Terminal velocity no relation volume
ρ
      
    
    {\displaystyle \rho }
   is the density of the fluid through which the object is falling, andA
      
    
    {\displaystyle A}
   is the projected area of the object.In reality, an object approaches its terminal speed asymptotically.
Buoyancy effects, due to the upward force on the object by the surrounding fluid, can be taken into account using Archimedes' principle: the mass 
  
    
      
        m
      
    
    {\displaystyle m}
   has to be reduced by the displaced fluid mass 
  
    
      
        ρ
        V
      
    
    {\displaystyle \rho V}
  , with 
  
    
      
        V
      
    
    {\displaystyle V}
   the volume of the object. So instead of 
  
    
      
        m
      
    
    {\displaystyle m}
   use the reduced mass 
  
    
      
        
          m
          
            r
          
        
        =
        m
        −
        ρ
        V
      
    
    {\displaystyle m_{r}=m-\rho V}
   in this and subsequent formulas.
The terminal speed of an object changes due to the properties of the fluid, the mass of the object and its projected cross-sectional surface area.
Air density increases with decreasing altitude, at about 1% per 80 metres (260 ft) (see barometric formula). For objects falling through the atmosphere, for every 160 metres (520 ft) of fall, the terminal speed decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal speed.ρ
      
    
    {\displaystyle \rho }
   is the density of the fluid,ρ
          
            s
          
        
      
    
    {\displaystyle \rho _{s}}
   is the density of the object,V
      
    
    {\displaystyle V}
   is the characteristic velocity (taken as terminal velocity, 
  
    
      
        
          V
          
            t
          
        
      
    
    {\displaystyle V_{t}}
  ).Substitution of equations (2–4) in equation (1) and solving for terminal velocity, 
  
    
      
        
          V
          
            t
          
        
      
    
    {\displaystyle V_{t}}
   to yield the following expression
no relation