Aerospace model

Delta-V

The minimum-energy Hohmann orbital transfer and a 3-stage rocket's total delta-v budget - real orbital mechanics from the vis-viva and Tsiolkovsky equations, computed in pure C#.

How to read it: each burn is the velocity change (delta-v, in m/s) an engine must supply. The panel on the right is the program's real captured run - the two headline totals on the left are the numbers to compare against the textbook values.

dotnet run --project KullGames.DeltaV -c Release

KullGames.DeltaV -- Hohmann transfer + multi-stage rocket budget
using OnlyCSharp.Engineering.Aerospace (1.8)
==================================================================

[1] Hohmann transfer: 200 km LEO -> GEO
    r1 (LEO) = 6,578,000 m   r2 (GEO) = 42,164,000 m
    burn 1 (leave LEO):        2,454.6 m/s  (2.455 km/s)
    burn 2 (circularize GEO):  1,477.3 m/s  (1.477 km/s)
    total Delta-v:             3,931.9 m/s  (3.932 km/s)
    well-known real-world value: ~3.9 km/s

[2] Multi-stage rocket: 3-stage serial Delta-v budget
    payload: 1,200 kg
    stage 1 (booster    ) Isp= 290s  prop=  180,000 kg  dry=  9,000 kg  ->  Delta-v =  4,564.5 m/s
    stage 2 (upper stage) Isp= 320s  prop=   30,000 kg  dry=  2,200 kg  ->  Delta-v =  5,516.4 m/s
    stage 3 (kick stage ) Isp= 420s  prop=    2,500 kg  dry=    350 kg  ->  Delta-v =  3,955.9 m/s
    sum of per-stage Delta-v:     14,036.9 m/s
    MultiStage.SerialDeltaV():    14,036.9 m/s
    breakdown matches total: True

[bonus] same propellant/structure, single non-staged engine (Isp=290s):
    Delta-v =  8,166.9 m/s -- staging gains 5,870.0 m/s

==================================================================
Summary:
  Hohmann LEO->GEO transfer:   3.932 km/s (real-world ~3.9 km/s)
  3-stage rocket total budget: 14.037 km/s for a 1,200 kg payload

What this computes

A Hohmann transfer is the minimum-energy way between two circular orbits: one burn to enter an elliptical transfer orbit, then a second burn at apogee to circularize. Each burn falls straight out of the vis-viva equation.

The Tsiolkovsky rocket equation - dv = Isp * g0 * ln(m0 / mf) - shows why rockets stage: the mass ratio sits inside a logarithm, so dragging spent tanks along punishes you badly. Shedding dead structure between stages here buys an extra 5.87 km/s over the same propellant burned as one engine.

This is a static render of the program's real captured output. All physics comes from OnlyCSharp.Engineering.Aerospace (1.8) - pure C#, nothing outside the .NET base class library.