It's the same with jet engines, for similar reasons. (Although in practice your maximum speed is largely dictated by "melting the engine is considered shortsigh

It's the same with jet engines, for similar reasons. (Although in practice your maximum speed is largely dictated by "melting the engine is considered shortsighted".) The theoretical upper-bound exhaust velocity of a Bussard ramjet is something like ~0.12c, assuming you start with 4 hydrogen and end with 1 helium. As such, the theoretical upper-bound speed limit relative to the interstellar medium of a Bussard ramjet is also ~0.12c. In actuality, it will be quite a bit lower, as quite a lot of the energy is carried off in the form of energetic photons and neutrinos. Personally? A Bussard ramjet will never work, even assuming we get the scoop part figured out. The lower bound on how fast it has to go before it can start working and the upper bound on how fast it can go are too close. Not to mention the Lawson criterion for hydrogen burning (4xH -> He), or, alternatively, the problem of containment of the catalyst and the beta-decay steps of the CNO cycle.