The forest area is in semi evergreen forest in central India, on around 100 ha of patch 138 families are dependent for the fuelwood for cooking. Daily extraction of wood is around 15 kg/ family.
I'm no expert, but I would estimate the growth rate, and ensure that it isn't exceeded. Then check the demography, to ensure that harvesting occurs across all age groups (e.g. Avoid too little or too much thinning of young plants). If possible, get a chemical analysis of the timber and the ash, and ensure that nutrient extraction is not exceeding supply. Is the ash being spread in the forest? If not, it's not sustainable in my opinion.
Based on your question I can make the following suggestion and if you need any further clarification you may contact me
1. The forest types and speceis has to be considered before taking up any silvicultural manipulation
2. If it is moist deciduous forest or semiever green forests normally lopping practice of once in three or four year would not harm the growth of trees provided the season of lopping should be just prior to the arrival of spring season
3. For taking up lopping, ideal thing is to divide the whole tree into three parts and lop only the braches in the bottom 2/3 rd portion of the tree in an interval of 3-4 years. However, it purely depends on the speceis and the site conditions.
If you count the wood extraction in kg, maybe you need to estimate approximate weight in kg of the forest on ha or smaller area. And if you are trying to create one formula, maybe you will need to count the quantity of families on 1 ha or smaller area.