13 calculators for propulsion, aerodynamics, compressible flow and orbits, each with its equation, units and assumptions, plus a mission planner.
Idea and research by Deep Patel, a 12th grader. AI coding assistants wrote the code under his direction. How I built it
Play runs the 45 min coast in 8 seconds.
Assumes circular orbits in one plane, instant burns and Earth's gravity only. Altitudes are measured from Earth's mean radius, 6,371 km.
Hohmann transfer from 200 km to 408 km
| Step | Altitude (km) | Speed before (m/s) | Speed after (m/s) | Delta-v (m/s) | Time after burn 1 |
|---|---|---|---|---|---|
| Burn 1 | 200 | 7,788.5 | 7,848.9 | 60.4 | 0 min |
| Burn 2 | 408 | 7,608.1 | 7,668.1 | 60.0 | 45 min |
| Total | 120.4 |
For education only: the models are simplified and are not for operational or safety decisions. See the terms of use.
Current tool: Tsiolkovsky rocket equation
Foundations
Gives the ideal velocity change of a rocket stage from its mass ratio and specific impulse.
Delta v equals I s p times g zero times the natural log of m zero over m f.
(1.1)Compares available thrust with vehicle weight at a given instantaneous mass.
Thrust-to-weight ratio equals thrust over mass times g zero.
(2.1)Below one
TWR < 0.95
Weight exceeds thrust, so the vehicle cannot accelerate upward from rest in a vertical model.
Around one
0.95 ≤ TWR ≤ 1.05
Thrust approximately balances weight, leaving little ideal vertical acceleration margin.
Above one
TWR > 1.05
Current resultThrust exceeds weight, so upward acceleration is possible in the ideal vertical model.
Finds lift force from air density, airspeed, reference wing area and lift coefficient.
Lift equals one half times rho times V squared times S times C L.
(3.1)Works out aerodynamic drag from dynamic pressure, reference area and drag coefficient.
Drag equals q times S times C D, where dynamic pressure q equals one half rho V squared.
(4.1)Returns temperature, pressure and density at an altitude in the troposphere, using the standard-atmosphere model.
Temperature T equals T zero minus L times h. Pressure p equals p zero times T over T zero, raised to g zero over R L. Density rho equals p over R T. Speed of sound a equals the square root of gamma R T.
(5.1)Combines atmosphere, dynamic pressure, lift and drag into one flight-condition calculation.
Mach number M equals V over a. Dynamic pressure q equals one half rho V squared. Lift L equals q S C L and drag D equals q S C D.
(6.1)Atmosphere
Altitude determines temperature, pressure, density, and acoustic speed.
Flow state
Density and velocity determine dynamic pressure; velocity and acoustic speed determine Mach.
Forces
Shared flow state feeds the lift and drag modules.
Performance
Returned forces determine lift-to-drag ratio.
Compressible flow
Converts static atmospheric properties into stagnation conditions with isentropic-flow ratios.
T t over T equals 1 plus gamma minus 1 over 2 times M squared. p t over p equals that ratio raised to gamma over gamma minus 1. rho t over rho equals it raised to 1 over gamma minus 1.
(7.1)Shows the flow state downstream of a one-dimensional normal shock.
M 2 squared equals gamma minus 1 times M 1 squared, plus 2, all over 2 gamma M 1 squared minus the quantity gamma minus 1. The pressure ratio equals 1 plus 2 gamma over gamma plus 1, times M 1 squared minus 1. The density ratio equals gamma plus 1 times M 1 squared over gamma minus 1 times M 1 squared plus 2. The temperature ratio equals the pressure ratio times rho 1 over rho 2.
(8.1)Solves an attached weak oblique shock from upstream atmosphere, Mach number and deflection angle.
Tan theta equals 2 cot beta times M 1 squared sine squared beta minus 1, over M 1 squared times gamma plus cos 2 beta, plus 2. The normal Mach number M n 1 equals M 1 sine beta. M 2 equals M n 2 over the sine of beta minus theta.
(9.1)Models staged external compression followed by a terminal normal shock, with the recovery after each stage, and compares the inlet with one normal shock at the same Mach number.
Inlet recovery equals the external shock recovery times the terminal normal shock recovery, where the total pressure ratio across a shock equals gamma plus 1 times M n squared over gamma minus 1 times M n squared plus 2, raised to gamma over gamma minus 1, times gamma plus 1 over 2 gamma M n squared minus gamma minus 1, raised to 1 over gamma minus 1.
(10.1)Each pressure loss is 1 minus its recovery ratio. Values are rounded to four decimal places.
Estimates convective heating at the stagnation point from velocity, nose radius and standard-atmosphere density. The atmosphere model stops at 11 km, so this is not an entry heating history.
Heat flux equals k times the square root of density over nose radius, times velocity cubed. Mach number M equals V over a.
(11.1)Velocity has the strongest influence in this approximation, so modest speed increases can produce much larger heat flux.
Standard-atmosphere density falls with altitude, leaving fewer air particles available to transfer convective heat.
A larger, blunter radius spreads the stagnation region and lowers the model's predicted peak heating.
Orbits and missions
For two circular orbits in one plane, finds both burns and the coast time of a Hohmann transfer, and draws the transfer.
The transfer semi-major axis a t equals r 1 plus r 2 over 2. The circular speed squared at radius r is mu over r. The transfer-orbit speed squared at radius r is mu times 2 over r minus 1 over a t. Delta v 1 is the size of the transfer speed at r 1 minus the circular speed at r 1. Delta v 2 is the size of the circular speed at r 2 minus the transfer speed at r 2. Transfer time t equals pi times the square root of a t cubed over mu.
(12.1)The first burn puts the craft on an ellipse that touches both orbits. It coasts half way round, and the second burn makes the orbit circular at the new height. Total delta-v leaves out launch, drag, finite burns and course corrections.
Assumes two-body gravity, circular orbits in one plane, instant burns, no drag and no gravity assists.
Uses the circular-orbit speed at an altitude to find the delta-v for an impulsive inclination change.
Circular velocity v equals the square root of mu over r. Delta v equals 2 v times the sine of half the inclination change.
(13.1)A very demanding ideal maneuver relative to common spacecraft velocity budgets.
Plane-change delta-v rises with the orbital speed at the maneuver point. This display band is educational context only and does not determine mission feasibility.
A plane change redirects the spacecraft's velocity vector. When orbital speed is high, changing that direction requires a larger ideal velocity change, which is why mission designers often seek lower-speed locations for major inclination maneuvers.
Pick a preset mission or your own altitudes. The planner lists each step in flight order with its delta-v, computed or preset, and compares the presets on one axis.
Preset: Two-impulse transfer from parking orbit to circular low Earth orbit.
LEO satellite deployment (shown above)
ISS-style resupply
Lunar transfer concept
Mars transfer concept (preset allowances, not computed)
Delta-v by mission and step
| Mission | Step | Delta-v (m/s) |
|---|---|---|
| LEO satellite deployment | Burn 1 | 100.4 |
| LEO satellite deployment | Burn 2 | 99.1 |
| LEO satellite deployment | Total | 199.5 |
| ISS-style resupply | Burn 1 | 60.4 |
| ISS-style resupply | Burn 2 | 60.0 |
| ISS-style resupply | Total | 120.4 |
| Lunar transfer concept | Burn 1 | 3,133.1 |
| Lunar transfer concept | Burn 2 | 831.6 |
| Lunar transfer concept | Plane change | 88.8 |
| Lunar transfer concept | Total | 4,053.5 |
| Mars transfer concept | Departure orbit setup (allowance) | 200 |
| Mars transfer concept | Trans-Mars injection concept (allowance) | 3,600 |
| Mars transfer concept | Cruise correction allowance (allowance) | 100 |
| Mars transfer concept | Arrival capture concept (allowance) | 1,500 |
| Mars transfer concept | Total | 5,400 |
Assumes circular orbits, instant burns and Earth's gravity only. A plan lists delta-v; it does not say whether a mission is feasible.
