Warship Transit Formulas

Helper notes for calculating warship propulsion and transit values from dd.xlsx.

The spreadsheet contains several transit blocks. The most useful card-level profiles use the ship’s own delta-v budget and tactical acceleration.

Source Cells

Per ship sheet:

Field	Spreadsheet source	Meaning
Total mass	B2	Wet mass, metric tons
Dry mass	B3	Dry mass, metric tons
Mass ratio	B4 = B2 / B3	Wet/dry mass ratio
Exhaust velocity	B5	Exhaust velocity, m/s
Total delta-v	B6 = B5 * LN(B4)	Total available delta-v, m/s
Total delta-v	B7 = B6 / 1000	Total available delta-v, km/s
Tactical acceleration	G17	Assumed tactical acceleration, m/s^2
Thrust	G18 = B2 * 1000 * G17 / 1000000	Thrust required for tactical acceleration, MN
Drive power	G22 = (G20 * G21) / 2	Drive power, MW; with G20 in MN and G21 in m/s

The older visible transit blocks use fixed, scenario-level acceleration values and are useful as examples, but less useful as card data because they do not depend strongly on each ship.

Constants

AU_M = 149597870691
REFERENCE_DISTANCE_AU = 5
REFERENCE_DISTANCE_M = REFERENCE_DISTANCE_AU * AU_M
BURN_COAST_BURN_TOTAL_BURN_H = 50
BURN_COAST_BURN_HALF_BURN_S = 25 * 3600

Delta-v

delta_v_m_s = exhaust_velocity_m_s * ln(total_mass_t / dry_mass_t)
delta_v_km_s = delta_v_m_s / 1000

Tactical Thrust And Power

thrust_MN = total_mass_t * 1000 * tactical_acceleration_m_s2 / 1000000
drive_power_MW = thrust_MN * exhaust_velocity_m_s / 2
drive_power_PW = drive_power_MW / 1000000000

Pure Brachistochrone / Flip-And-Burn Profile

Use a symmetric accelerate/decelerate transfer over a reference distance, accelerating for the first half and decelerating for the second half.

required_dv_m_s = 2 * sqrt(reference_distance_m * tactical_acceleration_m_s2)
total_time_s = 2 * sqrt(reference_distance_m / tactical_acceleration_m_s2)
burn_time_s = total_time_s
coast_time_s = 0
peak_velocity_m_s = sqrt(reference_distance_m * tactical_acceleration_m_s2)
delta_v_reserve_m_s = delta_v_m_s - required_dv_m_s

If delta_v_reserve_m_s is negative, the ship cannot fly this pure brachistochrone profile at the listed tactical acceleration without exceeding its delta-v budget.

Fixed-Burn Burn-Coast-Burn Profile

For a fixed total burn duration of 50 h, split into 25 h acceleration and 25 h deceleration:

burn_time_each_s = 25 * 3600
burn_time_total_s = 2 * burn_time_each_s
delta_v_used_m_s = 2 * tactical_acceleration_m_s2 * burn_time_each_s
peak_velocity_m_s = tactical_acceleration_m_s2 * burn_time_each_s
burn_distance_m = tactical_acceleration_m_s2 * burn_time_each_s^2
coast_distance_m = reference_distance_m - burn_distance_m
coast_time_s = coast_distance_m / peak_velocity_m_s
total_time_s = burn_time_total_s + coast_time_s
delta_v_reserve_m_s = delta_v_m_s - delta_v_used_m_s

If coast_distance_m is negative, the fixed burn is too long for that distance at the selected acceleration. If delta_v_reserve_m_s is negative, the ship does not have enough delta-v for the profile.

Maximum Flip-and-Burn Range

This is the maximum distance the ship can cover using a pure accelerate/decelerate profile at tactical acceleration without coasting:

max_flip_burn_distance_m = (delta_v_m_s / 2)^2 / tactical_acceleration_m_s2
max_flip_burn_distance_au = max_flip_burn_distance_m / AU_M

This value is useful because it shows whether a ship can cross a given theater under continuous acceleration, or whether it must coast.