Zero-lift drag coefficient
In aerodynamics, the zero-lift drag coefficient 
  
    
      
        
          C
          
            D
            ,
            0
          
        
      
    
    {\displaystyle C_{D,0}}
   is a dimensionless parameter which relates an aircraft's zero-lift drag force to its size, speed, and flying altitude. Mathematically, zero-lift drag coefficient is defined as 
  
    
      
        
          C
          
            D
            ,
            0
          
        
        =
        
          C
          
            D
          
        
        −
        
          C
          
            D
            ,
            i
          
        
      
    
    {\displaystyle C_{D,0}=C_{D}-C_{D,i}}
  , where 
  
    
      
        
          C
          
            D
          
        
      
    
    {\displaystyle C_{D}}
   is the total drag coefficient for a given power, speed, and altitude, and 
  
    
      
        
          C
          
            D
            ,
            i
          
        
      
    
    {\displaystyle C_{D,i}}
   is the lift-induced drag coefficient at the same conditions. Thus, zero-lift drag coefficient is reflective of parasitic drag which makes it very useful in understanding how "clean" or streamlined an aircraft's aerodynamics are. For example, a Sopwith Camel biplane of World War I which had many wires and bracing struts as well as fixed landing gear, had a zero-lift drag coefficient of approximately 0.0378. Compare a 
  
    
      
        
          C
          
            D
            ,
            0
          
        
      
    
    {\displaystyle C_{D,0}}
   value of 0.0161 for the streamlined P-51 Mustang of World War II which compares very favorably even with the best modern aircraft.
In aerodynamics, the zero-lift drag coefficient 
  
    
      
        
          C
          
            D
            ,
            0
          
        
      
    
    {\displaystyle C_{D,0}}
   is a dimensionless parameter which relates an aircraft's zero-lift drag force to its size, speed, and flying altitude.
Mathematically, zero-lift drag coefficient is defined as 
  
    
      
        
          C
          
            D
            ,
            0
          
        
        =
        
          C
          
            D
          
        
        −
        
          C
          
            D
            ,
            i
          
        
      
    
    {\displaystyle C_{D,0}=C_{D}-C_{D,i}}
  , where 
  
    
      
        
          C
          
            D
          
        
      
    
    {\displaystyle C_{D}}
   is the total drag coefficient for a given power, speed, and altitude, and 
  
    
      
        
          C
          
            D
            ,
            i
          
        
      
    
    {\displaystyle C_{D,i}}
   is the lift-induced drag coefficient at the same conditions. Thus, zero-lift drag coefficient is reflective of parasitic drag which makes it very useful in understanding how "clean" or streamlined an aircraft's aerodynamics are. For example, a Sopwith Camel biplane of World War I which had many wires and bracing struts as well as fixed landing gear, had a zero-lift drag coefficient of approximately 0.0378.  Compare a 
  
    
      
        
          C
          
            D
            ,
            0
          
        
      
    
    {\displaystyle C_{D,0}}
   value of 0.0161 for the streamlined P-51 Mustang of World War II which compares very favorably even with the best modern aircraft.
The drag at zero-lift can be more easily conceptualized as the drag area (
  
    
      
        f
      
    
    {\displaystyle f}
  ) which is simply the product of zero-lift drag coefficient and aircraft's wing area (
  
    
      
        
          C
          
            D
            ,
            0
          
        
        ×
        S
      
    
    {\displaystyle C_{D,0}\times S}
   where 
  
    
      
        S
      
    
    {\displaystyle S}
   is the wing area). Parasitic drag experienced by an aircraft with a given drag area is approximately equal to the drag of a flat square disk with the same area which is held perpendicular to the direction of flight. The Sopwith Camel has a drag area of 8.73 sq ft (0.811 m2), compared to 3.80 sq ft (0.353 m2) for the P-51 Mustang. Both aircraft have a similar wing area, again reflecting the Mustang's superior aerodynamics in spite of much larger size. In another comparison with the Camel, a very large but streamlined aircraft such as the Lockheed Constellation has a considerably smaller zero-lift drag coefficient (0.0211 vs. 0.0378) in spite of having a much larger drag area (34.82 ft2 vs. 8.73 ft2).
Furthermore, an aircraft's maximum speed is proportional to the cube root of the ratio of power to drag area, that is:

  
    
      
        
          V
          
            m
            a
            x
          
        
         
        ∝
         
        
          
            
              p
              o
              w
              e
              r
              
                /
              
              f
            
            
              3
            
          
        
      
    
    {\displaystyle V_{max}\ \propto \ {\sqrt[{3}]{power/f}}}
  .

Estimating zero-lift drag
As noted earlier, 
  
    
      
        
          C
          
            D
            ,
            0
          
        
        =
        
          C
          
            D
          
        
        −
        
          C
          
            D
            ,
            i
          
        
      
    
    {\displaystyle C_{D,0}=C_{D}-C_{D,i}}
  .
The total drag coefficient can be estimated as:

  
    
      
        
          C
          
            D
          
        
        =
        
          
            
              550
              η
              P
            
            
              
                
                  1
                  2
                
              
              
                ρ
                
                  0
                
              
              [
              σ
              S
              (
              1.47
              V
              
                )
                
                  3
                
              
              ]
            
          
        
      
    
    {\displaystyle C_{D}={\frac {550\eta P}{{\frac {1}{2}}\rho _{0}[\sigma S(1.47V)^{3}]}}}
  ,where 
  
    
      
        η
      
    
    {\displaystyle \eta }
   is the propulsive efficiency, P is engine power in horsepower, 
  
    
      
        
          ρ
          
            0
          
        
      
    
    {\displaystyle \rho _{0}}
   sea-level air density in slugs/cubic foot, 
  
    
      
        σ
      
    
    {\displaystyle \sigma }
   is the atmospheric density ratio for an altitude other than sea level, S is the aircraft's wing area in square feet, and V is the aircraft's speed in miles per hour. Substituting 0.002378 for 
  
    
      
        
          ρ
          
            0
          
        
      
    
    {\displaystyle \rho _{0}}
  , the equation is simplified to:

  
    
      
        
          C
          
            D
          
        
        =
        1.456
        ×
        
          10
          
            5
          
        
        (
        
          
            
              η
              P
            
            
              σ
              S
              
                V
                
                  3
                
              
            
          
        
        )
      
    
    {\displaystyle C_{D}=1.456\times 10^{5}({\frac {\eta P}{\sigma SV^{3}}})}
  .The induced drag coefficient can be estimated as:

  
    
      
        
          C
          
            D
            ,
            i
          
        
        =
        
          
            
              C
              
                L
              
              
                2
              
            
            
              π
              A
              
              
              
                R
              
              ϵ
            
          
        
      
    
    {\displaystyle C_{D,i}={\frac {C_{L}^{2}}{\pi A\!\!{\text{R}}\epsilon }}}
  ,where 
  
    
      
        
          C
          
            L
          
        
      
    
    {\displaystyle C_{L}}
   is the lift coefficient, AR is the aspect ratio, and 
  
    
      
        ϵ
      
    
    {\displaystyle \epsilon }
   is the aircraft's efficiency factor.
Substituting for 
  
    
      
        
          C
          
            L
          
        
      
    
    {\displaystyle C_{L}}
   gives:

  
    
      
        
          C
          
            D
            ,
            i
          
        
        =
        
          
            
              4.822
              ×
              
                10
                
                  4
                
              
            
            
              A
              
              
              
                R
              
              ϵ
              
                σ
                
                  2
                
              
              
                V
                
                  4
                
              
            
          
        
        (
        W
        
          /
        
        S
        
          )
          
            2
          
        
      
    
    {\displaystyle C_{D,i}={\frac {4.822\times 10^{4}}{A\!\!{\text{R}}\epsilon \sigma ^{2}V^{4}}}(W/S)^{2}}
  ,where W/S is the wing loading in lb/ft2.


== References ==