The spar carries the wing’s bending, and its size is a calculation: root bending moment, divided by the section modulus, must stay below the timber’s allowable stress at the highest load the aircraft will meet. For a 400 kg aircraft on a 10 m span the 1 g root moment is about 4,905 N·m, and the flight loads multiply it. The calculation needs the real strength of your timber, which this corpus cannot supply for salvaged wood of unknown species and history, and a spar that merely looks strong is not evidence: without the arithmetic and the properties, do not build the aircraft.
Part of Aerodynamics and Flight
The main beam of a wing, the bending it must resist, and the arithmetic that decides whether a section is adequate.
A Wing Is A Cantilever Loaded By Lift
The lift on each half wing acts on the spar like a load along a beam fixed at the fuselage. The bending moment is greatest at the root and falls to zero at the tip. The spar’s job is to carry that moment, the shear, and the twist from the rear spar and skin. The carrier describes a laminated spruce main spar or a spruce cap with plywood web, and a rear spar at 65-70% of the chord (Aerodynamics and Flight).
Worked Example: The Root Bending Moment
Inputs: mass 400 kg, so W = 400 × 9.81 = 3,924 N; span 10 m, so each half is 5 m; load factor n (1 for level flight at 1 g). Each half wing carries n × W ÷ 2 = 1,962 N at n = 1.
- If the lift were uniform along the span, its resultant acts at the middle of the half span, 2.5 m out: M = 1,962 × 2.5 = 4,905 N·m.
- If the lift followed an elliptical pattern, the resultant sits at 4 ÷ (3π) of the half span = 0.424 × 5 = 2.12 m out: M = 1,962 × 2.12 = 4,163 N·m.
Both ignore the wing’s own weight, which relieves the root slightly, and any strut or wire bracing, which relieves it much more but loads the struts and fittings. The moment is multiplied by the load factor: at n = 2 it is 9,810 N·m for the uniform case.
Worked Example: The Stress For A Chosen Section
Bending stress = M ÷ Z, where Z is the section modulus. For a solid rectangle of width b and depth h, Z = b × h² ÷ 6. Take b = 40 mm and the root moment 4,905 N·m = 4,905,000 N·mm.
| Depth h | Z = 40 × h² ÷ 6 | Stress at n = 1 |
|---|---|---|
| 100 mm | 66,667 mm³ | 4,905,000 ÷ 66,667 = 73.6 MPa |
| 200 mm | 266,667 mm³ | 4,905,000 ÷ 266,667 = 18.4 MPa |
Doubling the depth cut the stress to a quarter. Depth is the cheapest strength in a beam, and the thickness of the aerofoil limits it (Airfoil Geometry). A real spar is an I-shape or box, with caps carrying the stress and a web carrying shear, so a solid rectangle is only an illustration.
The Number This Corpus Cannot Give You
To use the table you must know the highest stress the wood can carry, the allowable stress. Allowable stress depends on the species, the grain slope, knots, moisture, age, glue joints and decay, and it is a statistical quantity: the weakest piece matters, not the average. The corpus cannot supply it for salvaged timber of unknown species and history. The load factor the aircraft must be designed for, and the safety margin applied to the allowable stress, come from a published airworthiness standard; they are not stated here because a figure from memory could be wrong in either direction.
What You Can Do To Find Out
- Test pieces to destruction. Cut sample beams from the same boards as the spar, load them to failure with weights, and record the failing load; compute the stress from M ÷ Z. Use the lowest result, not the average, and take a generous margin below it.
- Proof-load the finished wing with sandbags spread to follow the lift pattern, to a multiple of the highest flight load that the standard prescribes, with everyone clear and the wing supported so that its collapse harms nobody (Ground Testing).
- Inspect for defects: grain running out of the beam, knots in the caps, cracks, glue lines that open, decay and insect damage.
A passed test proves the tested wing at the tested load on the day; it does not prove a worse day.
Compression And Joints
A beam in bending is compressed on one face and stretched on the other. Timber commonly fails first on the compressed side, which can crush or buckle thin caps, so the caps need sideways support from ribs and the web. The splices and fittings at the root and at the strut attachments are the usual failure points, and a glue joint is only as good as the glue and the fit (Wood Airframe).
Common Mistakes
- Judging by appearance — thickness and feel are not stress.
- Using the average strength of test pieces — design to the weakest.
- Forgetting that loads multiply — pull-ups, gusts and rough air load the wing beyond 1 g.
- Lengthening the span or raising the weight after sizing the spar — the moment rises with both.
Safety
Structural failure in flight is not survivable
There is no recovery from a wing that folds. If you cannot show by arithmetic, with measured properties of the actual timber, that the spar carries the load factor plus a margin, you must not fly the aircraft. Do not rely on a resemblance to another aircraft, a spar that looks heavy, or a ground load test without a calculation behind it.
What’s Next
- Learn next: Wood Airframe, the material question
- Combine with: Force Calculation, the basic arithmetic of beams and ropes