Using aluminium busbar/cables in an aircraft instead of copper
While it is true that copper is 1.6 times more conductive than aluminum per volume, 


  Conductivity in $\frac{\mathrm{MS}}{\mathrm{m}} = \frac{\mathrm{10^6}}{Ω\,\mathrm{m}}$:
  
  
  copper:    56
  aluminium: 36
  $$\frac{56}{36} = 1.56$$
  


aluminium is 2.1 times more conductive than copper per weight.


  Density in $\frac{\mathrm{g}}{\mathrm{cm^3}}$:
  
  
  copper:    8.96
  aluminium: 2.7
  $$\frac{36 \cdot 8.96}{56 \cdot 2.7} = 2.13$$
  


Another important metric concerns the cost. The conductivity per cost is 7.1 times higher for aluminium. 


  Base metal price in $\frac{\mathrm{US$}}{\mathrm{lb}}$ (as of today):
  
  
  copper:    2.71
  aluminium: 0.81
  $$\frac{36 \cdot 8.96 \cdot 2.71}{56 \cdot 2.7 \cdot 0.81} = 7.14$$
  


Aluminium wiring is safe if it is sized and terminated correctly. In comparison with copper, aluminium is softer, shows more creep, and has 30% stronger thermal expansion.