Not sure what your theory is going to say, but the problem you're going to run into - and have done so, in fact, with the example given - is that takeoff and landing are radically different configurations, and the rules for setting speeds associated with the speeds are also different as they address different considerations, and those two speeds don't even address the same factors. Any aircraft with a very "clean" takeoff configuration will need correspondingly high takeoff speeds, including Vr. The same aircraft in a very dirty highest-lift configuration could have very low landing speeds. In fact, since you can do all kinds of configuration changes, they are almost two different aircraft, in some ways.
i am wondering, from some clues in what you've said, if there is a constraint in your question that you've left unspoken? Are you asking about the case where both the takeoff and landing performance is equally limited by available runway length? (Almost certainly at different weights for almost any aircraft...)
Last edited by Mad (Flt) Scientist; 2nd Nov 2018 at 03:03.