I installed transmission on my raspberry pi and set it up to download directly onto a mounted external hdd. The drive is mounted using following fstab entry:
/dev/sda1 /mnt/old ntfs uid=pi,gid=pi,umask=000 0 0
I've added the user debian-transmission to group pi and also added user pi to group debian-transmission, just to be safe. The service runs under user pi.
I've tried every suggestion I found here Transmission: permission denied on USB disk but none of them worked.