## Energy requirements for orbital inclination change

Using equation (5.11), the variation in incremental velocity with altitude as a function of plane change angle is given in Figure 5.12 for five orbital altitudes, from 100 nautical miles (185.2 km) to 19,323 nautical miles (35,786 km). For a 90-degree plane change at 100 nautical mile orbital altitude the incremental velocity is just over 35,000 ft/s (10,668 m/s). Compare that to the incremental velocity for the orbital altitude change from 100 nautical miles to 19,323 nautical miles of 12,900 ft/s (3,992m/s) in Figure 5.7. So the incremental velocity requirements for a orbital plane change are much more demanding than an orbital altitude change. For an Plane Change Angle (degrees)

Figure 5.12. Velocity increment to rotate orbital plane for different orbital altitudes. Higher altitude requires less energy.

Plane Change Angle (degrees)

Figure 5.12. Velocity increment to rotate orbital plane for different orbital altitudes. Higher altitude requires less energy.

incremental velocity of 12,900 ft/s an orbital plane change of about 29 degrees is possible. That is, less plane change than required to move from the latitude of NASA Kennedy to the latitude of the International Space Station.

Shown in Figure 5.13 is an impulse turn made from the GSO orbital altitude of 19,323 nautical miles (35,786 km), which requires about 11.5 hours to execute. This is one of the lower-energy solutions for the plane change. Increasing the altitude for the impulse turn to 36,200 nautical miles (67,042 km) decreases the incremental velocity to about 1,000 ft/s (304.8 m/s) but increases the mission time to 24 hours. As shown, the breakeven orbital plane change is 50 degrees. So if the orbital plane change is less than 50 degrees, it is best made from the spacecraft's orbital altitude, without any orbital altitude change. However, there remains the interesting possibility of using aerodynamics to change orbital plane.

The aerodynamic plane change requires slowing the hypersonic glider to about 22,000 ft/s (6,706 m/s) so it can enter the upper atmosphere between 240,000 and 260,000 ft (73,152 to 79,248 m) altitude. At that point the rocket engines are ignited, and a thrust-equals-drag turn at the lift coefficient corresponding to maximum lift-to-drag is initiated, turning through the orbital plane change angle desired. The aircraft is then leveled at the correct orbital heading and the engines ignited to regain orbital velocity. For the class of hypersonic gliders evaluated, this maneuver requires an incremental velocity of about 1,022 ft/s (311.5 m/s) to

35,000

30,000

25,000

—D" - Model 176 —*—Circular, 200 ra.mi. —à—Elliptical ,22,400 nm —ù - FDL-7C/D —O— DynaSoar Lifting

Plane Change 200 nautical miles

35,000

30,000

25,000

—D" - Model 176 —*—Circular, 200 ra.mi. —à—Elliptical ,22,400 nm —ù - FDL-7C/D —O— DynaSoar Lifting

Plane Change 200 nautical miles 