Wing Box Sizing (vehicle-design/structures-integration/wing-box-sizing)
Use when the task is sizing the wing box structure at the conceptual
level: root bending moment from the load factor, weight, and span,
ultimate moment from the factor of safety, spar cap area, and spar web
thickness from the shear flow.
Domain quick reference
- Root bending moment from the elliptical spanwise lift distribution:
M = (2/(3pi)) * n * W * b, with n the design load factor, W the
design weight in newtons, and b the span in meters; result in N m.
A uniform distribution gives M = n * W * b / 4. The elliptical
constant 2/(3pi) is about 0.2122; the uniform constant is 0.25.
- Root shear force per half-wing: V = n * W / 2.
- FAR-25.303 context: the factor of safety between limit and ultimate
loads is 1.5, so M_ultimate = 1.5 * M_limit.
- Spar cap area from the box-beam bending relation M = sigma * A * h:
A = M / (sigma * h), with h the box depth between cap centroids and
sigma the allowable stress in pascals; the result is the area per
cap (upper and lower caps each take the full couple).
- Spar web shear flow: q = V / (n_webs * h), and web thickness
t = q / tau with tau the allowable shear stress.
- Worked example: n = 2.5, W = 600000 N, b = 30 m gives a root bending
moment of about 9.55 MN m (elliptical) and an ultimate moment of
about 14.32 MN m; with sigma = 400 MPa and h = 0.6 m the spar cap
area is about 0.0597 m^2; with tau = 240 MPa and two webs the web
thickness is about 2.6 mm.
Workflow
- Collect the design maneuvering load factor, the design weight, the
span, the box depth, and the allowable stress and shear.
- Compute the root bending moment with wing_root_bending_moment
(elliptical distribution by default).
- Scale the limit moment to ultimate with ultimate_moment.
- Size the spar cap with spar_cap_area and the web with
web_shear_flow followed by web_thickness.
- Compare the required values against the available cap area and web
thickness with wing_box_verdict, and gate the structure integration
on the verdict.
Pitfalls
- Using the limit moment for the cap sizing: the caps must carry the
ultimate moment, the limit moment times the 1.5 factor of safety.
- Mixing the distribution models: elliptical gives about 0.2122 times
nWb, uniform gives 0.25 times nWb; state which model the load
case uses.
- Confusing the box depth with the airfoil thickness: h is the distance
between the spar cap centroids, not the maximum airfoil thickness.
- Sizing the web with the full root shear: the shear splits over the
web count, and web_shear_flow divides by the number of webs.
- A single undersized item fails the box: the verdict requires both the
spar cap area and the web thickness to fit the available values.
- Zero or negative inputs raise ValueError instead of returning a
nonsense area or thickness.
Behavior contract (gate 3)
The sizing logic is exercised by the gate 3 contract test:
scripts/test_wing_box_sizing.py against
scripts/wing_box_sizing_logic.py (stdlib unittest, offline). Run:
python3 scripts/test_wing_box_sizing.py
Compliance
- FAR-25 is US government work (public domain) and CS-25 is a free
EASA download; standards referenced, not reproduced, per
standards-map.yaml. Wing box sizing methodology (box-beam
idealization, elliptical loading) is common conceptual design
practice.
- compliance: STANDARDS-REF, gated: false.
1---2name: wing-box-sizing3description: Use when you must perform wing box sizing at the conceptual level: compute the root bending moment from the load factor, weight, and span with the elliptical lift distribution, scale the limit moment to ultimate with the 1.5 factor of safety, size the spar cap area from the bending moment and the allowable stress, and size the spar web thickness from the shear flow. Produces the root bending moment, ultimate moment, spar cap area, web thickness, and a box sized verdict that gate the wing structure integration. Trigger: wing box sizing, root bending moment, spar cap, shear flow, ultimate load, factor of safety, allowable stress.4license: Apache-2.05---6# Wing Box Sizing (vehicle-design/structures-integration/wing-box-sizing)78Use when the task is sizing the wing box structure at the conceptual9level: root bending moment from the load factor, weight, and span,10ultimate moment from the factor of safety, spar cap area, and spar web11thickness from the shear flow.1213## Domain quick reference1415- Root bending moment from the elliptical spanwise lift distribution:16 M = (2/(3*pi)) * n * W * b, with n the design load factor, W the17 design weight in newtons, and b the span in meters; result in N m.18 A uniform distribution gives M = n * W * b / 4. The elliptical19 constant 2/(3*pi) is about 0.2122; the uniform constant is 0.25.20- Root shear force per half-wing: V = n * W / 2.21- FAR-25.303 context: the factor of safety between limit and ultimate22 loads is 1.5, so M_ultimate = 1.5 * M_limit.23- Spar cap area from the box-beam bending relation M = sigma * A * h:24 A = M / (sigma * h), with h the box depth between cap centroids and25 sigma the allowable stress in pascals; the result is the area per26 cap (upper and lower caps each take the full couple).27- Spar web shear flow: q = V / (n_webs * h), and web thickness28 t = q / tau with tau the allowable shear stress.29- Worked example: n = 2.5, W = 600000 N, b = 30 m gives a root bending30 moment of about 9.55 MN m (elliptical) and an ultimate moment of31 about 14.32 MN m; with sigma = 400 MPa and h = 0.6 m the spar cap32 area is about 0.0597 m^2; with tau = 240 MPa and two webs the web33 thickness is about 2.6 mm.3435## Workflow36371. Collect the design maneuvering load factor, the design weight, the38 span, the box depth, and the allowable stress and shear.392. Compute the root bending moment with wing_root_bending_moment40 (elliptical distribution by default).413. Scale the limit moment to ultimate with ultimate_moment.424. Size the spar cap with spar_cap_area and the web with43 web_shear_flow followed by web_thickness.445. Compare the required values against the available cap area and web45 thickness with wing_box_verdict, and gate the structure integration46 on the verdict.4748## Pitfalls4950- Using the limit moment for the cap sizing: the caps must carry the51 ultimate moment, the limit moment times the 1.5 factor of safety.52- Mixing the distribution models: elliptical gives about 0.2122 times53 n*W*b, uniform gives 0.25 times n*W*b; state which model the load54 case uses.55- Confusing the box depth with the airfoil thickness: h is the distance56 between the spar cap centroids, not the maximum airfoil thickness.57- Sizing the web with the full root shear: the shear splits over the58 web count, and web_shear_flow divides by the number of webs.59- A single undersized item fails the box: the verdict requires both the60 spar cap area and the web thickness to fit the available values.61- Zero or negative inputs raise ValueError instead of returning a62 nonsense area or thickness.6364## Behavior contract (gate 3)6566The sizing logic is exercised by the gate 3 contract test:67scripts/test_wing_box_sizing.py against68scripts/wing_box_sizing_logic.py (stdlib unittest, offline). Run:6970python3 scripts/test_wing_box_sizing.py7172## Compliance7374- FAR-25 is US government work (public domain) and CS-25 is a free75 EASA download; standards referenced, not reproduced, per76 standards-map.yaml. Wing box sizing methodology (box-beam77 idealization, elliptical loading) is common conceptual design78 practice.79- compliance: STANDARDS-REF, gated: false.
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