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.
Crowns do not grow to the compass. In practice, the surveyor measures each extent to where the crown actually reaches and books it to the nearest cardinal point. A crown whose longest reach is to the east-north-east has that reach recorded as its east spread, in the knowledge that the canopy will be turned back to its true position when it is drawn. Measuring strictly along the compass would miss that reach altogether, and no drawing could recover it.
The four spreads are therefore exact in length but only accurate to the nearest cardinal point in direction. A canopy drawn straight from them is correct in size and shape but orientated to the compass, out by whatever angle separated the crown's real bias from the cardinal point it was booked to. Try the two ways of recording below.
Interactive
Recording a crown, and turning it back
The crown and both drawn canopies use the same canopy geometry as our survey drawings. Shared area is measured on a 0.1 m grid.
Shared area: the overlap between the drawn canopy and the crown, as a share of the ground either covers
field practice, turned back field practice, not turned along the compass, best possible turn along the compass, not turned
Two things follow. Turned back by the right angle, a canopy recorded in the usual way matches the crown as closely as the drawing allows, whatever the direction of its bias. Left unturned, it is worse than a strict compass record would have been, because its extents are the right length but in the wrong place. Turning is not a finishing touch; it completes the record.
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 turning was done 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. The difficulty is that the four spreads record which cardinal point each extent was booked to, but not which side of it the crown actually reached, or how far round.
What this is not: the method does not measure the direction of a crown's bias. It estimates the angle the surveyor saw on site but did not write down, from the most common and predictable cause of a crown's bias: competition from the neighbouring crowns as they stand today. Crowns are also shaped by light from open ground, wind, structures, pruning, past failures and neighbours that are no longer there, and the method leaves those to the surveyor.
Why only rotation
Because of the way crowns are recorded, turning the canopy is not a departure from the survey. Every extent keeps the length the surveyor measured; the turn returns it to the bearing it was measured at. The stem stays exactly where it was recorded and the canopy covers exactly the same area.
The same recording practice sets the limits. The record already places the crown's bias within 45° either side of the cardinal point its longest extent was booked to; beyond 45°, the surveyor would have booked it to the next cardinal point. The competition model therefore adds only what the record lacks: which side of that cardinal point the bias falls (clockwise or anticlockwise), and roughly how far. No turn exceeds 45°.
A crown biased squarely between two cardinal points, to the north-east for example, is recorded differently. Its reach is split between the north and east spreads, which come out similar in length, and the drawn canopy already shows the bias where it belongs. Turning such a canopy either way would move it off the bias the surveyor recorded, so split records are not turned (see How far to turn).
Moving a canopy off its stem, stretching it or reshaping it would each produce 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 is the one change the record itself calls for.
- Every measured length is kept
The same four spreads, the same outline, the same canopy area, about the surveyed stem.
- The turn stays within the record
No canopy turns more than 45°, the furthest a crown can be from the cardinal point it was booked to.
- Split records are left as drawn
A bias recorded across two cardinal points is already in place, and the turn is reduced or withheld.
- 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 split record is the edge-of-group case again, but with the crown recorded 5 m to both south and west: its south-west bias is already drawn, so it is left alone.
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, its bias is to the east, whatever any model says, because the surveyor stood under it and saw it. What the record cannot say is which side of east, and how far round.
So the turn starts from the difference between the direction the spreads point and the direction of the competition bias, and takes a share of it. How large a share depends on 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 the most likely to have been booked well away from its true bearing; a nearly round crown gives nothing to turn and is left as drawn. No turn exceeds 45°.
Two further tests follow from the record. Where the longest spread has a neighbouring spread of similar length, the bias has been recorded across both cardinal points and is already drawn in place: the turn is reduced as the two lengths approach each other, and withheld once the shorter is 95% of the longer. And where the competition bias and the measured bias 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.
The split ratio is the longer of the two spreads beside the longest spread, divided by the longest. Move it past 0.8 and the whole line flattens; past 0.95 it lies on zero.
The turn formula
The spreads (N, E, S and W, in metres) point in the direction:
Its strength, the asymmetry, compares the size of that bias with the average spread:
The split ratio compares the longest spread with the longer of its two neighbours on the compass (for the east spread, north and south):
split factor = 1 up to 0.80, falling in a straight line to 0 at 0.95 A crown recorded 7 m east and 4 m north scores 0.57 and is turned in full. One recorded 7 m east and 7 m north scores 1.0: its north-east bias is already drawn, and it is not turned.
The turn applied is then:
turn = clamp( Δ × r̄ × strength × asym × split factor , −45°, +45° ) r̄ is the signal clarity and strength the competition strength, both from the competition sum. Positive turns are anticlockwise.
Five cases are left unturned: crowns whose only overlapping neighbours are less than half their height; crowns with no overlapping neighbour at all, which are left as the spreads have them since that is already the best information available; crowns with an asymmetry below 0.05, which are near circular (30% of crowns in the calibration survey were recorded equally all round); split records with a factor of 0; and crowns where Δ exceeds 90°, which are 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. |
| split_ratio | The longer spread beside the longest spread, divided by the longest. |
| split_factor | The reduction applied to the turn for a split record, from 1 (full turn) to 0 (not turned). |
| 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 split record, 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.
Surveyors can also note the offset they saw on site against individual trees. For now these notes are used to check the turns the method produces rather than to replace them; where the two consistently agree, the notes will become part of the survey record.
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°, consistent with extents booked to the nearest cardinal point. 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 the method was refined in two steps. The half-height cut-off and the strength scaling were added after testing showed that a much shorter neighbour could turn a tall tree as far as a tall neighbour could. The limit was then brought down from 60° to 45°, and the split-record reduction added, once the recording practice described above was written into the method.
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. |