A typical launch vehicle flight path starts with a vertical ascent from the launch pad. The vehicle accelerates slowly with the thrust-weight ratio somewhat greater than one for a typical liquid first stage booster. As sufficient altitude is gained a pitch maneuver in the desired downrange direction is introduced. For the remainder of the flight through the atmosphere the angle of attack is maintained at zero with the thrust vector aligned with the vehicle velocity to minimize aerodynamic loads. This is known as a gravity turn trajectory and is usually flown open loop with a preprogrammed pitch schedule. Subsequent ascent once through the atmosphere will utilize a closed-loop adaptive inertial guidance system.
The Surveyor terminal descent system introduced the concept of a gravity turn to the vertical on approach to the lunar surface. However this cannot be done open-loop as velocity and slant range to the lunar surface are required. This is provided in body coordinates by the Radar Altimeter and Doppler Velocity System (RADVS), an L-band radar, that provides the four beams required to determine range and velocity. The bulk of the lunar approach velocity is removed by a solid rocket motor. Before ignition, the vernier engines are turned on for attitude control of the spacecraft during the burn and final descent. The attitude reference for the spacecraft is provided throughout by a pair of rate integrating gyros. The attitude is changed as needed by precessing the gyros. At burnout, the vernier engines are throttled to 0.9 lunar g until the solid motor is released and separated.
When the RADVS acquires the lunar surface and range and velocity data are available, the attitude control system acts to align the vehicle thrust axis with the velocity vector. This is done by precessing the gyro attitude reference to null the transverse velocity measured by the RADVS. Thereafter the vehicle follows a parabolic profile of range versus velocity designed to bring both close to zero at the surface. The difference between the measured range and the target range is used to control the combined thrust of the vernier engines. This profile is followed until a speed of 10 ft/sec is reached at which time the thrust axis is nearly aligned with the lunar vertical. The attitude then remains fixed and a velocity of 5 ft/sec is maintained to an altitude of 13 feet where thrust is terminated and the spacecraft free falls to the lunar surface.
A novel feature of the Surveyor gravity turn in final descent is that it works over a wide range of approach angles. That’s made possible by the RADVS which provides continuous measurements of the range and velocity in body coordinates. That in turn enables the on board controller to align thrust axis to the velocity vector and bring both the velocity and range to near-zero at the surface. The parabolic range-velocity profile used for thrust control was approximated with an analog function generator. There was no digital computer on board. A gravity turn trajectory is the natural result of gravity along the vertical and retro-thrust along the velocity vector bending the flight path toward the vertical.