Discharge curve — voltage vs. how much capacity you've pulled out. Each colored line is a fixed current; the bold emerald line is your configured draw. It shows how the pack's voltage sags down to the cutoff as it empties at that current.
Runtime curve — how many hours the pack lasts vs. the current you pull (log–log). The ★ operating point is your configured draw; the dashed line drops to the current axis.
Example: at 500 mA the runtime curve might read ~30 h, but doubling the draw to 1 A drops it well below half — that bend is Peukert's law: pulling harder wastes capacity.
A battery and a device have to agree on one voltage and current. The battery can only hand over a voltage that sags as you draw more current (the cyan source line). Your device demands a fixed power, so as the voltage sags it pulls more current (each colored load curve). The single point where a load curve crosses the source line is the only place the system can settle — that's the operating point, marked with a ★.
Load-line chart: follow a colored load curve to where it crosses the cyan line. If the ★ is above the red cutoff, that load runs; if the curve never reaches the source line, there's no ★ and the pack collapses under it.
Brown-down chart: each colored line is the loaded voltage as the pack drains (left → right). Where a line crosses the red cutoff is the % discharged at which that load browns out. The cyan no-load line above it shows how much voltage the load is costing you.
Example (defaults): a 12 V pack with R = 1 Ω, so the source line is V = 12 − I. Take Load2 = 20 W: the load needs 20/V, and setting 12 − I = 20/I gives I² − 12I + 20 = 0 → I = 2 A, V = 10 V (its ★), well above the 6 V cutoff. The four defaults (11/20/27/32 W) land on exactly 11/10/9/8 V at 1/2/3/4 A. The pack's ceiling is V²/4R = 36 W; push any load past that and its ★ vanishes — collapse.