section_path: Physics/Acceleration and thrust-to-weight ratio
section_name: Acceleration and thrust-to-weight ratio
paragraph_text: Acceleration and thrust-to-weight ratio
  
  From Newton's second law, the acceleration, a {\displaystyle a}, of a vehicle is simply:
  
  where m is the instantaneous mass of the vehicle and F n {\displaystyle F_{n}} is the net force acting on the rocket (mostly thrust, but air drag and other forces can play a part).
  
  As the remaining propellant decreases, rocket vehicles become lighter and their acceleration tends to increase until the propellant is exhausted. This means that much of the speed change occurs towards the end of the burn when the vehicle is much lighter. However, the thrust can be throttled to offset or vary this if needed. Discontinuities in acceleration also occur when stages burn out, often starting at a lower acceleration with each new stage firing.
  
  Peak accelerations can be increased by designing the vehicle with a reduced mass, usually achieved by a reduction in the fuel load and tankage and associated structures, but obviously this reduces range, delta-v and burn time. Still, for some applications that rockets are used for, a high peak acceleration applied for just a short time is highly desirable.
  
  The minimal mass of vehicle consists of a rocket engine with minimal fuel and structure to carry it. In that case the thrust-to-weight ratio of the rocket engine limits the maximum acceleration that can be designed. It turns out that rocket engines generally have truly excellent thrust to weight ratios (137 for the NK-33 engine; some solid rockets are over 1000), and nearly all really high-g vehicles employ or have employed rockets.
  
  The high accelerations that rockets naturally possess means that rocket vehicles are often capable of vertical takeoff, and in some cases, with suitable guidance and control of the engines, also vertical landing. For these operations to be done it is necessary for a vehicle's engines to provide more than the local gravitational acceleration.