# Fluid Mechanics Applications/B13:General Study Of Aerofoil Designing And Their Uses in Different Scenarios

This page is a brief introduction to airofoils and their uses in different technological spheres. Just as the wheel ushered a new era for transportation through land, airfoils have likewise made this possible through air. The intent is to understand how the Bernoulli's Theorem comes into play and how the same phenomenon can be used for diverse functions.

## Introduction

This project provides an insight into the functioning of airfoils and in particular specialized airfoils for small thrust large lift in airplanes with quick ascend capability. It also delves into the use of airfoils for providing the so called 'down' force, a force that keeps swift supercars to ditch the tarmac! Due to the constraints imposed on the time factor into this project, the applications have been typically restricted to the use of 'deep camber line' type airfoils in the design of the specialized aircrafts employed in aircraft carriers. The sampling and research of the aerodynamic properties of an airfoil are carried out by scaling down the actual aerofoil dimensions to more manageable dimensions and this is usually done by fabricating a model made of polystyrene. The aim is to investigate how the design is modified for these airfoils to increase the lift force generated for a given angle of attack.

## Basic Airfoil Theory

A structure with curved surfaces designed to give the most favorable ratio of lift to drag in flight, used as the basic form of the wings, fins, and tail planes of most aircraft is defined as an airfoil. Every aspect of an airfoil aims to produce the maximum lift by at the cost of the drag force.

### Thin Airfoil Theory

In most the transcript we will be keeping our discussion restricted to the 'Thin Airfoil Theory'. Before discussing the airfoil theory we must adhere to some of the common terminologies used in the theory-
The upper part is the 'Suction Surface'. It is also where the wind speed is high while the static pressure is low. Also the wind speed is lower at the bottom profile. This imbalance in pressure or the 'pressure gradient' is the prime cause for creation of 'lift'. However due to the relative speed between the foil and the wind, drag forces act on the airfoil. Thin airfoil theory is a simple theory of airfoils that relates angle of attack to lift for incompressible, inviscid flows. It was devised by German-American mathematician Max Munk and further refined by British aerodynamicist Hermann Glauert and others in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing an airfoil of zero thickness and infinite wingspan. Thin airfoil theory was particularly notable in its day because it provided a sound theoretical basis for the following important properties of airfoils in two-dimensional flow: (1) on a symmetric airfoil, the center of pressure and aerodynamic center lies exactly one quarter of the chord behind the leading edge (2) on a cambered airfoil, the aerodynamic center lies exactly one quarter of the chord behind the leading edge (3) the slope of the lift coefficient versus angle of attack line is units per radian Thin airfoil theory does not account for the stall of the airfoil, which usually occurs at an angle of attack between 10° and 15° for typical airfoils.

### Derivation of Thin Airfoil Theory
## Statement Of the Bernoulli's Theorem

Bernoulli's Theorem is usually subject to the following restrictions- 1. Steady Flow 2. Frictionless Flows. 3. Flow along a streamline. 4. Incompressible Flow.
The Bernoulli equation is probably the most famous and abused equation in any fluid mechanics study. Due to the simple algebraic relations between the parameters involved, it is an easy bait for the amateur fluid mechanist. It is of utmost care that should be practiced while using this relation, keeping in mind clear the restrictions imposed!
We have omitted the derivation for the theorem here. It has been done to keep the text as simple and more practical based. For a further look in the theorem, links have been provided in the Bibliography.
or:
where:

## Deep Camber Airfoil

The designing of airfoils is not an easy task. It involves painstaking use of physics and of precision technology to fabricate them.
To come out confidently on a certain design for a certain application involves designing, modeling, improvising, and finally testing it under the work conditions. For a suitable airfoil for flight, we need the maximum lift possible.
By a simple experiment in the wind tunnel using the airfoils and calculating the lifts generated, for a given wind speed, it was noticed that the 'Deep Camber' shaped foil produced the maximum lift for the same relative speed on the foils.

## Impact of Airfoil Design on Evolution of Flight Technology and vice-versa

Flight technology has come a long way from the Wright brothers maiden flight. It was the first time that man was able to move through air majestically, replicating the flights of the avian kingdom. The longing finally ended and from them there was no turning back!
What was essentially a long glide was the first baby step towards the marvel of the modern state-of-the art fighters. As better propulsion systems were devised, the thrust force increased manifold times and so did the viscous drag. To overcome this drag larger lift was required. One way out was to increase the wing span-thereby increasing the area, this however was not a very good thing to do as this caused a decrease in maneuverability.
These are the prewar planes. Wars despite of their toll on human lives, also are a period of massive technolgical enhancements and breakthroughs! The planes that were faster, lighter, better armoured and essentially better designed were the ones that touched down in a single piece again.
With the war in Europe touching the skies, it became evident that better fire power was not the only factor in aerial dog fights. The better designed airfoils pioneered by the Germans made them a very potent force.
It is useful to realize the importance of wing design in the handling of the craft.
triplane due to its better design (and a unique ability to rain down bullets from within the propeller) to say the least caused the Allies some problems till the spring of 1918. As the Second World War came to date, there were further improvements in the flight designing and thrusting. The Japanese became the best in their class due to their very potent and agile planes. Once again the importance of better wing design were realized. The German Air force more famously the 'Luftwaffe' and the Americans were great at plane building and modernization.
ed
The senseless killings of the second world war however didn't necessarily bode too bad for the developments in aviation technology. The period came to see the development of the 'Jet' propulsions. Not only were these a large step ahead but were also the direct precursors to the modern planes. The modern aircraft is a marvel of technology. From the huge airbuses to the agile raptors the flight technology has seen unprecedented highs. The demanding purposes of these crafts require extraordinary designing capabilities.
The F-22 call sign 'Raptor'. Notice the shape of the wings crafted for better maneuverability at supersonic speeds.
The wings of the carrier A-320 have been designed for subsonic high lift characteristics. Two different scenarios using same theory for their working!

## Body Governing The Nomenclature for Airfoils

NACA is one of the bodies responsible for the assigning of names to the aerofoils which have passed for stability and can be fabricated by varying the well defined parameters.

## Caase Study in the Uses of Airfoil in Practical Applications
### FA/18 Hornets

In the August of 1973, the US Congress mandated a bill to introduce a new fighter to replace the aging F-14 from its carriers. The demands included to create a new fighter with much better abilities to carry larger payloads and go further. The U.S. Navy started the Naval Fighter-Attack, Experimental (VFAX) program to procure a multirole aircraft to replace the Douglas A-4 Skyhawk, the A-7 Corsair II, and the remaining McDonnell Douglas F-4 Phantom IIs, and to complement the modified F-14 Tomcats. The project was met with great zeal due to the ever looming Soviet threat. This lead to the NASA to get involved in creating a new aircraft with better wing design. The F-18, known as McDonnell Douglas Model 267, was drastically modified from the YF-17. For carrier operations, the airframe, undercarriage, the shape of the wings and arrestor hook were strengthened, folding wings and catapult attachments were added, and the landing gear widened. To meet Navy range and reserves requirements, McDonnell increased fuel capacity by 4,460 pounds (2,020 kg), by enlarging the dorsal spine and adding a 96 gallon fuel tank to each wing. A "snag" was added to the wing's leading edge and stabilators to prevent a flutter discovered in the F-15 stabilator. The wings and stabilators were enlarged, the aft fuselage widened by 4 inches (102 mm), and the engines canted outward at the front. These changes added 10,000 lb (4,540 kg) to the gross weight, bringing it to 37,000 lb (16,800 kg). The YF-17's control system was replaced with a fully digital fly-by-wire system with quadruple-redundancy, the first to be installed in a production fighter. These planes were later used by NASA.

### Rear Wing of the Bugatti Veyron

Bugatti produced it's masterpiece and wielded to the audience a 1,001 brake horse power monster. With top speeds of about 253 miles/hour and a W-16(combine of two v8s) under the bonnet, powerful braking systems were required for the beast. The disc braking simply couldn't on its own provide this power. The wing on the rear side of the car rose up to the task and delivered. The airfoil employed here essentially provides the necessary down force while accelerating and the drag when braking