require some kind of boost to get going in the first place; they are not capable of moving a stationary vehicle as they require supersonic air to be forced through their intakes by the vehicle's motion, adding yet another layer of complexity and taking away from the practicality.
So in the end, you need a rocket boost to get your air-breathing first stage going, then the air-breathing stage has to start up, then it's only good for a brief time before the air gets too thin, at which point it has to be separated or shut down and the actual rocket has to be started, but you're still low and slow enough that you're probably going to still need two more rocket stages.
Technically feasible? Probably. Practical? Unlikely.
Not to mention, ramjets and scramjets require some kind of boost to get going in the first place; they are not capable of moving a stationary vehicle as they require supersonic air to be forced through their intakes by the vehicle's motion, adding yet another layer of complexity and taking away from the practicality.
So in the end, you need a rocket boost to get your air-breathing first stage going, then the air-breathing stage has to start up, then it's only good for a brief time before the air gets too thin, at which point it has to be separated or shut down and the actual rocket has to be started, but you're still low and slow enough that you're probably going to still need two more rocket stages.
Technically feasible? Probably. Practical? Unlikely.
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