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Test RT-10 “Hammer” Solid Fuel Booster in flight over Kerbin challenge (how to calculate how far I will go)


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I'm new to the game and successfully completed this challenge by fidgeting with the thrust limiter and the fuel but there must be a better way to do this.

 

The contract required me to reach an altitude between 9k-12k m and a speed between 490-560 m/s.

 

How can I calculate how far I will go and what speed I'll achieve at a certain height? It must be possible to do this.

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Testing a part like a solid booster is best done with it completely empty- attach it to another rocket and fly that up to the required speed and altitude, then stage the test booster to trigger the contract, and then parachute the whole thing back to the surface to get (most of) your money back.

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