The problem
BS5837:2012 asks for crown spread to be recorded at the four cardinal points, and for good reason: four measurements taken the same way every time are quick, repeatable and comparable between surveyors. The canopy on the plan is then drawn through those four points, curving between each pair of neighbouring spreads.
The difficulty is that a crown's asymmetry can only be sampled at the cardinal points. A crown with a bias between two compass points has that bias shared between two spreads, and the drawn canopy is always orientated to the compass rather than to the direction the crown is actually biased. On an open parkland tree this hardly matters. In a belt or a group, where nearly every crown is pushed off centre by its neighbours, the plan stops looking like the site.
This is more than a matter of appearance. Canopies are the basis for judging the effect of a layout on the trees around it: where a building, road or service run meets a crown, and how much pruning a proposal would need. A canopy orientated to the wrong side of its stem can put a conflict on the wrong side of a tree.
For years the fix was to turn canopies by hand in CAD after the plan was drawn: slow, dependent on the drafter's memory of the site, and never recorded anywhere. On a large survey it took an hour or more.
What this is not: it is not a measurement of which way a crown is biased. Crowns are shaped by light from open ground, wind, structures, pruning, past failures and the neighbours they grew up with, some of which are no longer there. No model built from the survey can know all of that. The method handles the most common and predictable cause, competition between neighbouring crowns as they stand today, and leaves the rest to the surveyor.
Why only rotation
The four measured spreads already record the direction of a crown's bias, only rounded to the compass. A crown biased to the south-east is recorded with larger south and east spreads than north and west. The measured direction is therefore not something to be overridden but an anchor to be refined. The competition model adds one piece of information: which side of the measured direction the true bias most likely falls (clockwise or anticlockwise), and by roughly how much.
Several other things could be done to a canopy to make it look more like the tree. It could be moved off the stem, stretched, or reshaped. Each of those would create a drawing that no longer matched the survey schedule, and a drawing that disagrees with its own schedule is one a reviewing officer or another consultant is entitled to challenge.
Turning the canopy about its stem is the one change that keeps faith with the survey. The stem stays exactly where it was recorded, the canopy covers exactly the same area, and it is still built from the same four measured spreads; only the angle at which they are laid on the plan changes. That angle is recorded against every tree, so any canopy can be returned to the compass by reading one figure.
- The stem stays put
Every canopy turns about its surveyed stem position.
- The measured shape is kept
The same four spreads, the same outline, the same canopy area.
- The turn is limited
No canopy turns more than 60° from the compass, however strong the competition.
- Only real competitors count
Neighbours less than half the tree's height are ignored, and weak competition gives a smaller turn.
- Disagreements are not forced
Where the model and the spreads point substantially different ways, the canopy is left alone and flagged for the surveyor.
- The turn is recorded
Each tree carries the angle it was turned through and the working behind it.
- Nothing is moved, stretched or reshaped
The recorded spreads remain the record.
One: competition has a direction
Forestry has long measured how crowded a tree is using competition indices. One of the most widely used, Hegyi's index, adds up each neighbour's size relative to the tree in question, divided by the distance between them. It gives a single number: how much competition, but not from which side.
We turned it into a direction. Each neighbour whose crown overlaps the tree's crown, and which is at least half the tree's height, contributes a pull directly away from itself, weighted by its height relative to the tree and by how far the two crowns overlap. Adding those together gives the direction competition is acting on the crown, how consistent that direction is, and how strong the competition is overall. The situations every surveyor recognises come out of the same sum without being written as separate rules:
- two similar trees side by side are each biased away from the other, giving the familiar codominant pair;
- a small tree beside a larger one is biased away from it, and where several neighbours overlap it, the taller ones count for more;
- a tall tree is not turned by the understorey beneath it, because its crown overtops those trees rather than competing with them;
- a tree at the edge of a group has all its neighbours on one side and is biased out into the open, while a tree in the middle of the group has competition from every side that largely cancels, and is left almost as drawn.
Try each of these below. Drag the neighbouring trees, or select one to change its height and spread.
Interactive
Neighbours acting on a crown
The dashed outline is the canopy as drawn from its spreads. The filled outline is the canopy after turning.
measured bias (from the spreads) competition from each neighbour competition bias average spread, used to test overlap neighbour ignored as too short
Overlap is tested on the average of each tree's four spreads, shown as a dotted circle for the tree being turned and as the full circle for each neighbour. A neighbour can therefore count as overlapping just before it touches the short side of a lopsided crown. Lower a neighbour below half the tree's height and it drops out altogether.
The directional competition index
Hegyi's index for a tree i sums the relative size of each neighbour j over the distance between them:
The directional version replaces the sum of numbers with a sum of vectors, each pointing from the neighbour towards the tree:
Each crown is represented for this purpose by the average of its four spreads, r. Only neighbours whose crowns overlap on that basis, and which are at least half the tree's height, are counted. The overlap is measured from how far they intrude:
overlapij = (ri + rj − distij) / (ri + rj) Overlap is 0 when the crowns are just touching, rising towards 1 as the stems come together. A neighbour beyond reach has no influence however large it is, and a neighbour less than half the tree's height is treated as understorey, which the crown overtops rather than competes with.
Two figures come from the sum. The direction of B is the competition bias. The signal clarity, r̄, is the length of B divided by the total of the weights:
Because r̄ divides by the total weight, it says nothing about how strong the competition is, only how consistent. A single neighbour that barely overlaps has a clarity of 1, the same as a single large neighbour overlapping heavily. The strength of the competition is therefore taken separately, from the total weight:
Distance is not added as a separate term. The bearing from stem to stem already carries the direction, and the overlap already falls away as trees stand further apart, so a separate distance weighting would count the same thing twice.
What this is not: the average spread is a simplification. A crown recorded at 8 m to the north and 1 m elsewhere has an average of 2.75 m, so a neighbour to its north is counted only once it is well inside the real crown. Testing overlap against the crown's actual reach towards each neighbour is a planned refinement.
Two: how far to turn
The measured spreads carry the most important evidence. If a crown was measured at 6 m to the east and 3 m to the west, it is biased to the east, whatever any model says, because the surveyor stood under it and saw it. The competition model's job is only to refine that angle.
So the turn starts from the difference between the measured bias and the competition bias, and takes only part of it. How much depends on three things: how clear the competition signal is, how strong the competition is, and how asymmetric the measured crown is. A strongly one-sided crown is the typical form of a suppressed tree, and is the most likely to need turning; a nearly round crown gives nothing to turn and is left as drawn. Where the two directions disagree by more than 90°, the model has nothing useful to add, and the canopy is left alone and flagged.
Interactive
Deciding the turn
The line shows the turn applied for every possible disagreement between the competition bias and the measured bias. The dot is the current case.
Push the asymmetry high and the weight passes 1, so the turn is governed by the 60° limit rather than by the weight. That is intended: very one-sided crowns, typically the form of a suppressed tree, are the ones most likely to need turning.
The turn formula
The bias recorded by the measured spreads (N, E, S and W, in metres) points in the direction:
Its strength, the asymmetry, compares the size of that bias with the average spread:
The turn applied is then:
turn = clamp( Δ × r̄ × strength × asym , −60°, +60° ) r̄ is the signal clarity and strength the competition strength, both from the competition sum. Positive turns are anticlockwise.
Four cases are left unturned. Crowns whose only overlapping neighbours are less than half their height are left as the spreads have them. Crowns with an asymmetry below 0.05 are skipped as near circular, since turning them changes nothing but the record; in the calibration survey 30% of crowns were recorded equally all round. Crowns with no overlapping neighbour are left as the spreads have them, which is already the best information available. And where Δ exceeds 90°, the competition bias is at right angles to the measured bias or worse, so rather than force a turn the survey does not support, the canopy is flagged for the surveyor (see Checking the result).
No knock-on effects
Competition runs both ways. If trees were turned one at a time, with each turned canopy then used to work out its neighbours, an error in one tree could travel through a group from tree to tree, and the same survey could produce different drawings depending on the order its trees were listed in.
That cannot happen here. Every competition sum is worked out from the surveyed stem positions and spreads before a single canopy is turned, and all the turns are then applied together. No tree's result depends on another tree's turn, the order the trees are processed in makes no difference to the outcome, and the same survey always produces the same drawing.
The trees are nonetheless taken in order of dominance (tallest first, then by stem diameter, then by life stage). That order has no effect on the present results; it is in place for a planned refinement in which dominant trees are turned first and the overlaps worked out again before the trees beneath them are dealt with, which would follow more closely how a group of crowns actually develops.
Groups and hedges are handled separately. Their member trees count as neighbours, so a tree standing beside a group is biased away from it as it should be, but the members themselves are aligned by the rules that draw group canopies, not by this method.
Checking the result
Every canopy carries the working behind its turn, so the drawing can be questioned tree by tree rather than accepted or rejected as a whole.
| Field | What it records |
|---|---|
| applied_rot | The angle the canopy was turned through, in degrees, anticlockwise positive. Reversing it restores the compass-orientated canopy. |
| meas_dir | The direction of bias recorded by the measured spreads. |
| comp_dir | The direction of the competition bias. |
| r_bar | Signal clarity, from 0 (competition cancels out) to 1 (all from one side). |
| asym | Strength of the asymmetry in the measured spreads. |
| n_nbrs | Number of overlapping neighbours counted. |
| n_short | Number of overlapping neighbours ignored as less than half the tree's height. |
| total_w | Total competition weight of the counted neighbours. |
| strength | The strength factor applied to the turn, from 0 to 1. |
| review_flag | Set where the competition bias and the measured bias disagree by more than 90°. The canopy is not turned. |
| skip_reason | Why a canopy was left unturned: no overlapping neighbours, only neighbours too short to count, a near circular crown, a disagreement flagged for review, or a turn too small to matter. |
Filtering the canopies for the review flag gives the surveyor a short list to check against site notes and photographs. A strong disagreement usually means something the model cannot see: a neighbour removed years ago that shaped the crown as it grew, a wall or building not in the survey, or a crown shaped by an old failure or by pruning. Those are exactly the trees where the surveyor's own knowledge should decide, and the flag makes sure they are looked at rather than silently overruled.
The clarity figure is the best guide elsewhere. A turn driven by a low clarity (below about 0.3) rests on a weak signal and is worth a second look; a high clarity with a modest turn is the ideal result. A low strength explains a turn that is smaller than the measured spreads might suggest.
In practice
The limits were set against real drawings. On a major highways project in Norwich, a survey of 309 trees, the canopies had already been turned by hand in CAD to match the site, and 274 of the hand-turned canopies were paired with their compass-orientated originals. Most of the hand turns fell between 15° and 45°, with a few reaching around 85°. The 60° limit covers the great majority without allowing implausible swings. Trees at the edges of groups and belts, where the competition signal is clearest, were matched best, as expected.
The method has been used on every survey since it was built, and has almost removed the need to turn canopies by hand. In September 2026 two refinements were added, the half-height cut-off and the strength scaling, after testing showed that a much shorter neighbour could turn a tall tree as far as a tall neighbour could. The 60° limit and the review angle are unchanged.
Why build it this way
The point was never to replace the surveyor's judgement, only to stop spending it on the predictable cases. Competition between neighbouring crowns is the commonest reason a canopy is biased, and it is the one reason the survey data can speak to. Handling that automatically, within limits the measurements set, leaves the surveyor free to deal with the handful of trees that genuinely need a person to decide.
Because the turned canopy is the canopy used everywhere else, the benefit carries through. The tree constraints plan, the section elevations and the matching of trees to survey photographs all read the same turned outline, so a crown biased one way on the plan is biased the same way in every other drawing made from it.
Version
This note describes the canopy orientation method as used in our current survey processing. It is written and maintained by Tony Sorensen, and will be revised if the method changes in a way that affects the drawings it produces.
| Version | Date | Changes |
|---|---|---|
| 1.0 | September 2026 | First publication. |