tippingangle

Tippingangle is a term used to describe the critical incline angle at which a resting rigid body becomes unstable and tips about its lower edge under the influence of gravity. It is determined mainly by the position of the center of gravity (CG) and the geometry of the base of support.

In static conditions, tipping occurs when the vertical line through the CG passes outside the base of contact with the supporting surface. For a simple rectangular block with base width b along the slope and CG height h above the plane, the tipping angle θ is approximately arctan((b/2)/h). More generally, the tipping angle is found by locating the edge of the support polygon and ensuring the CG projection onto the plane coincides with that edge. If the CG is lower or the base is wider, θ increases, making tipping less likely.

Friction and dynamics play important roles. If the friction is insufficient, sliding may occur before tipping, preventing tipping at the static angle. In dynamic situations, accelerations along the plane alter the effective gravity, potentially lowering the tippingangle as inertial forces shift the CG projection.

Applications of tippingangle include assessing stability in furniture and packaging, vehicle and robot design, architectural safety, and geotechnical contexts such as slope stability. Understanding tippingangle helps engineers and designers ensure objects remain stable under expected inclines and loads.

See also: center of gravity, stability, base of support, tipping moment, critical angle.