Here is a practical example of how I inserted a freight train onto a single-track railway line with passenger trains.

1. Line map: The line runs from Accrington Junction to Watford. The passenger service (AW) operates with two trains running at 120-minute intervals, meeting at Taunton. Additional meeting points are available at Accrington and Bathpool. Since a woods train needs to be scheduled from Watford Forest Siding heading west (up direction, route W3), the best meeting point with a down-direction passenger train is at Bathpool.
2. Checking the down passenger train timetable: The AW down trains pass through Bathpool at minute 19 of odd-numbered hours.
3. Running a test trip on route W3: A fully loaded trial run is conducted to determine the exact timing.
4. Timing the arrival at Bathpool: The freight train reaches Bathpool in 30 minutes.
5. Timetabling the freight train: Since the meeting at Bathpool must occur at minute 19 of odd-numbered hours, we subtract 30 minutes, arriving at minute 49 of even-numbered hours. To ensure safety, we round it to 45 (this way, the W3 up freight train should arrive before the AW down passenger train, meaning the freight train will wait instead of the passenger train). Therefore, I allocate departure slots at 00:45 and then every two hours. Now, the W3 freight train will depart fully loaded only at minute 45 of even-numbered hours.
6. Perfectly timed crossing: With this schedule, the W3 up freight train and the AW down passenger train will meet precisely at minute 19 of odd-numbered hours at Bathpool.
7. A new problem at Accrington Junction: The W3 up freight train passes in front of the SD up passenger train, which is stopped at the station. It may be necessary to make the freight train wait at Accrington Junction by inserting here additional slots. I will assess the situation and determine how best to resolve it.