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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1984

Applications of numerical optimization methods to helicopter design problems - A survey

A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.

Miura, H.↗
NASA NTRS1979

Supercritical wing design using numerical optimization and comparisons with experiment

A numerical minimization scheme is used in conjunction with two-dimensional and three-dimensional inviscid transonic flow analysis codes to provide procedures for wing leading edge aerodynamic design. The procedures are demonstrated in the design of a new leading edge to improve C-141 cruise performance. For the high aspect ratio moderately swept C-141 wing, the 2-D procedure is shown to yield results which are in close agreement with those obtained using the 3-D technique. Although the 2-D approach uses much less computation time than the 3-D technique, the latter requires fewer manhours than the former. Comparisons of predicted and wind tunnel measured performance improvements are presented which verify the design procedures.

Lores, M. E.↗
NASA NTRS1989

Numerical optimization in Hilbert space using inexact function and gradient evaluations

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Carter, Richard G.↗
NASA NTRS1972

Calculation of free fall trajectories based on numerical optimization techniques

The development of a means of computing free-fall (nonthrusting) trajectories from one specified point in the solar system to another specified point in the solar system in a given amount of time was studied. The problem is that of solving a two-point boundary value problem for which the initial slope is unknown. Two standard methods of attack exist for solving two-point boundary value problems. The first method is known as the initial value or shooting method. The second method of attack for two-point boundary value problems is to approximate the nonlinear differential equations by an appropriate linearized set. Parts of both boundary value problem solution techniques described above are used. A complete velocity history is guessed such that the corresponding position history satisfies the given boundary conditions at the appropriate times. An iterative procedure is then followed until the last guessed velocity history and the velocity history obtained from integrating the acceleration history agree to some specified tolerance everywhere along the trajectory.

Source record↗
NASA NTRS1973

A mesh gradient technique for numerical optimization

A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

Willis, E. A., Jr.↗
NASA NTRS1974

An assessment of airfoil design by numerical optimization

A practical procedure for optimum design of aerodynamic shapes is demonstrated. The proposed procedure uses an optimization program based on the method of feasible directions coupled with an analysis program that uses a relaxation solution of the inviscid, transonic, small-disturbance equations. Results are presented for low-drag, nonlifting transonic airfoils. Extension of the method to lifting airfoils, other speed regimes, and to three dimensions if feasible.

Hicks, R. M.↗
NASA NTRS1975

Application of numerical optimization to the design of low speed airfoils

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on the method of feasible directions coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full potential equation. Results are presented for airfoils designed to have small adverse pressure gradients, high maximum lift, and low pitching moment.

Hicks, R. M.↗
NASA NTRS1975

Design of low-speed airfoils by numerical optimization

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (1) adverse pressure-gradient minimization, (2) pitching-moment minimization; and (3) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.

Hicks, R. M.↗
NASA NTRS1976

Airfoil section drag reduction at transonic speeds by numerical optimization

A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.

Hicks, R. M.↗
NASA NTRS1976

Airfoil section drag reduction at transonic speeds by numerical optimization

A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.

Hicks, R. M.↗
NASA NTRS1977

Propeller design by numerical optimization

A computer program designed to optimize propeller characteristics was developed by combining two main programs: the first is the optimization program based on the gradient algorithm; the second is based on a propeller blade element theory and uses an aerodynamics subprogram to approximate the lift and drag characteristics of the NACA 16-series airfoil section. To evaluate the propeller program alone (with its aerodynamics subprogram), propeller characteristics were computed and compared to those from wind tunnel investigations conducted on three different NACA propellers. Although the thrust and power coefficients which were computed using the blade element theory were generally higher than the experimental results for two of the three propellers, the corresponding efficiencies showed good agreement for all three propellers. The propeller optimization program was then used to study the NACA 4-(5)(08)-03 propeller at various Mach numbers from 0.175 to 0.60. Improvements in propeller efficiency and thrust were obtained through the use of the propeller optimization program.

Mendoza, J. P.↗
NASA NTRS1979

Numerical optimization techniques for bound circulation distribution for minimum induced drag of nonplanar wings: Basic formulations

A theoretical method was developed for determining the optimum span load distribution for minimum induced drag for subsonic nonplanar configurations. The undistorted wing wake is assumed to have piecewise linear variation of shed vortex sheet strength, resulting in a quadratic variation of bound circulation and span load. The optimum loading is obtained either through a direct technique, whereby derivatives of the drag expression are calculated analytically in terms of the unknown wake vortex sheet strengths. Both techniques agree well with each other and with available exact solutions for minimum induced drag.

Kuhlman, J.↗
NASA NTRS1980

Application of numerical optimization to the design of wings with specified pressure distributions

A practical procedure for the optimum design of transonic wings is demonstrated. The procedure uses an optimization program based on the method of feasible directions coupled with an aerodynamic analysis program which solves the three-dimensional potential equation for subsonic through transonic flow. Two new wings for the A-7 aircraft were designed by using the optimization procedure to achieve specified surface pressure distributions. The new wings, along with the existing A-7 wing, were tested in the Ames 11 ft transonic wind tunnel. The experimental data show that all of the performance goals were met. However, comparisons of the wind tunnel results with the theoretical predictions indicate some differences at conditions for which strong shock waves occur.

Haney, H. P.↗
NASA NTRS1981

Numerical optimization techniques for bound circulation distribution for minimum induced drag of Nonplanar wings: Computer program documentation

A two dimensional advanced panel far-field potential flow model of the undistorted, interacting wakes of multiple lifting surfaces was developed which allows the determination of the spanwise bound circulation distribution required for minimum induced drag. This model was implemented in a FORTRAN computer program, the use of which is documented in this report. The nonplanar wakes are broken up into variable sized, flat panels, as chosen by the user. The wake vortex sheet strength is assumed to vary linearly over each of these panels, resulting in a quadratic variation of bound circulation. Panels are infinite in the streamwise direction. The theory is briefly summarized herein; sample results are given for multiple, nonplanar, lifting surfaces, and the use of the computer program is detailed in the appendixes.

Kuhlman, J. M.↗
NASA NTRS1984

Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

Cosentino, G. B.↗
NASA NTRS1985

Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure disributions and drag-to-lift ratio minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

Cosentino, G. B.↗