Battery Sizing

Battery Sizing (vehicle-design/sizing/battery-sizing)

Use when the task is sizing the traction battery pack of an electric aircraft or eVTOL at the conceptual level: converting the mission energy draw into a required pack energy through the depth of discharge and the discharge efficiency, adding the reserve, laying out the series and parallel cell arrangement for the target pack voltage, checking the discharge C-rate against the cell capability, verifying the minimum cell voltage under the peak load against the cutoff with the cell internal resistance, and estimating the pack mass and volume from typical cell and pack energy densities. This leaf implements the model in pure Python, stdlib only, in scripts/battery_sizing_logic.py. It pairs with vehicle-design/sizing/fuel-tank-sizing as the energy storage counterpart for conventionally fueled aircraft and with vehicle-design/sizing/weight-estimation for carrying the pack mass into the vehicle mass budget; the mission energy itself comes from vehicle-design/conceptual/sizing-mission-profile.

Domain quick reference

• Required pack energy: E_pack_req = E_mission * (1 + reserve) / (DOD_MAX * EFF_DISCHARGE). The depth of discharge limit keeps the pack inside the cycle-life window and the discharge efficiency converts stored energy into energy delivered to the load.
• Series cells: n_s = round(V_target / V_nom), the integer series count that reaches the nominal pack voltage target.
• Parallel cells: n_p = ceil(E_pack_req * 1000 / (n_s * V_nom * C_ah)), the integer number of parallel strings that covers the required energy with the cell energy per string.
• Installed pack energy: E_pack = n_s * n_p * V_nom * C_ah / 1000 (kWh), the as-built energy after the count rounding.
• Energy margin: E_usable = E_pack * DOD_MAX * EFF_DISCHARGE against E_required = E_mission * (1 + reserve); pass when usable covers the required energy.
• Discharge C-rate: C = P_max / E_pack against the cell max C-rate; pass when C <= C_max.
• Voltage drop under load: I_total = P_max * 1000 / V_pack, I_branch = I_total / n_p, drop = I_branch * R_internal, V_min = V_nom - drop; pass when V_min >= V_cutoff.
• Mass and volume: cell mass = E_pack / gravimetric cell density, pack mass = E_pack / gravimetric pack density, and the same split with the volumetric densities for volume. The density constants are documented typicals for NMC lithium-ion cells; actual cells vary and the estimates must be re-run with supplier data.
• Discharge heat (simple check only): Q = THERMAL_LOSS_FRACTION * P_max * t. Thermal management system design is out of scope.
• FAR 25 and CS 25 frame the energy storage and electrical system certification context for transport category airplanes; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the design mission: mission energy E_mission (kWh), reserve fraction (for example 0.20 for 20 percent), peak discharge power P_max (kW), and the target nominal pack voltage V_target (V).
2. Define the cell: nominal voltage V_nom, capacity C_ah, internal resistance R_internal, cutoff voltage V_cutoff, and max C-rate.
3. Convert the mission draw to the required pack energy with required_pack_energy; the reserve rides on top of the mission draw before the depth of discharge and efficiency division.
4. Lay out the pack: series_cells for the series count at the target voltage, then parallel_cells for the strings that cover the required energy, then pack_energy_kwh for the as-built installed energy.
5. Check the energy margin with energy_margin (usable against required including the reserve).
6. Check the discharge C-rate with c_rate_check against the cell limit.
7. Verify the minimum cell voltage under the peak load with voltage_drop_check against the cutoff.
8. Estimate the pack mass and volume with mass_estimate and volume_estimate for the vehicle mass budget and installation envelope, and run thermal_estimate for the discharge-loss heat check when the load duration is known.
9. Run size_battery for the full sizing dict and the overall verdict, which FAILs with its reasons when any of the three checks fails.
10. Confirm the deterministic checks with the contract test scripts/test_battery_sizing.py.

Worked example

eVTOL design mission: E_mission = 50 kWh, reserve 0.20, P_max = 400 kW, V_target = 400 V. Cell: V_nom 3.7 V, 5 Ah, 0.002 ohm internal resistance, 3.0 V cutoff, 4 C max.

• Required pack energy: E_pack_req = 50 * 1.2 / (0.8 * 0.95) = 78.947 kWh.
• Series cells: n_s = round(400 / 3.7) = 108 (108 * 3.7 = 399.6 V).
• Parallel cells: n_p = ceil(78947 / (108 * 3.7 * 5)) = ceil(39.51) = 40.
• Installed pack energy: 108 * 40 * 3.7 * 5 / 1000 = 79.92 kWh.
• Energy margin: usable 79.92 * 0.8 * 0.95 = 60.74 kWh against the required 50 * 1.2 = 60 kWh, margin 0.74 kWh, pass.
• C-rate at 400 kW: 400 / 79.92 = 5.01 C against the 4 C limit, FAIL. At 300 kW the C-rate is 300 / 79.92 = 3.75 C, pass.
• Voltage drop: I_total = 400000 / 399.6 = 1001 A, I_branch = 1001 / 40 = 25.0 A, drop = 25.0 * 0.002 = 0.05 V, V_min = 3.65 V against the 3.0 V cutoff, pass.
• Mass: cell level 79.92 / 0.25 = 319.7 kg, pack level 79.92 / 0.18 = 444.0 kg. Volume: cell level 145.3 L, pack level 266.4 L.
• Overall verdict for the 400 kW case: FAIL with the C-rate reason; the 300 kW case passes all checks.

Pitfalls

• Sizing energy without the reserve and the DOD chain: the required pack energy is E_mission * (1 + reserve) / (DOD_MAX * EFF_DISCHARGE), so a pack sized on raw mission energy alone is roughly a factor DOD * efficiency too small (50 kWh mission needs 78.95 kWh in the worked example).
• Checking only the energy margin: size_battery FAILs when ANY of the three checks fails - the worked 400 kW case has a passing energy margin and voltage drop yet fails on the 5.01 C discharge rate against the 4 C cell limit.
• Forgetting the count rounding on the energy: n_s rounds while n_p ceils, and the installed pack energy (79.92 kWh) comes from the rounded counts, not from the required value; the usable-versus- required margin is checked against the as-built pack.
• Ignoring the branch current in the voltage drop: the drop uses the per-string current I_total / n_p times the internal resistance (25.0 A * 0.002 ohm = 0.05 V in the worked example), so a parallel-count slip changes the minimum cell voltage under load.
• Quoting the density estimates as datasheet values: the mass and volume constants are documented NMC lithium-ion typicals (0.25 and 0.18 kg/kWh cell and pack levels) and must be re-run with supplier data for a real cell.
• Confusing this traction pack with spacecraft storage: this leaf covers aircraft and eVTOL traction batteries; the spacecraft eclipse battery chain belongs to space-systems/subsystems/ spacecraft-battery-sizing.

Verification

• Confirm required_pack_energy(50, 0.2) returns 78.947 kWh within 1e-6.
• Confirm series_cells(400, cell) returns 108 and parallel_cells on the required energy returns 40, with the installed pack energy 79.92 kWh.
• Confirm the energy margin dict reports usable 60.74 kWh at least the required 60 kWh and passes.
• Confirm c_rate_check(400, 79.92, cell) rounds to 5.01 C and fails the 4 C limit, while the 300 kW case rounds to 3.75 C and passes.
• Confirm voltage_drop_check reports about 0.05 V drop and a 3.65 V minimum cell voltage, passing the 3.0 V cutoff.
• Confirm mass_estimate returns 319.7 kg cell level and 444.0 kg pack level for the 79.92 kWh pack.
• Confirm size_battery gives the overall FAIL verdict with the C-rate reason at 400 kW and PASS at 300 kW.
• Confirm every non-positive mission energy, power, voltage and cell value, every negative reserve, and every missing or unknown cell key raises ValueError.
• Run the contract test offline: python3 scripts/test_battery_sizing.py (31 tests, deterministic).

Related leaves

• vehicle-design/sizing/fuel-tank-sizing: liquid fuel energy storage counterpart for conventionally fueled aircraft.
• vehicle-design/sizing/weight-estimation: carries the pack mass into the vehicle weight and balance budget.
• vehicle-design/conceptual/sizing-mission-profile: the source of the mission energy and power requirements.
• vehicle-design/sizing/engine-sizing: propulsion power sizing boundary; the pack is sized from the resulting power draw, not the engine or motor itself.
• space-systems/subsystems/power-thermal-budget and space-systems/subsystems/solar-array-sizing: the spacecraft electrical power system side owns eclipse batteries and solar arrays; this leaf covers aircraft and eVTOL traction storage only.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_battery_sizing.py

The test covers the worked-example sizing contract (required pack energy 78.947 kWh, 108 series and 40 parallel cells, 79.92 kWh pack, usable 60.74 kWh against 60 kWh required, C-rate fail at 400 kW and pass at 300 kW, voltage drop 0.05 V with a 3.65 V minimum against the 3.0 V cutoff, 319.7 kg cell and 444.0 kg pack mass), the energy margin branches, C-rate and voltage drop boundaries, mass, volume and thermal estimates, the overall verdict for both power cases, and ValueError rejection of non-positive mission energy, power, voltage and cell values, negative reserve, and missing or unknown cell keys.

Compliance

• Standards referenced, not reproduced: FAR 25 and CS 25 frame the transport category energy storage context; the sizing relations above are standard engineering methodology, summary-only per standards-map.yaml. The battery energy density constants are documented typical values (NMC lithium-ion); actual cells vary.
• compliance: STANDARDS-REF, gated: false.