Framework for Establishing Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis

This paper describes the use of the Euler equations for the generation and testing of tabular aerodynamic models for flight dynamics analysis. Maneuvers for the AGARD Standard Dynamics Model sharp leading-edge wind-tunnel geometry are considered as a test case. Wind-tunnel data is first used to validate the prediction of static and dynamic coefficients at both low and high angles, featuring complex vortical flow, with good agreement obtained at low to moderate angles of attack. Then the generation of aerodynamic tables is described based on a data fusion approach. Time-optimal maneuvers are generated based on these tables, including level flight trim, pull-ups at constant and varying incidence, and level and 90 degrees turns. The maneuver definition includes the aircraft states and also the control deflections to achieve the motion. The main point of the paper is then to assess the validity of the aerodynamic tables which were used to define the maneuvers. This is done by replaying them, including the control surface motions, through the time accurate computational fluid dynamics code. The resulting forces and moments are compared with the tabular values to assess the presence of inadequately modeled dynamic or unsteady effects. The agreement between the tables and the replay is demonstrated for slow maneuvers. Increasing rate maneuvers show discrepancies which are ascribed to vortical flow hysteresis at the higher rate motions. The framework is suitable for application to more complex viscous flow models, and is powerful for the assessment of the validity of aerodynamics models of the type currently used for studies of flight dynamics.

The practical implications of using standardized estimation equations in calculating the prevalence of chronic kidney disease

Background. Kidney Disease Outcomes Quality Initiative (KDOQI) chronic kidney disease (CKD) guidelines have focused on the utility of using the modified four-variable MDRD equation (now traceable by isotope dilution mass spectrometry IDMS) in calculating estimated glomerular filtration rates (eGFRs). This study assesses the practical implications of eGFR correction equations on the range of creatinine assays currently used in the UK and further investigates the effect of these equations on the calculated prevalence of CKD in one UK region Methods. Using simulation, a range of creatinine data (30–300 µmol/l) was generated for male and female patients aged 20–100 years. The maximum differences between the IDMS and MDRD equations for all 14 UK laboratory techniques for serum creatinine measurement were explored with an average of individual eGFRs calculated according to MDRD and IDMS 30 ml/min/1.73 m2. Observed data for 93,870 patients yielded a first MDRD eGFR 3 months later of which 47 093 (71%) continued to have an eGFR

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.