Crown Reduction and Leaf Area Removed
The geometry is why a modest-sounding reduction is a large removal, and it compounds twice.
Example
You enter
- Crown radius (ft) 20
- Reduction off the radius (ft) 4
- Share of leaf area in the outer third (0 to 1) 0.75
- Live crown removal cap (%) 25
You get
- Original area (ft²) 1256.64
- Reduced area (ft²) 804.248
- Area removed (%) 36
- Radius removed (%) 20
- Leaf area removed (%) 48.6
- Amplification 1.35
- Radius for cap (ft) 1.94658
Details, formula, and sources
First, crown projection goes as the SQUARE of the radius, so taking a fifth off the radius takes over a third of the projected area. Second, LEAVES ARE ON THE OUTSIDE: the outer third of the crown holds the large majority of the foliage, so the shell the cut removes is the densest part of it. The two together mean a reduction described as a few feet off the ends can remove far more leaf area than the number of feet suggests, and the amplification between the two is reported here because that is the figure a client and an arborist argue about. ANSI A300 addresses pruning DOSE and the limits are what the estimate has to land inside. Removing more than about a quarter of the live crown in a season is widely regarded as excessive for a mature tree, and young, over-mature and stressed trees tolerate considerably less -- a stressed tree should have no live foliage removed until it recovers. The reduction that just reaches the entered cap is worked out here for that reason: it turns the limit into a number of feet the crew can work to. HEAVY REDUCTION TRIGGERS EPICORMIC SPROUTING, and that is a cost that arrives later. The tree responds to the loss of foliage with weakly attached shoots along the remaining branches, which then need managing for years and which are structurally worse than what was removed. A reduction planned to a defensible dose avoids that; one planned to a client's sight line does not. And topping is not pruning: it removes leaf area indiscriminately, leaves stubs that cannot compartmentalise, and creates a decay entry at every cut. A geometric estimate of leaf area against a dose limit. The outer-third share is entered rather than known, because it varies by species, by age, by light exposure and by how the crown has been managed before, and a dense conifer and an open-grown oak do not distribute foliage alike. It treats the crown as a circular projection with foliage in radial shells, which no real crown is, and it does not measure leaf area, which needs destructive sampling or an optical method. It does not select cuts, which is the actual craft -- a reduction is made to lateral branches large enough to assume the terminal role, and where those laterals are decides what is possible. It does not assess the tree's condition, its species tolerance, the season, or whether the reduction is the right treatment at all. ANSI A300 Part 1, the ISA Best Management Practices, and a qualified arborist govern.
crown projection area = pi/4 x diameter squared, so it goes as the SQUARE of the radius; leaf area is distributed by radial shell with the entered majority share in the outer third of the radius, and the reduction removes the outer shell first; the reduction that just reaches the dose cap is that relation bisected.
The crown projection and leaf-area distribution relations by name, checked against the ANSI A300 live crown removal dose -- about 25% of the live crown in a season for a mature tree, less for young, over-mature and stressed trees. The outer-third share is ENTERED: it varies by species, age, light exposure and prior management. A geometric estimate on a circular crown projection; it does not measure leaf area, select cuts, or assess the tree. ANSI A300 Part 1, the ISA Best Management Practices, and a qualified arborist govern.
Two areas and a share the reader supplies; no A300 text is reproduced.
Estimate. AHJ and licensed professional govern.
Field names used by the API: crown_radius_ft, reduction_ft, outer_third_leaf_share, live_crown_cap_pct, original_area_ft2, reduced_area_ft2, area_removed_pct, radius_removed_pct, leaf_area_removed_pct, amplification, radius_for_cap_ft
- The outer-third share is entered it varies by species, age, light exposure and prior managementa qualified arborist
- A circular projection in radial shells no real crown is that, and leaf area is not measured herethe ISA Best Management Practices
- It does not select cuts a reduction is made to laterals large enough to assume the terminal roleANSI A300 Part 1