SS: Fiber Moorings, Recent Experiences and Research: Fiber Rope Mooring Assessment - Original API RP 2SM Piecewise Linear Stiffness versus Non-linear Stiffness with Integrated Permanent Rope Elongation

2010 ◽  
Author(s):  
Evan H. Zimmerman ◽  
Robert Garrity
Keyword(s):  
Piecewise Linear ◽  
Non Linear ◽  
Piecewise Linear Stiffness

scholarly journals An Approximate Analytic Solution to a Non-Linear ODE for Air Jet Velocity Decay through Tree Crops Using Piecewise Linear Emulations and Rectangle Functions

2019 ◽  
Vol 9 (24) ◽  
pp. 5440 ◽  
Author(s):  
Dario Friso
Keyword(s):  
Relative Error ◽  
Piecewise Linear ◽  
Single Equation ◽  
Air Velocity ◽  
Tree Crops ◽  
Mean Relative Error ◽  
Air Jet ◽  
Significant Difference ◽  
Non Linear ◽  
Velocity Decay

The velocity of air that crosses the canopy of tree crops when using orchard sprayers is a variable that affects pesticide dispersion in the environment. Therefore, having an equation to describe air velocity decay through the canopy is of interest. It was necessary to start from a more general non-linear ordinary differential equation (ODE) obtained from the momentum theorem. After approximating the non-linearity with some piecewise linear terms, analytic solutions were found. Subsequently, to obtain a single equation for velocity decay, a combination of these solutions was proposed by using rectangle functions formed through the hyperbolic tangent function. This single equation was assessed in comparison to the experimental value obtained on a vineyard row by measuring the air velocity at exit of canopy. The results have shown good correspondence, with a mean relative error of 6.6%; moreover, there was no significant difference. To simplify, a combination of only two linearized solutions was also proposed. Again, there was no significant difference between the experimental value and the predicted one, but the mean relative error between the two equations was 3.6%.

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