A shelf pan is a simply supported beam under a roughly uniform load: δ = 5 w L4 / (384 E I) with w = m g / L. Steel E = 200 GPa. Shelf stiffness I is an illustrative value (heavy-duty lower shelves 1.2e-8 m4, light upper shelves 3.4e-9 m4). Limit used here: L/200 (a common serviceability rule of thumb). The in-page check solves the same beam with finite differences (two Poisson solves, Thomas algorithm) and compares.
Heavy boxes belong low: the box masses are 22, 16, 12, 9, 7, 5, 3 and 2 kg; the upper shelves cannot carry more than ~9 kg (box + clutter) within the L/200 limit.
For a rigid centred stack the topple angle is θ = atan( (b/2) / hcm ), b = base width, hcm = height of the centre of mass. Heavier/larger crates go underneath; the goal is θ ≥ 12° (a bump or a sloped floor). Crates are treated as rigid and uniformly filled.
Preload F = T / (K d) with nut factor K ≈ 0.2 (typical, dry steel; real K varies +-30 %). M6 class 8.8: proof stress ~600 MPa x 20.1 mm² = 12.1 kN; a safe preload is ≤ 75 % of proof (9.0 kN, T ≈ 10.9 N m). Spec here: 8 N m +-10 %. Over-torque strips the thread. Tighten in a cross pattern so the flange seats evenly.
Breakdown voltage from the empirical Paschen fit for air Vb = 24.22 p d + 6.08 √(p d) kV (p in atm, d in cm), valid for roughly uniform fields. At ~8 atm compression the coil (24 kV available, 30 % margin) fires up to about 0.9 mm; too small a gap gives a weak kernel. Spec 0.8 mm +-0.05. Real engines add the effects of mixture, temperature and electrode shape that this fit ignores.
At constant volume the absolute pressure scales with temperature (Gay-Lussac): P2 = P1 T2/T1. Set cold pressures (20 °C): front 2.2 bar, rear 2.5 bar; after a ride at 40 °C the gauge reads ~0.15 bar higher. Pump strokes for isothermal filling: N = g V / (patm v) (V = 2.4 L tyre, v = 0.12 L stroke). Tyre volume change is neglected.
A slack chain of span a with excess length e sags at mid-span by s = √(3 a e / 8) (parabolic approximation). Spec 25 - 35 mm. Moving the rear axle back 1 mm removes about 1 mm of excess (A real chain also stretches and the swingarm arc changes the span.)
Coins and XP are game scores, not physical. Prices of decorations and rewards are illustrative. Models are 1.4x scale for tools so they read on the pegboard. Not affiliated with any brand; the motorcycle is a generic design.