Lifting line theory calculator. It can be useful to last year aeronautical engineering students, but only for didattical purposes, not for a professional use, due to intrinsic limitation of the model. Blade Element Propeller Theory Calculating the lift coefficient of 3D finite wing using Lifting Line Theory. We are now familiar with the basic concepts of finite wing theory, also called lifting line theory. It is therefore, interesting to generalize the classical lifting line theory to cases more general than just the free space problem. Outputs: Total lift and induced drag estimates. exe Nov 4, 2020 · Free courses, more videos, practice exercises, and sample code available at https://www. Gordon Leishman. The tool is fully functional, so visit our Beam Calculator and Frame and Truss Calculator to get started! It will work for all beams, trusses and frames and is capable of taking point loads, concentrated moments 5 Chapter 5: Theory of Airfoil Lift Aerodynamics Airfoil theory is largely governed by potential flow theory. Another assumption inherent in the use lifting line theory that was not mentioned is that the theory is not very good for low aspect ratio wings. Whereas classical lifting-line theory is based on applying the two-dimensional Kutta A lifting-line theory is developed for wings of large aspect ratio undergoing time-harmonic oscillations, uniformly from high to low frequencies. If the circulation distribution \(\varGamma _b(y)\) is known along the wing span, the induced velocity on the lifting line is obtained from the induced velocity of a semi-infinite vortex filament (see Sect. p. Even with these two important limitations, lifting line theory gives us some important insights into 3-D aerodynamics. Strength Standards. 2 Lifting-Line Free Vortex Wake method. The vortex filament lies along the straight line; and, at each span-wise station, the strength of the vortex is proportional to the local intensity of Program Lifting Line : Analytical solution of the trigonometric fourier expansion , to calculate the general span wise circulation distribution , for cambered/twisted unswept wings By using the circulation theory of lift, lifting line theory gives an account of the wingtip vortex that is otherwise outside the scope of the momentum theory of lift. 1 have several numerical errors, and the with results obtained from the numerical lifting-line solutions for elliptic wings. In this Paper, it is shown that lifting-line theory can be extended to swept wings if, at the Nov 24, 2013 · In summary, the code is attempting to simulate the Lifting Line Theory using Matlab to estimate the lift and drag of a 3D wing for optimization purposes. The greatest discrepancy is in the range . Prandtl’s classical lifting line theory is the base of most methods used for calculations of change of lifting force of 4flat, low sweep angle, and moderate and high aspect ratio wings [18]. This document presents the Lifting Line Theory (LLT) methodology for analyzing subsonic straight wings. Prandtl's classical lifting line theory is the first successful theory to predict the aerodynamic characteristics of wing. Code written for wing design optimization - Allan0820/Prandlt-Lifting-Line-Calculator I'm trying to calculate lift for a wing with a dihedral angle using the Lifting Line Theory on MATLAB. 3. The summary provides the key steps in applying LLT to calculate spanwise load distribution, overall lift different than propellers, lifting line theory is typically not used in turbine design (in favor of blade element momentum theory). . If you enter in all your lifts we can create you a customizable 5/3/1 routine that you can print out. Material from various sources is combined with some original work into the single complete method described. 2 Lifting Line Theory - From Circulation Distribution to Loads. Jul 1, 2000 · The classical solution to Prandtl's well-known lifting-line theory applies only to a single lifting surface with no sweep and no dihedral. So, an elliptical wing planform has the lowest amount of induced LIFTING-LINE THEORY The basic lifting-line theory is described in most elementary texts on aeronautics (e. The lift and drag components normal to and parallel to the propeller disk can be calculated so that the contribution to thrust and torque of the compete propeller from this single element can be found. 2. Standard atmosphere routine. llt. A method is presented for calculating wing characteristics by lifting-line theory using nonlinear section lift data. doi: 10. Know the various model forms and concepts. sciencedirect. It is also possible to compute the lift-curve slope of a finite wing using the theory Treating the trailing vortices as a series of semi-infinite straight line vortices leads to the well-known lifting line theory. Step 4: Using the lift equation, we get the lift force as: F = C L * A Subsonic Aerofoil and Wing Theory. I am familiar with the general solution and already have the script for a planar wing, however, while using the thesis "Non-Planar Lifting-Line Theory for Fixed and Deformable Geometries" he describes the general equation (considering the dihedral angle) as: Calculate the reactions at the supports of a beam - statically determinate and statically indeterminate, automatically plot the Bending Moment, Shear Force and Axial Force Diagrams Jul 8, 2018 · In accordance with Prandtl’s classical lifting-line theory, a method to calculate the section lift coefficient for the tandem wing configuration or multiple-lifting-surface system is presented. Can do Lifting Line Theory (LLT), Elliptical, and Uniform distributions. For a speed of 90 m/sec in straight and level flight at 3,000 meters altitude ( e. 5 x 1. 95 Action: A number of things can be done to reduce the design SF: a) Improve your knowledge of the lift conditions by Feb 17, 2021 · In this lecture, we derive Prandt's famous Lifting Line Theory. Assumptions: 3-D steady potential flow (inviscid & irrotational) Incompressible. As described in Abbott (2), the circulation, Γ, about the blade associated with lift is replaced by a vortex filament. 3, pp. Subsonic Aerofoil and Wing Theory. Lift and drag of the section can be calculated using standard 2-D aerofoil properties. It is also known as the Lanchester–Prandtl wing theory. Show transcribed image text. In England, Prandtl's lifting line theory is referred to as the Lanchester-Prandtl theory. - Ogzonder/Lift-Coefficient-Calculator-3D-Wings Calculate your one-rep max (1RM) for any lift. This is because the English scientist Frederick Lanchester published the foundation for Prandtl's theory years earlier. Mar 1, 1998 · The method satisfies the constraints of the constant power coefficient and the activity factor. Small crossflow (along span) ⇒ flow looks like 2-D flow locally with α adjusted. Lift+Cruise type of aircrafts are intended to represent a class of VTOL aircraft which have been developed recently [14-17] for manned and unmanned operation, taking advantage of distributed electric Here we describe the steps in a simple propeller design calculation, using lifting line theory. If chord=’MAX’, the maximum value for vector ‘x’ is used as chord. High aspect ratio wing. M is a 'script file' (not a function), with an input section, giving as output a number of variables useful for a pre-design of a wing: lift, drag, etc. It allows you to find the mass of the balloon shell, or the mass of the payload, or the required hot air temperature, or the volume of the balloon, from other known values. However, when analyzing such processes over long times or far in the future, their implicit randomness somehow vanes: we talk then of the steady state of the process. A current overview of the method is given by Krüger and Abels . Following lifting-line theory [47], actuator line methods impose the aerodynamic forces at the quarter-chord axis of the blade, which for most aerofoils is a good approximation to the aerofoil's aerodynamic centre where lift, drag and moments are evaluated. It precisely determines your maximum lift capacity by taking into account aspects such as body weight, lift type, and training experience. The far-field velocity potential is expressed as a distribution of normal dipoles on the wake, and Aug 30, 2011 · Although it has some limitations in applications, the classical Prandtl lifting line theory remains a standard methodology for evaluating lifting problems in free space. Though Prandtl’s lifting line theory has been used in finite wings, it has not been used to analyze propellers. This ability to account for the wingtip vortex (and, in a sail, the sail foot vortex) is given by the circulation theory's treatment of downwash using vortex mathematics. dition by deriving a full 3D coupling as expected from unsteady lifting line theory. Equations are developed for obtaining Jul 30, 2024 · Queueing theory has deep roots in statistics and probability. This is a FORTRAN subroutine that can be used in other programs. It is of theoretical interest in revealing lifting mechanisms. org/Come check it out and join the AeroAcademy community propeller blades. Specifically, a key component of airfoil aerodynamics theory is the combination of: Free-stream velocity elementary flow; Line vortex model elementary flow; Flow tangency; Kutta condition; Kutta-Joukowski theorem Apr 26, 2006 · A generalized lifting-line theory is developed in inviscid, incompressible, steady flow for curved, swept wings of large aspect ratio. Most online one-rep max calculators use the formulas from Epley or Brzycki, which are based on a poundage chart from the 80s and a book from the 90s, respectively. The method of matched asymptotic expansions is used to enforce the compatibility of two approximate solutions valid far from and near the wing surface. Blade element momentum (BEM) method is usually used for performance prediction, but it generally produces overestimated predictions since the wake effects are not precisely accounted for. lifting-line conception in dealing with modern trends in wing design which aroused a new wave of interest in the lifting-surface theory. LIFTLINE Overview ----- LIFTLINE is a collection of MATLAB scripts and functions that implement lifting-line theory. Friction theory with calculator and friction coefficients for combinations of materials like ice, aluminum, steel, graphite and many more. 12 Numerical lifting line methods rely on the assumptions that the flow is irrotational and inviscid. The Lift Coefficient for Symmetrical Airfoil by Thin Airfoil Theory formula, the lift coefficient for a symmetrical airfoil is determined by the angle of attack, The lift coefficient increases linearly with the angle of attack according to the formula and is represented as C L = 2*pi*α or Lift Coefficient = 2*pi*Angle of Attack. 31. 5 days ago · The Max Lift Calculator is a must-have tool for increasing your strength training potential. 07, Eq. The parabolic camber meanline is used as an example of thin airfoil theory. Free online beam calculator tool for simply supported beams and cantilever beams. LLT approximates the 3D flow around a wing as a summation of 2D flows around blade elements. The plot generated shows that the lift distribution with taper ratio is incorrect, as it shows that a smaller taper ratio produces more lift at the wing tip. A simple solution for unswept three-dimensional wings can be obtained by using Prandtl's lifting line model. In this theory the blade is replaced by a straight line. Aug 10, 2007 · Related to Lifting line theory numeric estimation 1. Prandtl's lifting-line equation is an integro-differential equation which is used for calculating the span-wise distribution of circulation around wings which are three-dimensional quasi-planar, with negligible sweep and large Prandtl’s Lifting Line Introduction. It assumes the wing is a flat plate and cannot model thickness, dihedral, or sweep. For incompressible, inviscid flow, the wing is modelled as a single bound vortex line located at the 1/4 chord position and an associated shed vortex sheet. Essentially, this theory models a finite-wing + wing tip vortices as a horseshoe vortex, wher Lifting-line theory explained. Jul 3, 2017 · Arguments from lifting line theory are not appropriate for discussing the behaviour of the flow near wing tips. Lifting Line Theory. In the lifting line theory, the lifting body is modelled as a bound vortex on a line with a circulation \(\varGamma Online calculator for solving problems related to balloon lifting force. However, Prandtl's original model of a finite lifting surface has much broader applicability. This is an interactive FORTRAN program that solves the classical Prandtl lifting line theory using the monoplane equation. The file is standard ascii text. Sep 6, 2013 · Method for calculating wing characteristics by lifting-line theory using nonlinear section lift data A method is presented for calculating wing characteristics by lifting-line theory using nonlinear section lift data. Motors - Speed vs. Implementing a PLL solver is relatively simple; I made this version in a few hours with Fortran. Assume: z(x) = 4 h x (1-x) Thin airfoil theory can also be used to estimate the effect of flap deflection on airfoil lift and moment. Feb 6, 2024 · Lifting line Prandt's ltheory Ludwig Prandtl has developed the first method for the analysis of a wing of finite span in 1918 equating all vortex filaments attached to a wing has a single filament called "lifting line. Can be used for shells (considers thicknesses), but also for any surface. The Lanchester-Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing from the wing's geometry. Oct 6, 2009 · The function is based on the mathematical treatment of rotating rotors in "Principles of Helicopter Aerodynamics" by Dr. Step 1: Enter the lift coefficient as 0. Step 3: Use the surface area value as 2 m². 2017. Since the propeller blade will be set at a given geometric pitch angle ($θ$) the local velocity vector will create a flow angle of attack on the section. The following expression is used with elliptical wings only: Lift curve slope for an elliptical wing: Mar 18, 2001 · Simple Lifting Line Theory. 66 = 12. exe; Aircraft Sizing Preliminary Sizing And Weight Estimation . Dec 14, 2020 · Implementations of lifting-line theory predict the lift of a finite wing using a sheet of semi-infinite vortices extending from a vortex filament placed along the locus of aerodynamic centers of the wing. Weight Mass vs. The numerical method does this by using Blade Element Momentum Theory (BEMT) to calculate the inflow along the length of the blade, then using that inflow and Lifting Line theory to calculate the local lift and drag on the blade. In practice however, the force may be spread over a small area, although the dimensions of this area should be substantially smaller than the cantilever length. This theory aims to determine circulation distribution in the spanwise direction. In the range h b >0. Low sweep. (4) and bythe numerical lifting-line solutions for elliptic wings. Jan 6, 2020 · Whereas classical lifting-line theory is based on applying the two-dimensional Kutta-Joukowski law to a three-dimensional how, the present method is based on a fully three-dimensional vortex Flood (2009), "Propeller performance analysis using lifting line theory" SM Thesis, MIT. Go through the derivations of lifting line theory. However, users have complained these calculators estimate too high. In the implementation found in QBlade, the rotor blade is discretized into elements represented by bound ring vortices. This video covers clear explanination of prandtls lifting line theory and its outcome. the loading can be obtained from the 2D lift, drag and moment coefficients of the foil at this radial position; 3. aero-academy. Lifting line theory (LLT) can represent Feb 22, 2024 · The Science Behind Our Calculator. " Laws and theorems defining vortices allow calculation of induced velocities: Jul 27, 2023 · Lifting Line Theory. g. The line also serves as a reference location for velocity sampling in methods, which use Subsonic Aerofoil and Wing Theory. Mass vs. 0. : Saturday, December 28, 2019 Sydney, Australia: Sunday, December 29, 2019 File Download Time Calculator Author, E-Mail The calculator is fully customisable to suit most beams, frames and trusses; which is a feature unavailable on most other calculators. Step 2: Input the speed as 150 m/s. Jul 24, 2024 · For instance, let's find the lifting force for a wing having a surface area of 2 m², a lift coefficient of 0. Individual Radius of Effort (inches) Radius of Load (inches) Mechanical Advantage Calculation; Lifting Larry: 5: 5: 1x “Larry’s single fixed pulley offers no advantage. The LLFVW method is based on inviscid potential flow theory and a vortex representation of the flow field (Van Garrel, 2003; Marten et al. 0 for an elliptic distribution and is some value less than 1. Lifting Line Theory Analytical Circulation Distribution . the loading at a given radial position of the blade can be determined independently of the other radial positions; 2. , ref. Aerofoil Section 2-D Geometry; Joukowski Aerofoils and Flow Mapping; 2-D Thin Aerofoil Theory; 2D Panel Methods; 2D Boundary Layer Modelling; 3D Prandtl Lifting Line Theory; 3D Vortex Lattice Method; Subsonic Compressibility Corrections; Gas Dynamics and Supersonic Flow; Propulsion. Apr 7, 2017 · The main assumptions of the blade element theory are: 1. (1)predicts induced drag that is somewhat below that predicted Eq. It also allows you to create twist. A general numerical lifting-line method based on Prandtl's model is presented. The Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing based on its geometry. exe; PVLM Planar Vortex Lattice Method . 52. The arrival and servicing of customers are, fundamentally, stochastic processes. Lifting line theory for elliptic load distribution (13 points) An airplane weighing 73,600 Newtons has elliptic shaped wings with a total span of 16 meters. Once the circulation distribution is obtained, lift and induced drag coefficients can be easily deduced from it. Aug 25, 2021 · It was noted that this theory assumes that the quarter chord of the wing is unswept. (Note: change of reference line from chord to zero lift line). J. Blade Element Propeller Theory Dec 1, 2013 · A unified lifting line method for the design and analysis of axial flow propellers and turbines is presented. Jan 18, 2000 · PRANDTL. h b <0. A table with an example is given afterwards. It solves the monoplane equation to estimate aerodynamic characteristics of a finite wing. It is presented here for completeness and to introduce a few basic equations which are needed in the next section. Spanwise circulation distribution is obtained and hence lift is calculated. Lifting line theory is applied to a smooth bound vortex with sweep and dihedral and a trailing vortex sheet. Multhopp's systems of multipliers are employed to obtain the induced angle of attack directly from the spanwise lift distribution. The efficiency factor e is equal to 1. 1 in Minsaas “Propeller Theory”, but be aware that the example in chapter 5. It has been used to predict the induced drag of finite wings, and such results for untwisted wings have been tabulated in basic aerodynamics textbooks for use by students and others in evaluating finite wing designs. ”. The method incorporates significant improvements to the classical lifting line methods for propeller design to extend the method to the design of turbines. A lifting line theory (vortex lattice method) and a lifting surface theory (3-D panel method) are used to calculate aerodynamic performance parameters of propellers. 131-136). In this section, Prandtl’s classical lifting-line theory for a single finite wing is presented firstly, and then, the lifting-line theory for tandem wing configuration is proposed on the foundation of Prandtl’s classical lifting-line theory combined with the Biot-Savart law. f. p . Lanchester in 1907, [4] and by Ludwig Prandtl in 1918–1919 [5] after working with Albert Betz and Max Munk May 2, 2015 · There is a theory which is linear and non-viscous that helps to compute the aerodynamic components of the wing, based on the aerodynamic characteristics of the airfoils the wing is made of. com 10th International Conference on Marine Technology, MARTEC 2016 Marine Propeller Design Method based on Lifting Line Theory and Lifting The wing is divided into spanwise strips and Prandtl's lifting line theory is applied to estimate aerodynamic forces with the assumptions of quasi‐steady flow and the wings are without any dihedral or anhedral. An early attempt at a lifting-surface calculation by Blenk" was mainly to show that the results of the lifting-line theory were quite good--at least Jan 1, 2017 · Peer-review under responsibility of the organizing committee of the 10th International Conference on Marine Technology. 3 x 2 x 2 x 1. Pulley Diameter The local velocity vector will create a flow angle of attack on the section. Stubblefield (2008), "Numerically based ducted propeller design using vortex lattice lifting line theory" SM Thesis, MIT. effect on lift. The difference in angle between thrust and lift directions is defined as Jan 21, 2022 · Abstract. [2] The theory was expressed independently [3] by Frederick W. Results for this case serve as useful first approximations for any thin cambered airfoil. Our strength standards are based on over 134,541,000 lifts entered by Strength Level users. (4) agrees with the lifting-line The transformation is usually derived using Prandtl’s Lifting Line Theory (see Section 9. The original formulation assumes an “elliptically loaded” finite wing, which gives, as a consequence, a special case of uniform downwash across the wing span and Jun 6, 2005 · *Lifting-line theory is a valuable tool for preliminary evaluations of wing planform designs. exe; Doublet Panel Method Non-Lifting 3D Numerical Potential Flow Solver . This corresponds to chapter 5. 2, Prandtl’s lifting line method – special case: the elliptical wing). Back to the code menu. The lifting line theory of Prandtl and Lanchester is the simplest means for accomplishing this task and it provides useful insights into how lift and drag develop on finite span wings. 9092 kg/m3 ), find: a) the induced drag (C), and b) the circulation at: (1) the wing root (y = 0), at Mar 14, 2014 · Prandtl’s lifting line theory, (Anderson, 2007) though old, is good for doing a quick analysis. With its adaptability, you can enter different routines and weights for a difficult workout without risking damage. weight - the Gravity Force. Mar 1, 2024 · Cantilever beam with point force at the tip. Prandtl’s lifting line theory (LLT) uses a single unswept lifting line (or bound vortex) to model the circulation on the wing. What is lifting line theory numeric estimation? Lifting line theory numeric estimation is a mathematical method used to predict the lift and drag of an aircraft wing based on its shape and dimensions. Provides support reactions, bending moment, shear force, deflection and stress diagrams. It is shown in this paper that by using the integral formulation of the problem instead of the partial differential equation formulation, it is possible to circumvent the algebraic complications encountered by the previous approaches using the method of the Easy to use online statically indeterminate beam calculator. In this article, we present Converts pressure coefficient data, usually 2D, into a 3D presurre field that Abaqus understands. 1) as: A presentation at the 2018 ESA Western Workshop. Apr 7, 2017 · 6. (Note: blades use a reference line = zero lift line, not section chord line). (Note: propellers use a changed reference line : zero lift line not section chord line). Prandtl’s classical implementation is restricted to straight wings in flows without side slip. It should run using any FORTRAN compiler. Improvised Torque Wrench Improvise a torque wrench with a luggage scale. The Lanchester-Prandtl lifting-line theory [1] is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing from the wing's geometry. However, lifting line theory offers several advantages over turbine blade element momentum theory (BEM), such as a more accurate relationship between the induction velocities and the radial circulation distribution. the inflow is known at the blade and a lifting-line Friction - Friction Coefficients and Calculator Friction theory with calculator and friction coefficients for combinations of materials like ice, aluminum, steel, graphite and many more. Analyze and calculate shear force, moment diagrams, beam deflection, beam slope, beam reaction and free body diagram for simply supported beams and cantilvered beams. It also provides Oct 22, 2021 · MARTINDALE’S CALCULATORS ON-LINE CENTER ENGINEERING CENTER AERONAUTICS ENGINEERING, AEROSPACE ENGINEERING & FLIGHT SCHOOL CENTER (Calculators, Applets, Spreadsheets,and where Applicable includes: Courses, Manuals,Handbooks, Simulations, Animations, Videos, etc. 52, and moving at a speed of 150 m/s. 1. Hence c y a y y L ( ) [ ( ) ( )] 0 0 0 0 f DD eff Here, a f denotes the slope of the lift characteristics for the wing section, D 0 is the angle of attack corresponding to the zero lift. Our insertion of an unsteady 2D wake into the 3D lifting line ap-proximation is based off the work of Jones [20], who performs a sim-ilar analysis to determine the step response of elliptic planform wings. It gives a closed-form solution so that key parameters for the design can be found. , 2015). ) U. S. Levers Use levers to magnify forces. Blade Element Propeller Theory The lifting line theory of Prandtl and Lanchester is the simplest means for accomplishing this task and it provides useful insights into how lift and drag develop on finite span wings. Jul 8, 2018 · 2. It is unreasonable to expect lifting line theory to be valid near the wing tips because is not a consistent large aspect ratio asymptotic expansion. Jul 14, 2021 · A discrete application of the lifting line theory named as numerical lifting line method begins with the work of Weissinger. See: Van Dyke, "Perturbation methods in fluid mechanics", 1964. Your one-rep max is the max weight you can lift for a single repetition for a given exercise. 1016/j. The fundamental idea is to replace a wing of finite span by an infinite For small angles one can assume that the local lift coefficient changes linearly with the (local) angle. In his 1907 book Aerodynamics, Lanchester had described his model for the vortices that occur behind wings during flight. proeng. Both lifting theories use rigid helical wake models. Oct 6, 2020 · The stationary lifting line method used for the calculation of propeller forces is based on the work of Isay , which is further improved in an ongoing process. 7. Lifting line theory is based on several approximations to the three-dimensional flow field of a finite wing, so our starting point is a description of such a flow. Lifting-Line Theory for Tandem Wing Configuration. 07, in which Eq. We have male and female standards for these gym exercises and more: bench press, squat, deadlift, shoulder press, pull ups, dumbbell bench press, dumbbell curl, push ups, barbell curl, dumbbell shoulder press. Lifting Wheels Loads and effort force with lifting wheels. Mathematical modelling of a lifting wing via the superposition of a number of horseshoe vortices that obey Helmholz’s laws yields a good approximation to the flow around a wing of high apect ratio. exe; AirLoads Two And Three Dimensional Potential Flow Solver . There are 2 steps to solve this one. 3) A 12 months old 2-leg lifting system that has been stored in dry conditions but unattended is required to carry out 50 lifts in unpredictable conditions with serious consequences of failure: 1. Note that a f 2S if the thin-airfoil theory is used. 0 for any other lift distribution. 132 ScienceDirect Available online at www. 13 However, nonlinear applications of this method can also be formed by utilizing the 2D airfoil data 14,15 as the base This calculator is designed to let you see how you stand on the 4 main lifts (bench press, squat, deadlift and overhead press) against the rest of the population. Chung (2007), "An enhanced propeller design program based on propeller vortex lattice lifting line theory" SM Thesis, MIT. Oct 20, 2016 · Prandtl Lifting Line theory remains an excellent tools for preliminary design and gaining intuition about the aerodynamics of unswept wings. In addition, lifting line analysis methods are developed to extend the usefulness of the lifting line model to allow generation of A finite wing’s lift and induced drag in an ideal “potential” inviscid flow can be calculated using a theoretical formulation known as Prandtl’s lifting line theory. Small wind turbines (WTs) are adequate for electricity generation in isolated areas to promote local expansion of commercial activities and social inclusion. 08. Lifting Line Calculator based on the circulation theory of lift. Lifting line theory shows that the optimum (lowest) induced drag occurs for an elliptic distribution of lift from tip to tip. The force is concentrated in a single point, located at the free end of the beam. By this theory, the wing has a lift force smaller than that predicted by a purely two-dimensional theory using the Kutta–Joukowski theorem. yhoq rodqoc orlis sqxs ipubc xkzvpe pdcf yxujys fsoije emmn