Energy travels with the propellant.
Combustion or decomposition heats the exhaust. For a chosen 350 s example, vₑ = 3.432 km/s. Include oxidizer in consumed mass. This is often the right comparison for short, forceful burns.
01 / Mission calculator
Ideal · single stageAvailable ideal delta-v
7.903 km/s
90% propellant10% retained
- Propellant consumed
- 90 t
- Mass ratio / m₀ ÷ mꜰ
- 10
- Initial / post-burn mass
- 100 t / 10 t
- Effective exhaust velocity
- 3.432 km/s
- Thrust
- 1 MN
- Propellant mass flow
- 291.3 kg/s
- Total engine-on time
- 308.9 s
- Ideal directed jet power
- 1.716 GW
- Initial acceleration
- 10 m/s²
- Final acceleration
- 100 m/s²
Constant thrust and exhaust velocity. Burn duration is engine-on time, not a journey time.
Faster exhaust. Less mass. Less push.
The same delta-v; thrust compared at the current ideal jet power.
Propellant fractionThrust at fixed jet power
Model: constant effective exhaust velocity and thrust, with no gravity, drag or steering losses. Jet power assumes a nonrelativistic axial exhaust stream with negligible pressure thrust, using effective exhaust speed as the axial speed. It is an ideal comparison, not a measured power requirement for every engine. Equations and limits ↓
Isp → exhaust speed
vₑ = Isp × g₀g₀ = 9.80665 m/s² everywhereRequired mass ratio
m₀ / mꜰ = e^(Δv / vₑ)Final mass includes payloadPropellant fraction
1 − e^(−Δv / vₑ)Fraction of initial wet massIdeal jet power
Pⱼ = ½ F vₑAxial jet model; see assumptions02 / Choose the mechanism
Propulsion, on one scale.
Isp measures impulse delivered per unit propellant weight. It does not measure thrust, travel time or electrical efficiency. Use the numbers below to orient a design, then use the operating point of a particular engine.
| Mechanism | Isp / exhaust speed | Thrust | Basis & decision |
|---|---|---|---|
| Cold gas | 40–110 s | 10 μN–3.6 N | Small-spacecraft survey. Simple small impulses; expensive in propellant for large delta-v. [1] |
| Hydrazine monopropellant | 180–285 s | 0.25–28 N | Small-spacecraft survey. Catalytic decomposition; handling and feed systems matter. [1] |
| Solid motor | 187–269 s | 37–461 N | Small-spacecraft survey. Use a specified impulse package; do not assume restart or throttle. [1] |
| Electrothermal | 20–350 s | 0.1 mN–1 N | Small-spacecraft survey. Electric heating; performance depends on working fluid and temperature. [1] |
| Electrospray | 225–3,000 s | 20 μN–20 mN | Small-spacecraft survey. Precision impulses; avoid treating all emitted droplets as identical ions. [1] |
| Gridded ion | 500–3,000 s | 0.1–20 mN | Small-spacecraft survey. Propellant savings when sustained electrical power is available. [1] |
| Hall effect | 200–1,920 s | 0.25–55 mN | Small-spacecraft survey. Compare complete systems and their power supply. [1] |
| Hydrogen nuclear thermal | ≈900 s or more | Design dependent | NASA 2015 NTR design assessment, not a flown engine specification. Reactor heats expelled hydrogen. [5] |
| Direct Fusion Drive | 56.5 km/s ≈5,761 s, derived | 40 N, proposed | Razin et al. 2014 design point. Fusion products plus added propellant; not demonstrated performance. [6] |
| Long Passage Titan design | 200 km/s ≈20,394 s, derived | 63.7 kN, assumed | Fictional colony ship. An ambitious challenge value, not a prediction or a DFD specification. Explore the ship ↓ |
The power plant comes along.
At an assumed 30 km/s exhaust and 1 MW directed jet power, F = 66.67 N. At 60% source-to-jet efficiency that needs 1.667 MW input. Power-supply mass belongs in post-burn mass.
Energy source and nozzle are separate choices.
A fission reactor can heat hydrogen directly or supply electricity to ion thrusters. A fusion concept can add reaction mass. “Nuclear” alone does not specify Isp, thrust or efficiency.
03 / Follow the arithmetic
Three burns, very different constraints.
Spend nine tenths of the mass.
Assume 100 t initially, 10 t after the burn, Isp 350 s and constant 1 MN thrust. These are teaching inputs, not a named rocket.
Δv = 350 × 9.80665 × ln(10)
7.903 km/s
90 t consumed; ṁ = 291.347 kg/s; engine-on time 308.91 s. Thrust acceleration rises from 10 to 100 m/s² as mass falls. The high final acceleration may constrain a real design.
Spend time to save propellant.
Assume 1,200 kg initially, 1,000 kg after the burn, Isp 3,000 s and constant 0.1 N thrust. This is an illustrative electric spacecraft.
Δv = 29,419.95 × ln(1.2)
5.364 km/s
200 kg consumed; initial acceleration 0.00008333 m/s². The burn takes 681.02 days at 100% duty cycle, with 1.471 kW ideal jet power. Real trajectories and duty cycles change the calendar time.
A little fuel; a lot of exhaust mass.
Fictional design / challengeTitan assumes a 10,000 t ship, 100 km/s ideal delta-v, 200 km/s exhaust and 63.7 kN thrust.
mꜰ = 10,000 × e^(−100/200)
3,934.69 t
That is expelled mass, mainly added hydrogen; 6,065.31 t remains. Ideal jet power is 6.37 GW. This rounded constant-thrust case takes 142.98 burn days, not the trip's elapsed time.
04 / Working reference
The equations behind the desk.
1. Ideal delta-v
Δv = vₑ ln(m₀ / mꜰ)Natural log; masses in matching units, vₑ and Δv in matching speed units. At mass ratio 2 and vₑ = 3 km/s, capability is 2.079 km/s. Gravity, drag and steering losses require their own model. [2]
2. Solve the mission backwards
m₀ = mꜰ e^(Δv/vₑ)mₚ = mꜰ [e^(Δv/vₑ) − 1]
For 10 t final mass, 3 km/s required and 3 km/s exhaust, start with 27.183 t and consume 17.183 t. “Final” means everything still aboard, including reserves. [2]
3. Isp is a velocity in disguise
vₑ = Isp g₀g₀ = 9.80665 m/s²
350 s converts to 3,432.3275 m/s. Seconds are a reporting convention, not a burn duration. Use the same standard g₀ on Titan, Earth and in deep space. [3] [4]
4. Mass flow and burn duration
ṁ = F/vₑt = mₚ/ṁ
100 N at 20 km/s consumes 0.005 kg/s; 1,000 kg lasts 200,000 s, or 2.315 days. This assumes constant thrust and exhaust velocity, no shutdowns and no propellant lost elsewhere. [3]
5. Acceleration increases during the burn
a(t) = F/[m₀ − ṁt]At fixed 100 N, a spacecraft falling from 2,000 to 1,000 kg goes from 0.05 to 0.10 m/s² thrust acceleration. The tool reports thrust acceleration, not net acceleration in a gravity field. Mass stays positive through the specified burn.
6. Faster exhaust has a power cost
Pⱼ = ½ ṁvₑ² = ½ FvₑF = 2Pⱼ/vₑ
At 1 MW directed jet power, 10 km/s gives 200 N; 100 km/s gives 20 N. These use a single axial exhaust speed. Plume divergence, velocity spread and pressure thrust complicate a real power budget. [7]
7. Source power and rejected heat
Pᵢₙ = Pⱼ/ηPₗₒₛₛ = Pᵢₙ − Pⱼ
If 60% of 10 MW input becomes directed jet power, the jet carries 6 MW and the other 4 MW leaves by other channels. Only the part deposited aboard loads the radiators. Never label jet power as reactor thermal power.
8. Pressure thrust changes the interpretation
F = ṁvₐₓ + (pₑ − pₐ)Aₑvₑ,eff = F/ṁ
Effective exhaust velocity includes pressure thrust. It need not equal the actual exhaust speed vₐₓ. The rocket equation can use effective velocity, but ½Fvₑ,eff is only an equivalent jet-power estimate when those velocities differ. [3]
What about staging, solar sails and relativistic rockets?
Staging: calculate each stage's delta-v and add the magnitudes for aligned ideal burns; upper stages and payload count in the lower stage's final mass. Jettisoned hardware changes the next stage's mass accounting.
Solar sails: photon momentum is supplied externally, so this consumed-propellant rocket equation is not their mission model.
Relativistic motion: these are Newtonian equations. The calculator limits exhaust and delta-v to 1,000 km/s and mass ratio to 10¹²; those are tool bounds, not feasibility claims. Very large propellant loads will usually fail structural or power constraints long before reaching the numeric bounds.
05 / Common mistakes
Eight ways to design the wrong spacecraft.
Calling delta-v “top speed”
5 km/s of capability is a velocity-change budget. Your starting orbit, burn directions and gravity determine actual speed. A braking burn uses capability too.
Calling burn time “time to Saturn”
143 engine-on days can be split around a coast and arrival burn. A real Earth–Saturn itinerary also needs departure geometry and a trajectory solution.
Confusing high Isp with high thrust
At the same 1 MW jet power, raising exhaust from 10 to 100 km/s cuts ideal thrust tenfold. A propellant-efficient engine can still accelerate slowly.
Counting fuel but forgetting oxidizer
A hypothetical 1 t methane load paired with 3.6 t oxygen consumes 4.6 t in total. Nuclear and electric systems separate energy fuel from expelled reaction mass.
Using destination gravity to convert Isp
350 s means 3.432 km/s exhaust by the standard g₀ convention. A weaker local gravity changes weight and landing requirements, not that conversion.
Leaving the power plant out of final mass
At 10 t retained mass, adding a 5 t power system raises retained mass to 15 t. Higher Isp must pay for engines, tanks, conversion systems and thermal hardware.
Mixing an impulsive delta-v with a low-thrust route
An electric spiral does not generally have the same delta-v or duration as a short-burn transfer. This tool sizes an assumed delta-v; it does not optimize the trajectory.
Comparing numbers from different operating points
Use thrust and Isp from the same throttle setting and ambient condition. A catalogue's maximum thrust and maximum Isp may describe different tests.
06 / Put the equations in a world
Meet the fleet
that made you do the math.
Titan 2100 is David Veksler's browser-explorable vision of a Saturn-system civilization. Its ships are fictional designs built around explicit physics and ambitious engineering assumptions.
Design values, not real missions
The calculator's Long Passage preset treats 200 km/s exhaust and 63.7 kN thrust as challenge/design values. Its 6.37 GW ideal jet power is a calculated requirement, not evidence of an available engine.
The generated Titan budget separately tracks fusion fuel and thousands of tonnes of added hydrogen reaction mass. That distinction explains why an energy-dense reaction does not make the propellant tanks disappear.
Primary sources / basis
Where the numbers come from.
- NASA, Small Spacecraft Technology: In-Space Propulsion, Table 4-1 and mechanism descriptions. Survey ranges accessed November 2026; they describe selected small systems rather than all engines.
- NASA Glenn, Ideal Rocket Equation. Constant-exhaust relation and inverse mass ratio. Teaching examples here are computed from the displayed inputs.
- NASA Glenn, Specific Impulse. Isp convention, mass flow, pressure thrust and effective velocity.
- BIPM/JCGM, VIM §2.12. Standard acceleration of free fall, 9.80665 m/s², as a conventional quantity value.
- NASA, Affordable Development and Demonstration of a Small NTR Engine and Stage (2015). Approximately 900 s or more is an NTR design capability, not a current flight specification.
- Razin et al., A Direct Fusion Drive for Rocket Propulsion (2014), Acta Astronautica 105. The abstract's 40 N and 56.5 km/s are a proposed design point. Titan's 200 km/s is a separate challenge assumption.
- NASA NTRS 19760011112, electric propulsion study, p. 85. Pⱼ = ½Fvₑ, efficiency and the thrust/power tradeoff.
- Titan's generated vehicle budget, snapshot November 2026. Fictional inputs for Long Passage, cargo tug and ascent vehicle. Calculations on this sheet use unrounded equations, so rounded published totals can differ slightly.