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Motor

Battery Runtime (Motor Load)

Calculate battery runtime for motor-driven systems accounting for motor current draw, efficiency, and depth of discharge.

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Formula

t = C_usable / I_draw, C_usable = C × DoD

C— Battery capacity (mAh)
DoD— Depth of discharge (%)

How It Works

Battery runtime for a motor-driven system depends on the battery's usable energy capacity and the motor system's average power consumption. Runtime (hours) = (Battery capacity in Wh × DoD) / P_average, where DoD is the depth of discharge (typically 80% for lead-acid, 90% for Li-ion/LiFePO4). For a DC motor drawing current I at voltage V, P_average = V × I / η_system, where η_system accounts for motor, controller, and wiring losses. For variable-load applications, use average duty cycle power rather than peak power.

Worked Example

A 24 V robot with a 20 Ah LiFePO4 battery uses two drive motors drawing 8 A total at full speed, but runs at 60% duty cycle on average. Motor system efficiency is 82%. Step 1 — Battery usable energy: E_usable = V × Ah × DoD = 24 × 20 × 0.90 = 432 Wh Step 2 — Average electrical power drawn: P_elec = V × I_avg = 24 × (8 × 0.60) = 24 × 4.8 = 115.2 W Step 3 — Input power from battery (accounting for efficiency): P_battery = P_elec / η = 115.2 / 0.82 = 140.5 W Step 4 — Battery runtime: t = E_usable / P_battery = 432 / 140.5 = 3.08 hours Step 5 — Capacity check at C-rate: I_avg = P_battery / V = 140.5 / 24 = 5.85 A → 5.85/20 = 0.29C — well within LiFePO4 continuous discharge rating Result: The robot operates for approximately 3.1 hours on a full charge at 60% duty cycle.

Practical Tips

  • ✓Log actual current draw with a current sensor during representative operation cycles — real-world average current is almost always lower than worst-case estimates
  • ✓For Li-ion cells, limit depth of discharge to 80% for longest cycle life; NMC cells degrade rapidly below 2.8 V/cell during repeated deep discharges
  • ✓Add a 20–25% runtime safety margin to your calculated runtime when sizing the battery — allows for aging (capacity loss over charge cycles) and higher-than-expected loads

Common Mistakes

  • ✗Using peak motor current instead of average current — for a robot running at 60% duty cycle, this overestimates power consumption by 67% and underestimates runtime accordingly
  • ✗Ignoring controller and wiring losses — motor controller switching losses of 5–15% and cable resistance drops reduce actual runtime compared to motor-only calculations
  • ✗Forgetting that battery capacity drops significantly at high discharge rates (Peukert effect) — a 20 Ah lead-acid battery delivers only ~14 Ah at 2C discharge

Frequently Asked Questions

The Peukert effect describes how battery capacity decreases at higher discharge rates. It primarily affects lead-acid batteries (Peukert exponent 1.1–1.3) and to a lesser extent LiFePO4 (exponent ~1.05). At high C-rates, the effective capacity is lower, reducing runtime below the simple Wh/P calculation. Use manufacturer discharge curves at the appropriate C-rate for accurate estimates.
Size the battery energy (Wh) for average power consumption to meet runtime goals. Size the battery's continuous current rating for peak current draw to avoid excessive voltage sag. For pulsed loads, add bulk capacitance to absorb current peaks so the battery sees only smoothed average current.
Battery capacity decreases at low temperatures: a Li-ion cell delivers roughly 80% of rated capacity at 0 °C and 60% at −20 °C. Lead-acid batteries are even more sensitive. High temperatures (above 45 °C) accelerate capacity degradation over time. For outdoor applications, derate battery capacity and add thermal management for best results.

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