Lambda-4S

The Smallest Orbital Rocket

JSBSim L-4S-5 Flight Simulation

Note!
This is still a work in progress. These following numbers are likely wrong!

Based on digitized data from the orginal paper a JSBSim model is built and run. Here we compare the simulation results to charts in the technical papers.

Download a copy of the Lambda-4S JSBSim configuration:

Table of Contents:

Mass Table

This is the mass and moment of inertia table output by JSBSim’s initialization report:

Vehicle Component Weight [kg] CG-X [m] CG-Z [m] Ixx [kg·m²] Iyy [kg·m²] Izz [kg·m²]
Base Vehicle 23.0 0.556 0.000 0.3 0.4 0.4
0 Nose Faring 10.0 0.500 0.000 2.6 2.2 2.2
1 3rd Stage 273.9 1.941 0.000 69.6 235.2 235.2
2 2nd Stage 619.4 5.999 0.000 334.6 978.0 978.0
3 Right Booster 190.5 13.401 0.523 18.3 538.0 538.0
4 Left Booster 190.5 13.401 -0.523 18.3 538.0 538.0
5 1st Stage 1089.4 12.329 0.000 588.6 6671.0 6671.0
0 Solid Fuel 312.0 13.400 0.523 16.6 874.5 874.5
1 Solid Fuel 312.0 13.400 -0.523 16.6 874.5 874.5
2 Solid Fuel 3887.0 12.000 0.000 1127.7 21294.5 21294.5
3 Solid Fuel 1845.0 5.000 0.000 535.3 2727.6 2727.6
4 Solid Fuel 547.5 2.000 0.000 80.5 770.2 770.2
5 Solid Fuel 88.0 0.500 0.000 10.1 6.8 6.8
Totals: 9388.2 9.393 0.000 3093.2 185157.8 184883.4

First Stage Thrust

Total thrust of the first stage and strap-on boosters compared to the published L-4S-2 vehicle data.

The differences here are likely becuase of a couple of factors. I tried to use data that best fit the L-4S-5 vehicle, but here we’re compairing to L-4S-2. They should be pretty similar, but are many years apart. Secondly there is going to be a difference in the approximate sea-level thrust and the actual thrust JSBSim will compute based on altitude and nozzel expantion ratio.

First 5 km Altitude/Downrage Plot

The trajectory paper included several downrange vs altitude charts. The difference cases are for a variaty of launch angles. This should define an expected operating envelope for our vehicle.

First Stage Performance

The first stage, though burnout compared to the flight overview numbers.

Second Stage Performance

Third Stage Performance

Combined 1st–3rd Stage Performace