How to control permissions on external USB hard disk

It all depends on the filesystem you are using on your external drive. Since you have mentioned that permission changing operations do not work, it is likely you have either NTFS or FAT32.

Since you want to make a backup, the best way to do that to different file-system would be to make an archive with a tool like tar or similar. They have command switches for preserving permissions etc.

Regarding permissions of NTFS/FAT32 filesystems: while you can't control permissions of individual files or directories, you can specify permission which will be used when mounting the drive using dmask, fmask and umask options:

• uid set the owner user of all files
• gid set the owner group of all files
• dmask controls permissions for directories
• fmask controls permissions for files
• umask controls the bitmask of the permissions that are not present (defaults to the umask of current process)

These can be either put into /etc/fstab or just added to mount command as -o arguments:

$ mount -o uid=1000,gid=1000,dmask=027,fmask=137 /dev/sdXY /mnt

If you want to put it in /etc/fstab instead, you have to put them under options (4th column):

$ cat /etc/fstab
/dev/sdXY    /mnt    ntfs   uid=1000,gid=1000,dmask=027,fmask=137    0     0