The client should have something to predict movements. For instance, it's what is used in all the FPS since Quake times.
On FPS it was used to compensate lag problems.
It's called
Client-side_prediction.
If you don't like reversing then you should try the human way: how that was acquired? how it works?
I don't think putting some random numbers will give you what you want. I'd try something more "mathematical". For instance, maybe starting with
Linear Motion and then going on til you find a real way than magical numbers or timers.
And it's not because I'm a math-freaky or programming-freaky, but I'd say that I like to find out things or get the closest answer to a problem.
(I'd say my favourite part of programming is maths... I can waste more than 10 hours in a row thinking about something and not paying attention to anyone. xD)