Yield is not all that sensitive to spacing. It should be about 1 to 4 metres depending on whether you want biomass or logs.
For the tightest possible packing, trees are planted to form triangles (blue lines in the following diagram).
Each tree can be then considered to have a hexagonal hinterland (green area). This provides each tree with a hinterland closest in shape to a circle, thus providing even space and lighting all round the tree. The perpendicular from the mid point of any of the 6 sides of this hexagonal hinterland to its centre is half the spacing between trees.
- Therefore if
- sp = spacing in metres
- each tree's hinterland area:
- a = 0.8660254037844 * sp² square metres
- 0.8660254037844 = half the square root of 3.
- The total number of trees required in the plantation
- N = A / a
- N = A / (0.8660254037844 * sp²)
Total annual wood yield of a plantation is not very sensitive to spacing. It should be about 1 to 4 metres depending on whether you want biomass or logs. For the ratio of just under 1.3 logs to biomass I need for heating and engine fuel production, I would go for a spacing of 3 metres with a mix of willow, poplar and sycamore and then learn from the results. The mix of tree types is to help in some way towards their biological protection.
A 3 metre spacing makes the area occupied by each tree 0.8660254037844 * 9 = 7.79422863406 m². A plantation of 1 hectare (10,000 m²) therefore requires 10000 / 7.79422863406 = 1283 trees.
I would also try to divide up the plantation into separate areas. This may be a little inconvenient from the point of view of maintenance, but it makes the whole less vulnerable to fire, disease and pests.
© January 2001 - Robert John Morton