To get started in astrophysics, it is mandatory to have good simulator. That is why we have created a simple simulator with minimum performances. My brother Juan have programmed a Visual Basic application based on OpenGL with the equations I have provided to him. You can configure basic launch parameters and see the results in a 3D environment.
The aim of this article is to show how the launch parameters can affect in the cost and time for a standard mission to the Moon with a pay load like a PicoRover of 500 grams. There is a trade-off between time of travel and cost due to the propellant mass. Also there is a trade-off between propellant mass and technology required to implement such ultralight launcher.
Using an APCP (solid-propellant) first stage:
Weight .. Cost .. Stg1 .. Start-End .. at .. Hover DryW .. Time .. Dimensions
3020 kg 102103$ APCP 52-90º 18-60km 14.5kg 20% 1:00:01 7.31m x 80.84cm
1470 kg 49636$ APCP 46-90º 16-60km 9.5kg 20% 2:11:48 5.75m x 63.59cm
552.0kg 18656$ APCP 43-90º 18-59km 2.5kg 20% 1:12:03 4.14m x 45.88cm
373.0kg 12603$ APCP 43-90º 19-59km 1.6kg 20% 2:00:23 3.64m x 40.26cm
255.0kg 8617$ APCP 38-90º 18-58km 0.9kg 10% 2:12:27 3.20m x 35.47cm
234.5kg 7923$ APCP 38-90º 18-58km 0.8kg 10% 3:13:26 3.11m x 34.49cm
234.0kg 7906$ APCP 38-90º 18-58km 0.8kg 10% 4:02:59 3.11m x 34.46cm
234.0kg 7906$ APCP 38-90º 18-58km 0.8kg 10% 4:02:59 3.11m x 34.46cm
Using a MMH (bi-propellant) first stage:
Weight .. Cost .. Stg1 .. Start-End .. at .. Hover .. DryWeight .. Total Time
119.5kg 1096$ MMH 39-90º 19-63km 0.9kg 10% 2:11:20 2.62m x 27.55cm
110.0kg 1009$ MMH 39-90º 19-63km 0.8kg 10% 3:15:29 2.55m x 26.80cm
110.0kg 1009$ MMH 39-90º 19-63km 0.8kg 10% 3:15:29 2.55m x 26.80cm
109.8kg 1007$ MMH 39-90º 19-63km 0.8kg 10% 4:05:38 2.54m x 26.78cm
These are the parameters.
Weight: Is the total weight included hover and payload
Cost: Is only the costdue to the propellant. Development, construction and operation cost not included
Stg1: Is the type of propellant. Hover is always MMH because landing control requires liquid propelant
Start-End: Is the angle of thrust from an initial angle to the final angle in degrees. The initial angle is when the engine starts respect to the zenith vector at a given altitude. The final angle is when the engine is stopped t a given altitude and also respect to the zenith vector.
at: Is the range of altitudes when the launcher angle is set respect to the zenith vector from an initial angle at he initial ltitude to the final angle in the final altitude in kilometers.
Hover: Is the total weight of the Hover in kilograms without payload
Hover-DryWeight: Is the percent in weight of structure, instruments, etc. Payload not included
Total Time: Is the time required to land in the Moon
Dimensions: Is the length in meters and the diameter of the launcher in centimeters
This is an example of optimum trajectory of minimum energy:
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