I know that many variables play into the required thrust for a take-off and for climb. Most of those specs boil down to a targeted gross weight, wing loading and L/D ratio. Intended flying speed range is also known but probably not even needed for this estimate. Using these specs then I can roughly assume that many specs have been taken into account for a thrust calculations.
For ex. aircraft is gross weight 400 lb with L/D ratio of 10. Assuming a non-accelerating level flight at optimal cruise speed 50 mph in no wind condition it will require at least 400 / 10 = 40 lb of thrust. Based on above numbers how to make rough estimate of the minimal thrust required for a reasonably short take-off (say within 500 to 1,000ft roll of runway) ?
Note: please keep in mind I am familiar with many other conditions and aircraft specs affecting the required thrust. Yet for 100 years practical aircraft designers used very simple math approach to estimate needed thrust. I personally knew one of old generation designers who did this well in many of his successful designs using simple math dealing with few numbers (he passed away years ago). He only used gross weight, wing loading and targeted L/D ratio chosen from his experience. Please share if you know the answer.