9,379 m/s -- ΔVtotal 6 m/s 0.043 ΔVdrag 2057 m/s 21.745 ΔVgravity assist 411 m/s 4.394 ΔVEarth 7727 m/s 82.606 ΔVleo Figure 4.2.2.1 shows a plot of the resulting trajectory and orbit for the 1 kg payload. Figure 4.2.2.1: Nominal trajectory and orbit for the 1 kg payload. (Allen Guzik) Besides the resulting the trajectory predicts, the important parameter other we require is ΔV the steering law coefficients. For D&C analysis we need these values to match the nominal ascending path the trajectory analysis calculates. These steering coefficients are found by optimizing the ending orientation of the vehicle. The orientation is defined by three angles, Ψ1, and where they represent and define the orientation of the vehicle at the end of the first, Ψ2, Ψ3, second, and third stages respectively. Figure 4.2.2.2 depicts how and define the Ψ1, Ψ2, Ψ3 orientation of the vehicle during the flight. Table 4.2.2.3 shows the steering angles defined for the nominal trajectory. Figure 4.2.2.2: steering law angle orientation definition. Ψ (Amanda Briden) Table 4.2.2.3 Angles from the Steering Law Variable Value Units End of 1st stage 30 deg End of 2nd stage -10 deg End of 3rd stage -10 deg From these steering angles the linear tangent steering law coefficients can be defined. Equation 4.2.2.1 defines the linear tangent steering law Trajectory uses. Eq. 4.2.2.1
ΔVtotal 9,379 m/s -- ΔVdrag 6 m/s 0.043 ΔVgravity 2057 m/s 21.745 ΔVEarth assist 411 m/s 4.394 ΔVleo 7727 m/s 82.606 Figure 4.2.2.1 shows a plot of the resulting trajectory and orbit for the 1 kg payload. Figure 4.2.2.1: Nominal trajectory and orbit for the 1 kg payload. (Allen Guzik) Besides the resulting ΔV the trajectory predicts, the important parameter other we require is the steering law coefficients. For D&C analysis we need these values to match the nominal ascending path the trajectory analysis calculates. These steering coefficients are found by optimizing the ending orientation of the vehicle. The orientation is defined by three angles, Ψ1, Ψ2, and Ψ3, where they represent and define the orientation of the vehicle at the end of the first, second, and third stages respectively. Figure 4.2.2.2 depicts how Ψ1, Ψ2, and Ψ3 define the orientation of the vehicle during the flight. Table 4.2.2.3 shows the steering angles defined for the nominal trajectory. Figure 4.2.2.2: Ψ steering law angle orientation definition. (Amanda Briden) Table 4.2.2.3 Angles from the Steering Law Variable Value Units End of 1st stage 30 deg End of 2nd stage -10 deg End of 3rd stage -10 deg From these steering angles the linear tangent steering law coefficients can be defined. Equation 4.2.2.1 defines the linear tangent steering law Trajectory uses. Eq. 4.2.2.1
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