Look I don't have a formula fetish like you and Victor. All I asked Victor to do was plug .9997c + .9997c and see if his formula got .99999995 c as I said he would get. If you want me to expose you my formula its
w= (u+v)/(1+uv) where w is the combined velocity of u and v approaching each other.
It's not as long as your formula but it will do the job although you two probably won't get off on it.
PS. Victor has no idea his formula is for combining Y's. I don't think he understands the difference between Y and v and obviously neither do you.
Yes, the relativistic velocity addition formula that you posted, is the correct one for adding velocities where either one, or the sum approach a significant fraction of the speed of light.
In fact, it is the correct formula for adding any two velocities lying along the same straight line, regardless of whether they are in the relativistic range or not. It is just that slow velocities can be summed according to Galilean relativity, u = v + u’ and the resulting approximate answer obtained is close enough for most applications.
The equation that Victor presented in post #71 is an esoteric one; used to combine the gamma factors for combined relativistic velocities where there is a rotation involved. As the Wiki page explains “this is related to the phenomenon of Thomas precession” and so is only tangentially related to the question raised in this thread about relativistic velocity addition. Posting it here is just a smokescreen, in my opinion.
Well, its back to sea for me