Using Elementary Mechanics to Estimate the Maximum Range of ICBMs

2018 ◽  
Vol 56 (4) ◽  
pp. 210-213
Author(s):  
Joseph Amato
Keyword(s):  
Maximum Range ◽  
Elementary Mechanics

The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Multipliers ◽  
Digital Computer ◽  
Necessary Conditions ◽  
Lagrange Equations ◽  
Initial Portion ◽  
End Conditions ◽  
Maximum Range ◽  
Isothermal Atmosphere

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

Method for comparison of the maximum range of chemical pollutants

2014 ◽  
Vol 84 (13) ◽  
pp. 2677-2680 ◽  
Author(s):  
S. Ketin ◽  
S. Sacirovic ◽  
S. Plojovic ◽  
R. Skrijelj ◽  
R. Biocanin
Keyword(s):  
Chemical Pollutants ◽  
Maximum Range

Maximum Range Of Ballistic Missiles

SIAM Review ◽  
1965 ◽  
Vol 7 (4) ◽  
pp. 544-550 ◽  
Author(s):  
Kasturi L. Arorat ◽  
Nguyen X. Vinh
Keyword(s):  
Ballistic Missiles ◽  
Maximum Range

scholarly journals ELEMENTARY MECHANICS

Science ◽  
1915 ◽  
Vol 42 (1071) ◽  
pp. 56-58
Author(s):  
W. S. Franklin ◽  
B. MacNutt
Keyword(s):  
Elementary Mechanics

scholarly journals Fermentación de la almendra de copoazú (Theobroma grandiflorum [Willd. ex Spreng.] Schum.): evaluación y optimización del proceso

2010 ◽  
Vol 11 (2) ◽  
pp. 107 ◽  
Author(s):  
Jenifer Criollo ◽  
Dagoberto Criollo ◽  
Angélica Sandoval Aldana
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Process Optimization ◽  
Fermentation Process ◽  
Raw Material ◽  
Sensory Panel ◽  
Yeast Saccharomyces Cerevisiae ◽  
Theobroma Grandiflorum ◽  
Cutting Test ◽  
Maximum Range ◽  
Low Levels

<p>La almendra de copoazú como producto promisorio para la industria de cosméticos, chocolate, bebidas, licores y conservas, se evaluó el proceso de fermentación variando el tiempo de remoción de la masa (24 y 48 horas) y la pulpa inicial (30 y 100%). Se tuvieron en cuenta las condiciones de los productores en el acceso a equipos de despulpado. Se cuantificó la temperatura de la masa en tres puntos (superior, medio e inferior), acidez, pH, humedad, prueba de corte y análisis sensorial. Se encontró bajo desarrollo de la temperatura de fermentación en los tratamientos con 100% de pulpa y se registraron las máximas temperaturas entre 35 y 36°C que indican deficiencias en el proceso; no se alcanzó los 40°C requeridos para la muerte del embrión. El 30% de pulpa inicial y la remoción cada 24 horas por 9 días, fueron las mejores condiciones encontradas. La optimización con 0,1% de levadura (Saccharomyces cerevisiae) aumentó la temperatura de fermentación hasta 44°C, los granos fermentados hasta 56,14% y el mayor desarrollo de sabores frutales con intensidad de 4, mostrando un mejor proceso de fermentación. El panel sensorial mostró que los licores de copoazú tienen notas frutales destacadas y bajos valores de otros sabores evaluados. Los resultados son semejantes a los cacaos criollos, conocidos en el mundo como materia prima de licores finos y de aroma.</p><p> </p><p><strong>Fermentation of the copoazu kernel (Theobroma grandiflorum [Willd. ex Spreng.] Schum.): Assessmente and process optimization</strong></p><p>The fermentation of copoazu kernels (a promising product for the cosmetics industry, chocolate, beverages, liquors and preserves) was evaluated varying the time of mass removal (24 and 48 hours) and the initial pulp (30 and 100%). This study took into account the degree of access the producers had to pulping equipment. We quantified temperature of the mass at three points (top, middle and bottom), acidity, pH, moisture, cutting test and sensory analysis. The observed temperatures during fermentation in the treatments with 100% pulp reached a maximum range between 35 and 36°C which indicated deficiencies in the process as the 40°C required for the death of the seed was not attained. Thirty percent initial pulp with removal every 24 hours for 9 days yielded the best results. Optimization with 0.1% yeast (Saccharomyces cerevisiae) increased the fermentation temperature to 44°C, augmented fermented beans to 56.14% and saw a development of fruit flavors with an intensity of 4, demonstrating a better fermentation process. The sensory panel showed that copoazu liquors have outstanding fruity notes and low levels of other evaluated flavors. The results are similar to the criollo cacao, known worldwide as a raw material for fine liquors and fragrances.</p>

scholarly journals OPTIMIZATION OF LONG-RANGE TRAJECTORY FOR AN UNPOWERED FLIGHT VEHICLE

2020 ◽  
Vol 57 (6A) ◽  
pp. 43
Author(s):  
Tuan Hung Pham ◽  
Duc Cuong Nguyen ◽  
Duc Thanh Nguyen
Keyword(s):  
Long Range ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Normal Load ◽  
Load Factor ◽  
Flight Vehicle ◽  
Maximum Range ◽  
Normal Acceleration

This report presents problems of optimization of long-range trajectory for an unpowered flight vehicle at subsonic and transonic speed. The results may be recommended to have a new long range trajectory. The optimization problem is solved by numerical experiments while  the normal load factor (normal acceleration) is used as optimization variables with compliance to flight constraints. The focus problem of this study is the investigation of the possibility of trajectory expansion according to the criteria of the maximum range in the first stage of the trajectory.  

scholarly journals Elementary Mechanics of Solids and Fluids

1910 ◽  
Vol 5 (87) ◽  
pp. 315
Author(s):  
A. C. Jones ◽  
C. H. Blomfield
Keyword(s):  
Mechanics Of Solids ◽  
Elementary Mechanics
Sign in / Sign up

Export Citation Format

Share Document