Here for our Helicopter Blade Design Calculations**? **Read through for the helicopter blade length and width guide. You will also find helicopter equations of motion in the post.

The procedure of the CST representation method is shown in Fig. 2. This method is based on analytical expressions to represent and modify the various shapes.^{2} The components of this function are “shape function” and “class function”.

## helicopter blade length and width

## Helicopter Blade Design Calculations

Using the CST method, the curve coordinates are distributed by the following equation:(1)y(x/c)=CN2N1(x/c)S(x/c)where CN1N2(x/c)=(x/c)N1(1-x/c)N2 represents class function, *N*_{1} and *N*_{2} are exponents; S(x/c)=∑i=0N[Ai(x/c)i] is shape function, *x* non-dimensional values from 0 to 1, and *c* curve length (if the shape is like an airfoil upper curve, *c* is the chord length).

For the formulation of the CST method, Bernstein polynomials are used as a shape function.(2)Si(x)=Kixi(1-x)n-iwhere K≡ni=n!i!(n-i)! represents binomial coefficients, *n* is the order of Bernstein polynomial, and *i* the numbers 0 to *n.*

The CST method follows the process shown in Fig. 2. First, the given data points are converted to non-dimensional values. Second, the class function exponents and the degree of the shape function are defined. Then, shape function coefficients are calculated by the fitting process. Finally, by multiplying the shape function and the class function, the distribution function is obtained.

Fig. 3 shows the airfoil geometry represented using the CST method and non-uniform rational basis B-spline (NURBS). In this case, the control variables are the coordinates of control points (five variables for the upper curve and five for the lower curve). The CST method with four control variables fits the existing airfoil better than NURBS, which uses ten control variables.

Fig. 4 shows the absolute errors *ɛ* of airfoil generation using CST and NURBS (five control points for each curve, fourth order blending functions). Generation by NURBS gives bigger errors at the tail part of the airfoil.

The advantage of the CST method in comparison with other methods such as Spline, B-Splines, or NURBS is that it can represent curves and shapes very accurately using few scalar control parameters.

In this study, the airfoil baseline was chosen as NACA0012. With the given data coordinate points in Cartesian coordinate space, a curve fitting was generated using fourth order Bernstein polynomials.

The class function for the airfoils is(3)C(x)=x0.5(1-x)

The airfoil distribution functions defined as upper and lower curves are presented sequentially as(4)y1(x)=C(x)[Al0(1-x)4+Al14x(1-x)3+Al26x2(1-x)2+Al34x3(1-x)+Al4x4]yu(x)=C(x)[Au0(1-x)4+Au14x(1-x)3+Au26x2(1-x)2+Au34x3(1-x)+Au4x4]where *A*_{u0} = 0.1718; *A*_{u1} = 0.15; *A*_{u2} = 0.1624; *A*_{u3} = 0.1211; *A*_{u4} = 0.1671; *A*_{l0} = −0.1718; *A*_{l1} = −0.15; *A*_{l2} = −0.1624; *A*_{l3} = −0.1211; *A*_{l4} = −0.1671.

Changes in the coefficients *A*_{0} and *A*_{4} in the CST method are sufficient for airfoil shape modification.These coefficients are also the design variables of the examined optimization problem.

Four coefficients of the airfoil distribution function are defined as the initial input data of the design process after obtaining the fitting curve of the airfoil baseline NACA0012. Then, airfoil coordinate points are generated by the CST function.

2KFoil, an airfoil analysis program for subsonic isolated airfoils, was adapted from the well-known XFOIL program to be suitable for the present study. The main algorithm of this code is a combination of high-order panel methods with a fully coupled viscous/inviscid interaction method.

The inviscid formulation of 2KFoil is a linear vorticity stream function panel method. A Karman-Tsien compressibility correction is incorporated, allowing good compressible predictions all the way to sonic conditions.

The viscous formulations come from the boundary layers and wake which are described with a two-equation lagged dissipation integral boundary layer and an envelope en transition criterion.

A sequence of angle of attack (AoA) from −20° to 20° is calculated for each Mach number *Ma _{∞}* from 0.05 to 0.70. The starting AoA of each calculation is set to 0°, and the AoA step is set to 0.5°, thereby ensuring that the Newton solution method using the last available solution as a starting guess for a new solution works well.

^{6}Moreover, an algorithm has been implemented in order to recognize any impossible predictions such as a very high AoA in the stall condition. Detected errors are handled by halting the calculation and proceeding to the next calculation at another

*Ma*. Therefore, the algorithm ensures good predictions and always completes sequence calculations automatically.

_{∞}The airfoil to be analyzed will be input into 2KFoil as airfoil coordinate points, and then 2KFoil will generate the lift, drag, and moment coefficients *C _{L}*,

*C*, and

_{D}*C*corresponding to a specific angle of attack,

_{M}*Ma*(from 0.05 to 0.70), and Reynolds number.

_{∞}#### 2.2.3. Konkuk helicopter design program (KHDP)

KHDP is a helicopter sizing, performance analysis, and trim analysis program that was developed at Konkuk University. These codes were developed for use in the conceptual design phase and hence they used empirical formulas to reduce computing times. The sizing process was based on graphical design techniques method called the fuel ratio or *R*_{F} method developed during the 1950s and 1960s and initially utilized with nomographs.

To quickly understand and image the helicopter behavior, the performance analysis module was developed. An analytical method was used to provide the designer with a reliable tool of sufficient fidelity to assist in the design process. The module is based on an energy approach and it has been written to yield results quickly and inexpensively.

Blade element theory was implemented to calculate the required power in different helicopter operations, namely hover, climb, cruise, descent, and autorotation.

Fig. 5 shows an integrated algorithm that was developed to predict the performance behavior of a helicopter by momentum theory and blade element theory (BET). BET needs to call trim module analysis to obtain the required power. Therefore, the required power is a function of the airfoil shape, and the blade planform.

The program KHDP with the performance analysis module provides many options for the objective function. The objective function of this study is chosen as the required hover power. Helicopter data are analyzed by the performance code obtained from either the sizing module or user inputs.

The KHDP program process using BET is shown in Fig. 5.

Validated results of each module are shown in Ref. ^{12} The differences between calculated results and the existing data are within 5% in general, hence acceptable for preliminary design phase.

After achieving the trim condition, meaning that the trim condition is attainable, the required power is evaluated in order to proceed to the next loop of the optimization process. So, a new set of initial data (root chord, the point of taper initiation, taper ratio, pretwist, and *A*_{0} and *A*_{4} of the airfoil distribution function) is generated depending on the optimization algorithm. This loop continues until the convergence condition is satisfied.

The harmonic balance method was used in the trim code module to calculate trim angles’ (collective pitch, cyclic pitch, etc.) forces and moments. Required power is then calculated using below equations:(5)PH=PHMR+PHTR(6)PHMR=MMR×ΩMR/746(7)PHTR=MTR×ΩTR/746where PH is helicopter required hover horsepower, PH_{MR} main rotor horsepower, PH_{TR} tail rotor horsepower, *M*_{MR} main rotor moment, *M*_{TR} tail rotor moment, *Ω*_{MR} rotational frequency of main rotor, and *Ω*_{TR} rotational frequency of tail rotor

## helicopter equations of motion

### Top 10 Luxury Helicopters in the World

Most people have heard of personal and charter jets, but **luxury helicopters** are the genuine gems. Not only are these aircraft comparatively less expensive, but helicopters can approach places that bulky jets can’t. Having a private or commercial helicopter is expedient, more environment friendly, and a symbol of status. Celebrities including Brad Pitt and Angelina Jolie and Donald Trump own a **luxury helicopter**, and this slot market has grown considerably in recent years due to demand from the rich.

They are well-appointed with all the newest technology, and interior seating marks that are designed in fine Italian leather upholstery.

Therefore the list of top 10 **luxury helicopters** is given below:

## 1. Augusta Westland AW119 Ke Koala:

The Koala is chiefly used by law enforcement, but it can easily provide accommodation to a group of corporate directors traveling on business. It has a VIP services quite adequately, with premium leather upholstery and seating for about 6 passengers and 2 operators. The Koala reaches a top speed of 166 mph (267 km/h) and a range of 618 miles (995 km). Price ranges from $1.8 to $3 million.

## 2. Eurocopter Hermès EC 135:

Though this brand of **luxury helicopters** is not suitable for long distant trips, is has a class apart built. The typical EC 135 will cost you a mere $4.2 million, but the one with the interior design from the best in class designer will cost you up to $6 million. The top speed is 178 mph, but the range is just 395 miles.

## 3. Augusta Westland AW109 Grand Versace VIP:

Augusta Westland teamed up with the Italian fashion house Versace to produce a super luxury interior for this fancier version of the AW109. The top speed is about 177 mph and a range of 599 miles. The mere difference is that all 599 of those miles will be more **luxurious** for the VIP passengers. Hence, will cost you $6.3 million price tag and the helicopter is fully covered in Versace leather, design and exterior.

## 4. Eurocopter Mercedes-Benz EC 145:

If you’re a Mercedes fan, now you can fly your preferred brand **helicopter** too. A regular EC 145 costs about $5.5 million, so the Mercedes version is going to cost anywhere around $7 million. But it’s totally worth it. No other Mercedes can go 153 mph while flying 17,000 feet above the ground. It has all the luxury of the famous German sports.

## 5. Eurocopter EC 175:

The EC 175 made its wonderful first appearance at the Paris Air Show in 2009. The chief feature of the EC 175 is that it can hold 16 passengers contentedly inside. The top speed reaches 178 mph (286 km/h), with a range of 345 miles (555 km). It costs whooping $7.9 million.

## 6. Eurocopter EC 155:

This is a luxurious chopper. Its top speed is an impressive 200 mph with a range of 533 miles. It can seat as many as 13 passengers; this spacious EC 155 aircraft will cost you $10 million.

## 7. Sikorsky S-76C:

The Sikorsky S-76C is more generally known as Black Hawk. The **massive interior** is large sufficient to fit up to a dozen passengers, but the seating occupies 4 passengers in Black Hawk model. It reaches a top speed of 178 mph (286 km/h) and has a range of 473 miles (761 km). It would cost you a $12.95 million.

## 8. Augusta Westland AW139:

The AW139 is appropriate for law enforcement, armed patrol and firefighters. It has a capacity to seat 8 passengers. The AW139 can reach an unbelievable top speed of 193 mph (310 km/h), with a range of 573 miles (922 km). It carries a **beautiful interior** costing you a hefty $14.5 million.

## 9. Bell 525 Relentless:

Like the Gulfstream 650 jet, the Bell 525 Relentless helicopter isn’t on the market currently. This chopper is going to cost $15 million. They predicted that the seating will be for 16, a top speed of 162 mph, and a range of 460 miles. This bright yellow Relentless with amazing seating will cost you a fortune.

## 10. Sikorsky S-92 VIP Configuration:

The S-92 can safely accommodate 9 passengers in its extensive interior cabin. The prices vary exponentially if you plan on decking the interiors with gold or crystal. The top speed of the S-92 is around 194 mph (312 km/h), with a range of 594 miles (956 km). The prices range from $17 million to $32 million.

Helicopter charter can be the most stress-free travel familiarity you will ever have. Which includes being able to travel outside of airports to reach vital meetings or even other flights in a different airport. Though rich class can afford these **luxury helicopters**, they are worth the investment.