Forklift Tip-Over Stability

What is modelled

A forklift with a load is a rigid body whose centre of mass (COM) sits higher and further forward as the load mass and lift height grow. In an accelerating frame gravity is replaced by an apparent gravity (g plus the inertial acceleration); the truck stays upright only while that line through the COM falls inside the wheel footprint.

Equations

• Composite COM h = (mL (0.72 + lift) + m0 0.91) / (m0 + mL), forward offset x = (1.30 mL - 0.13 m0) / m, lateral shift y = mL s / m.
• Static tip angle αtip = atan(support / h); lateral tip when alat / g > (T/2 - |y|) / h, forward tip when abrake / g + tan(slope) > (L/2 - x) / h.
• Steady turn alat = v2 tanδ / L, radius R = L / tanδ; tyres slide first if alat > μ g.
• Braking distance v2 / (2 a) with a = min(Fbrake/m, μ g).

Checks run in the page

• Tip angle from a numerical moment balance against atan(support / h).
• Critical load mass for forward tipping against bisection on the composite COM.
• One lap of a steady turn closes on its start point.
• Braking distance by integration against v²/(2a).

Honest simplifications

Rigid truck without suspension roll, tyre compliance or mast flex; quasi-static tip criterion (dynamic overshoot and cargo swing are not modelled); steady-state steering. Not an operator-safety tool.

• Raise the lift to 2.5 m and turn: the tip limit on the lateral graph drops sharply.
• Shift the load sideways by 0.3 m: the margin shrinks on one side only.
• Choose Wet floor: the tyres slide before the truck can tip.