The dynamics of parabolic flight: Flight characteristics and passenger percepts

Abstract

Flying a parabolic trajectory in an aircraft is one of the few ways to create freefall on Earth, which is important for astronaut training and scientific research. Here we review the physics underlying parabolic flight, explain the resulting flight dynamics, and describe several counterintuitive findings, which we corroborate using experimental data. Typically, the aircraft flies parabolic arcs that produce approximately 25 s of freefall (0g) followed by 40 s of enhanced force (1.8g), repeated 30–60 times. Although passengers perceive gravity to be zero, in actuality acceleration, and not gravity, has changed, and thus we caution against the terms “microgravity” and “zero gravity.” Despite the aircraft trajectory including large (45°) pitch-up and pitch-down attitudes, the occupants experience a net force perpendicular to the floor of the aircraft. This is because the aircraft generates appropriate lift and thrust to produce the desired vertical and longitudinal accelerations, respectively, although we measured moderate (0.2g) aft-ward accelerations during certain parts of these trajectories. Aircraft pitch rotation (average 3°/s) is barely detectable by the vestibular system, but could influence some physics experiments. Investigators should consider such details in the planning, analysis, and interpretation of parabolic-flight experiments.

Introduction

High-performance aviation and space flight have dramatically changed the forces and accelerations to which humans are exposed. During space flight humans have experienced freefall, which requires the body to operate in an environment different from the constant gravitational environment in which it evolved. Research to understand the effects of freefall on the body is important for sustaining humans during long-duration space flight, especially during taxing operational tasks. In addition, some research in physics and chemistry can only be performed in freefall, such as the study of fluid mechanics as applied to fuel flow in spacecraft.

It is important to distinguish between “freefall” and “weightlessness.” Even in orbital flight, for example when the space shuttle orbits 300 km above the Earth's surface, gravity is only slightly less than at sea level (9.37 m/s² compared to 9.81 m/s² at sea level). Thus terms like “microgravity,” “zero-gravity,” and “weightless” are technically incorrect when applied to orbital flight (and atmospheric aircraft maneuvers), although they are often used to describe the perception that astronauts experience during freefall. Spacecraft in Earth orbit are continually falling toward the earth under the force of gravity, but are given sufficient forward velocity so that the sum of their velocities toward and parallel to earth keeps them at the same distance from earth; as a spacecraft falls toward the earth, the earth curves away from under it. Astronauts perceive themselves to be weightless because they are falling under the influence of the same gravitational field as the spacecraft, so there is no reaction force on the astronaut by the spacecraft. According to Einstein's equivalence principle, no simple physical transducer can determine whether an applied acceleration is due to gravitational or inertial force, and this includes the sensors in the human body. Gravito-inertial acceleration (GIA), often expressed simply as g level, is defined as the sum of the linear accelerations due to gravity and inertial forces. It is measured in units of g, where $1g=9.81\mathrm{m}/{\mathrm{s}}^2$ at sea level. During freefall the net g level is 0g, but gravity is not zero.

Although space flight is the only way to provide long periods of true freefall, a much cheaper and more accessible method is available in an aircraft flying a parabolic trajectory. During such parabolic flight an aircraft flies a trajectory that provides freefall for up to 40 s. Parabolic flight generates freefall by following a trajectory wherein the acceleration of the aircraft cancels the acceleration due to gravity (Fig. 1), along the aircraft vertical (z) axis. Essentially, if the aircraft and its occupants “fall” together at 9.81 m/s², “0g” is achieved, where there is no reaction force on the occupants by the aircraft. Such a flight typically consists of 30–60 parabolas, each providing about 25 s of freefall. Between 0g parabolas, the aircraft must climb to regain altitude, and during this 40 s interval when downward velocity is reduced and eventually becomes upward velocity, g levels reach 1.8g. (Contrary to popular misconception, the 0g freefall phase of flight begins while the aircraft is climbing, and does not occur solely as the aircraft descends. Although the aircraft has upward velocity during the initial 0g phase, its acceleration is downward: the upward velocity is decreasing.)

Parabolic flight as a platform for astronaut training and engineering experiments was originally proposed in 1950 by Drs. Fritz Haber and Heinz Haber, of the Air Force School of Aviation Medicine, Brooks Air Force Base, Texas [1]. Early experimentation with the technique was conducted by legendary test pilots Scott Crossfield and Chuck Yeager in 1951 at Edwards Air Force Base, California, although initially only a few seconds of true freefall could be achieved, compared with 30 s envisioned by the Habers [2]. Between 1955 and 1958, a refined approach in the F-94 fighter allowed a variety of medical experiments to be performed during 30–40 s of freefall [3]. Between 1957 and 1959, the much larger C-131B cargo transport allowed simultaneous experiments on multiple subjects [4] and sufficient room for Mercury program astronauts to train (Fig. 2), although this slower, propeller-driven aircraft could only produce parabolas with 10–15 s of freefall.