Today we have another post on rocket science concepts, thrust to weight ratio! (Yes, I play Kerbal space program, if you haven't already guessed.)
Thrust to weight ratio (let's call it TWR from now on) is a concept in rocketry. It is how much thrust the rocket has to how heavy it is. If you have engines totaling 100 pounds of thrust, and 100 pounds of rocket (Including engines) you will have a earth TWR of 1. That means that at sea level, your rocket will hover, exerting no force upon the ground (aside from the rocket exhaust quickly making a crater), but appearing to rest on it. As the fuel inside your 100 pound rocket burns, your TWR slowly increases, and you begin to rise slowly. Because of the natural logarithm, your rocket will rise faster as it burns fuel. Also, as it rises, there will be slightly less gravity exerting it's force on it, and it will rise faster.
Here's the math:
This formula is more simple, and only requires this to be understood:
is the thrust of the engine, 
the total mass of the craft, and 
is the local gravitational acceleration (usually surface gravity).The unladen mass of a rocket engine is generally very high, since it needs to lift all that fuel. Wikipedia has a nice table on that.
TWR can be calculated for anything, for example, airplanes, machine guns, sci-fi, and video games:
(Note that the math for surface acceleration is definitely not guaranteed for earth rockets)
