Limit Cycle Analysis Applied to the Oscillations of Decelerating Blunt-Body Entry Vehicles

Many blunt-body entry vehicles have nonlinear dynamic stability characteristics that produce self-limiting oscillations in flight. Several different test techniques can be used to extract dynamic aerodynamic coefficients to predict this oscillatory behavior for planetary entry mission design and analysis. Most of these test techniques impose boundary conditions that alter the oscillatory behavior from that seen in flight. Three sets of test conditions, representing three commonly used test techniques, are presented to highlight these effects. Analytical solutions to the constant-coefficient planar equations-of-motion for each case are developed to show how the same blunt body behaves differently depending on the imposed test conditions. The energy equation is applied to further illustrate the governing dynamics. Then, the mean value theorem is applied to the energy rate equation to find the effective damping for an example blunt body with nonlinear, self-limiting dynamic characteristics. This approach is used to predict constant-energy oscillatory behavior and the equilibrium oscillation amplitudes for the various test conditions. These predictions are verified with planar simulations. The analysis presented provides an overview of dynamic stability test techniques and illustrates the effects of dynamic stability, static aerodynamics and test conditions on observed dynamic motions. It is proposed that these effects may be leveraged to develop new test techniques and refine test matrices in future tests to better define the nonlinear functional forms of blunt body dynamic stability curves

Oscillation Amplitude Growth for a Decelerating Object with Constant Pitch Damping

The equations governing the deceleration and oscillation of a blunt body moving along a planar trajectory are re-expressed in the form of the Euler-Cauchy equation. An analytic solution of this equation describes the oscillation amplitude growth and frequency dilation with time for a statically stable decelerating body with constant pitch damping. The oscillation histories for several constant pitch damping values, predicted by the solution of the Euler-Cauchy equation are compared to POST six degree-of-freedom (6-DoF) trajectory simulations. The simulations use simplified aerodynamic coefficients matching the Euler-Cauchy approximations. Agreement between the model predictions and simulation results are excellent. Euler-Cauchy curves are also fit through nonlinear 6-DoF simulations and ballistic range data to identify static stability and pitch damping coefficients. The model os shown to closely fit through the data points and capture the behavior of the blunt body observed in simulation and experiment. The extracted coefficients are in reasonable agreement with higher fidelity, nonlinear parameter identification results. Finally, a nondimensional version of the Euler-Cauchy equation is presented and shown to be a simple and effective tool for designing dynamically scaled experiments for decelerating blunt capsule flight

Multibody Modeling and Simulation for the Mars Phoenix Lander Entry, Descent and Landing

A multi-body flight simulation for the Phoenix Mars Lander has been developed that includes high fidelity six degree-of-freedom rigid-body models for the parachute and lander system. The simulation provides attitude and rate history predictions of all bodies throughout the flight, as well as loads on each of the connecting lines. In so doing, a realistic behavior of the descending parachute/lander system dynamics can be simulated that allows assessment of the Phoenix descent performance and identification of potential sensitivities for landing. This simulation provides a complete end-to-end capability of modeling the entire entry, descent, and landing sequence for the mission. Time histories of the parachute and lander aerodynamic angles are presented. The response of the lander system to various wind models and wind shears is shown to be acceptable. Monte Carlo simulation results are also presented

Validation of Multibody Program to Optimize Simulated Trajectories II Parachute Simulation with Interacting Forces

A capability to simulate trajectories of multiple interacting rigid bodies has been developed, tested and validated. This capability uses the Program to Optimize Simulated Trajectories II (POST 2). The standard version of POST 2 allows trajectory simulation of multiple bodies without force interaction. In the current implementation, the force interaction between the parachute and the suspended bodies has been modeled using flexible lines, allowing accurate trajectory simulation of the individual bodies in flight. The POST 2 multibody capability is intended to be general purpose and applicable to any parachute entry trajectory simulation. This research paper explains the motivation for multibody parachute simulation, discusses implementation methods, and presents validation of this capability

ASPIRE Flight Mechanics Modeling and Post Flight Analysis

The Advanced Supersonic Parachute Inflation Research and Experiment (ASPIRE) is a series of sounding rocket flights aimed at understanding the dynamics of supersonic parachutes that are used for Mars robotic applications. SR01 was the first sounding rocket flight of ASPIRE that occurred off the coast of Wallops Island, VA on Oct. 4, 2017 and showed the successful deployment and inflation of a Mars Science Laboratory built-to- print parachute in flight conditions similar to the 2012 Mars Science Laboratory (MSL) mission. SR02 was the second sounding rocket flight that also occurred off the coast of Wallops Island on March 31, 2018 and showcased the successful deployment and inflation of a new strengthened parachute being considered for the Mars 2020 mission at fifty percent higher dynamic pressure than observed on MSL. Prior to both flights, a multi-body flight dynamics simulation was developed to predict the parachute dynamics and was used, in conjunction with other tools, to target Mars-relevant flight conditions. After each flight, the reconstructed trajectory was used to validate the pre-flight dynamics simulation and recommend changes to improve predictions for future flights planned for the ASPIRE pro- gram. This paper describes the flight mechanics simulation and the post flight reconciliation process used to validate the flight models

Parachute Aerodynamics From Video Data

A new data analysis technique for the identification of static and dynamic aerodynamic stability coefficients from wind tunnel test video data is presented. This new technique was applied to video data obtained during a parachute wind tunnel test program conducted in support of the Mars Exploration Rover Mission. Total angle-of-attack data obtained from video images were used to determine the static pitching moment curve of the parachute. During the original wind tunnel test program the static pitching moment curve had been determined by forcing the parachute to a specific total angle-of -attack and measuring the forces generated. It is shown with the new technique that this parachute, when free to rotate, trims at an angle-of-attack two degrees lower than was measured during the forced-angle tests. An attempt was also made to extract pitch damping information from the video data. Results suggest that the parachute is dynamically unstable at the static trim point and tends to become dynamically stable away from the trim point. These trends are in agreement with limit-cycle-like behavior observed in the video. However, the chaotic motion of the parachute produced results with large uncertainty bands

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included

Entry, Descent, and Landing Operations Analysis for the Mars Phoenix Lander

The Mars Phoenix lander was launched August 4, 2007 and remained in cruise for ten months before landing in the northern plains of Mars in May 2008. The one-month Entry, Descent, and Landing (EDL) operations phase prior to entry consisted of daily analyses, meetings, and decisions necessary to determine if trajectory correction maneuvers and environmental parameter updates to the spacecraft were required. An overview of the Phoenix EDL trajectory simulation and analysis that was performed during the EDL approach and operations phase is described in detail. The evolution of the Monte Carlo statistics and footprint ellipse during the final approach phase is also provided. The EDL operations effort accurately delivered the Phoenix lander to the desired landing region on May 25, 2008

Mars Phoenix Entry, Descent, and Landing Simulation Design and Modelling Analysis

The 2007 Mars Phoenix Lander was launched in August of 2007 on a ten month cruise to reach the northern plains of Mars in May 2008. Its mission continues NASA s pursuit to find evidence of water on Mars. Phoenix carries upon it a slew of science instruments to study soil and ice samples from the northern region of the planet, an area previously undiscovered by robotic landers. In order for these science instruments to be useful, it was necessary for Phoenix to perform a safe entry, descent, and landing (EDL) onto the surface of Mars. The EDL design was defined through simulation and analysis of the various phases of the descent. An overview of the simulation and various models developed to characterize the EDL performance is provided. Monte Carlo statistical analysis was performed to assess the performance and robustness of the Phoenix EDL system and are presented in this paper. Using these simulation and modelling tools throughout the design and into the operations phase, the Mars Phoenix EDL was a success on May 25, 2008

LDSD POST2 Modeling Enhancements in Support of SFDT-2 Flight Operations

Program to Optimize Simulated Trajectories II (POST2) was utilized to develop trajectory simulations characterizing all flight phases from drop to splashdown for the Low-Density Supersonic Decelerator (LDSD) project's first and second Supersonic Flight Dynamics Tests (SFDT-1 and SFDT-2) which took place June 28, 2014 and June 8, 2015, respectively. This paper describes the modeling improvements incorporated into the LDSD POST2 simulations since SFDT-1 and presents how these modeling updates affected the predicted SFDT-2 performance and sensitivity to the mission design. The POST2 simulation flight dynamics support during the SFDT-2 launch, operations, and recovery is also provided