Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag CD Dynamic Pressure [Pa] CD % error [%] 486.9 -99.4 38.3 1.38 54 298.1 -60.8 38.3 0.85 279 17 (Jayme Zott) References 1Sutton, George P., and Biblarz. Rocket Propulsion Elements. New York: John Wiley & Sons, Inc., 2001. 2The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No. 11022, April 1960.
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
Axial Force [N] Shear Force [N] Center of Pressure [% length] Coefficient of Drag CD Dynamic Pressure [Pa] CD % error [%] 335.7 -43.0 40.0 1.44 63 168.9 -21.6 40.0 0.81 240 21 (Jayme Zott) References: 1Sutton, George P., and Oscar Biblarz. Rocket Propulsion Elements. New York: John Wiley & Sons, Inc., 2001. 2The Martin Company, “The Vanguard Satellite Launching Vehicle”, Engineering Report No. 11022, April 1960.
make one complete revolution and the period for our orbit is 6038.7878 seconds which is about 1 hour and 40 minutes. The velocity needed to reach our orbit is measured in the change of velocity also know as ΔV. Table 4.3.2.2 breaks down the ΔV budget for the 5 kg case of Project Bellerophon. 4.3.2.2 ΔV Breakdown Variable Value Percent of ΔVtotal ΔVtotal 9354 m/s -- ΔVdrag 4 m/s 0.043 ΔVgravity 2034 m/s 21.745 ΔVEarth assist 411 m/s -4.394 ΔVleo 7727 m/s 82.606 The ΔVtotal is a combination of all the other ΔVs which are: ΔVdrag, ΔVgravity, ΔVEarth assist, ΔVleo. ΔVdrag refers to the velocity needed to overcome the drag which we will experience. This value seems incredibly low, and it should be that way because we are launching from a balloon at an altitude of 30 km. Since we are launching from so high in the atmosphere the air density is relatively low and does not cause much resistance to the launch vehicle. ΔVgravity is the velocity needed to overcome gravity drag. ΔVEarth assist refers to the velocity the Earth’s spin is helping the launch vehicle reach orbit. This is the only ΔV which is helping us, the other ΔVs are velocities we need to overcome. ΔVleo is the velocity needed to achieve our orbit. Figure 4.3.2.1 shows the entire orbit mentioned above. Fig 4.3.2.1: Full orbit of 5kg payload. (Kyle Donahue) In order to obtain any orbit a steering law is needed to put the rocket on the correct path. We created and used a linear-tangent steering law for each stage. There are many other types of steering laws besides linear-tangent. Other types of steering laws include linear with any of the