Aircraft Copper Cable Replacement

An aircraft company has decided to replace the 15mm copper cables to the main aircraft generators onboard it’s Boeing 747s with aluminium cables that are capable of carrying the same current. There are three (3) cables each for the two (2) inboard generators with a length of 150 feet. There are three (3) cables each for the two (2) outboard generators with a length of 200 feet.

a. Calculate the present resistance of each of the inboard and outboard cables and the dimensions of the replacement cables.

In order to first work out the resistance we must use the formula:

R= (ρ x L)/A

Given that ρ for copper = 1.72 x10-8

Seen as all are SI units we must convert from feet to meters, to convert ft to meters 1ft = 0.3048m.

Therefore the length of the inboard and outboard cables are:

Inboard (150 x 0.3048) = 45.72m

Outboard (200 x 0.3048) = 60.96m

In order to work out the cross sectional area in mm, we must use the formula:

A = π r2 (r = D/2 in metres)

A = 3.142 x (0.0075 x 0.0075) = 1.77 x 10-4 m2

Putting those figures into the formula for resistivity R= (ρ x L)/A gives us:

R = (1.72 x10-8 x 45.72m)/ 1.77 x 10-4 m2 = 4.44 x 10-3

The 150ft inboard cables have a resistance of 4.44m(

(1.72 x10-8 x 60.96m)/ 0.0001767375m2 = 5.92 x 10-3

The 200ft outboard cables have a resistance of 5.92m(

In order to carry the same current the Aluminium cables would have to have a resistance the same as the Copper cables already fitted. The ρ for Aluminium is different than that for Copper, so therefore the new cables will have to be of a different cross sectional area.

ρ for aluminium = 2.9 x 10-8

For the inboard 150ft cables need to be 4.44m( therefore

Using R = (ρ x L)/A

0.00444 = (0.000000029 x 45.72m)/ A

A x 0.00444 = 0.000000029 x 45.72m

A = (0.000000029 x 45.72m)/ 0.00444

A = 0.000299m2

( 0.000000029 x 60.96m/0.00592 for the 200ft cable gives the same answer.)

To calculate the diameter of the cable...