Boundary Fence Height: Climb Delay, Cost per Metre, and the Height at Which Extra Panels Stop Paying

A boundary fence delays rather than stops, and the useful question is how much delay each additional increment of height buys for its cost. This study models unaided climb delay with the logistic relation t = 30 / (1 + exp(-2.6 (h - 1.75))) seconds for height h in metres, and fence cost as USD 34 + 52 (h - 1.2)^1.25 per metre run, both stated relations. Delay rises from 5.8 seconds at 1.2 m to 16.0 seconds at 1.8 m and 25.3 seconds at 2.4 m, while cost rises from USD 34.0 to USD 99.31 per metre over the same span. Delay bought per USD 100 peaks at 2.0 m in the table. A trellis or angled topping adding a stated 9 seconds at any height improves the 1.8 m fence by 56.2 percent for USD 11 per metre, which is a better purchase than the final increment of panel height. The resulting guidance is to build to about 1.8 m where regulations allow, add a topping that is awkward to grip, and treat heights beyond about 2.2 m as spending on appearance and privacy rather than on delay. SIMULATED, NOT MEASURED.