## Mercator projection and flight paths *

As a sidenote to the previous post on tailwinds and supersonic flights, if you love flying one of the many things that you would do is check out the flight path. But when you do so, you might lay your eyes on some bizarre looking routes.

This is the flight path taken by an emirates A380 flight operating from Dubai to Los Angeles.

First thing to note is this is not how the actual path looks like since this is the cylindrical projection of a sphere onto a 2D plane (known as Mercator projection)

The yellow path (great circle route) is the shortest route between SFO -LHR

And as a result of this projection, drawing a straight line across the map would not yield the shortest distance.

Instead, the shortest course between two points on the surface of a sphere is known as the Great circle route.

Pilots love to take advantage of jetstreams to save time and fuel

It is to be noted that although the distance is shorter when one takes the great circle route,one has to account for a lot of other factors while planning a flight path ( such as wind patterns, fuel consumption, air temperature, etc ) and it is not uncommon for pilots to deviate from the great circle route.

## Tailwinds and supersonic flight

In 2015, a 777-200 made the Newyork-London route in 5 hours,16 minutes where the usual journey time is ~7 hours.

The flight reached ground speeds of up to 1200 km/h (745 mph),
riding a powerful jet stream of up to 322 km/h (200 mph) tailwinds and  breaking the sonic barrier ( 1224 km/h (761 mph)).

The principle is analogous to those high school problems in relative velocity:

“A man rows a boat in a river. The velocity of the
boat is … Find the stream velocity”

If you are headed downstream i.e in the same direction as the river stream you will reach your destination faster than if you were rowing upstream.

Similarly a tailwind is one that blows along the same direction of the aircraft increasing the net speed of the aircraft ,and headwind is one that blows in the opposite direction and slows the craft down.

So, does this mean that if you are moving at v kmph and there is a headwind of -v kmph, you would just hover? Hell yeah!

Take a look at this video:

## Wind shear

A phenomenon known as ‘wind shear’ occurs when the wind speed changes abruptly, which can cause turbulence and rapid increase/decrease in velocity of flight.

This can be really challenging during landing since if the headwind turns tailwind, there is a possibility of the aircraft overshooting the runway due to the increased velocity.

## What causes this ?

The aviation industry takes advantage of trade winds and jet streams in order to cut time off the flight and save fuel.

Tradewinds are caused by the unequal heating of the atmosphere
at different latitudes and altitudes and by the effects of the Earth’s
rotation (Coriolis effect).

Trade wind pattern. Credit: Earth Wind Map

Jet streams on the other hand are this narrow current of fast moving
winds in the upper troposphere flowing west to east. And riding one can
definitely make your travel time shorter.

Jet streams in the northern hemisphere

As a result of jet streams, within North America  the time needed to fly east across the continent can be decreased by about 30 minutes if an airplane can fly with the jet stream, or increased by more than that amount if it must fly west against it.

Pilots receive a weather briefing actively during flight. Included in the briefing is the best combination of jetstreams and other wind patterns that the pilot can take advantage of saving time and fuel.

Many airports have runways facing in different directions in order to allow the pilots to use the runway that faces the wind during take off/landing.

Have a great day!

## A vortex portal to another universe.

This is known as wingtip vortex. It is a ramification of the design of the wing and how it works.

How does an aircraft fly? Think of it like this, due to the design of the wing, larger number of air molecules are hitting the bottom portion of the aircraft than the top.

As a result, a upward force acts on the wing, hence the wing lifts!

This works fine till we get to the wing tips.

In the wingtip, the air from a higher pressure wants to move to the region of lower pressure. And as a result, this forms vortices ( fancy name for the swirling motion of air ) known as Wingtip Vortex. ( because its formed in the wing tips!!! )

## Why do birds fly in a V formation?

Migratory birds take advantage of each other’s wingtip vortices by flying in a V formation so that all but the leader are flying in the upwash from the wing of the bird ahead. ( Look at the image, each one is exactly out of phase in its wing motion ).

This upwash makes it easier for the bird to support its own weight, reducing fatigue on migration flight.

Wow! There is so much more to a bird’s flight that that meets the eye. I will take up the same sometime down the line. But, If you are really curious to find out why, read this nature article.

Have a Good Day!

PC: John Benson, boldmethod,mathcareer, natgeo, NASA.

EDIT – Also do check out the Smoke Angels.

Now we now know about stalls, boundary layers and wing tip vortices. In the concluding post of this mini series we will try to apply the knowledge gathered thusfar in the context of a F1 car. Stay tuned…

## Vortex Generators

So we now understand about boundary layers, flow separation, stalls, what causes them, how to detect and get out of one  (previous post).

One way to delay stalls is by inserting is a small angled plate  on the wing known as Vortex Generators. They impart a rotational/swirling motion to the flow of air on the surface of a wing.

## Why do Vortex generators work?

Basically, creating a vortex over a surface allows you to delay boundary
layer* separation.

The swirling/rotational motion of air prevents the separation of air from the wing earlier on. This increases the lift and/or also reduces drag.

## Benefits of vortex generators

As you saw in the gif above the stallspeed when using VGs drastically
reduces. This means that you can fly (and land safely) at low speeds without stalling.

And it has also been shown that VGs reduce the noise generated by air inside the aircraft.

Some more benefits have been listed below (source) for the sake of completion:

● An added safety margin for low-speed flight

● Improved low-speed handling characteristics

● Improved cross wind handling at low speeds

● Increased safety margin in the event of an engine failure

● Reduced take-off distance, improving short field performance

Now this idea of forcibly generating vortices to increase lift and/or reduce drag finds application in some crazy places and we shall be looking at that in the next post.

Good day!

## The Physics of the ‘Stall’

The proposition that more the angle of attack, more the lift does not hold at all angles.

At about 14 degrees, something weird happens and the aircraft instead of soaring the skies starts to plummet to the ground.

When this happens it is known as a stall.

## What causes Lift ?

The main thing to know is that a difference in pressure across the
wing–low pressure over the top and higher pressure below–creates the net
upward force we call lift.

Upon reaching a certain velocity, the aircraft’s lift is more than its weight and as a result, the aircraft takes off .

## The Concept of a Boundary Layer (BL)

There is a high chance that you might have heard this word even in a casual conversation about wings and that’s because its an important concept in the context of aerodynamics and associated fields.

To understand the physics of a stall, lets consider the interaction of a moving air on a flat plate.

The nature of airflow over a wing/plate is the result of stickiness or viscosity of air.

The first layer sticks to the wing/plate not moving at all.

The second layer in frictional contact with the first moves slowly over it.

And the third layer moves somewhat faster than the second

Thus layer by later the flow builds up to the free stream velocity or airspeed. These layers of flow are known as boundary layers.

What happens to the BL during a stall?

During a stall, these successive tiers of air that form the boundary layer lose their gripping on the surface and break away into turbulence.

( what i mean by turbulence is the chaotic wiggling of the test leads attached to the wing in the animation )

It takes a pressure difference between the top and bottom parts of the wing in order to produce lift. But when the flow of air becomes turbulent ( i.e during a stall ), this pressure difference is no longer established.

As a result of which, the lift drastically decreases and the aircraft starts dropping to the ground.

## How to get out of a stall ?

Stalls can cause problems only when the pilot is not aware that the aircraft is stalling. ( Unlikely but has caused accidents in yester times )

As the airplane loses altitude, its nose dips down and airspeed picks up quickly. This restores the lift and the pilot would be able to regain control and bring the aero-plane into level flight.

## How are stalls detected ?

On light aircraft there is a reed (much like used on a musical wind
instrument) mounted on one wing root, which is angled such that at the
Angle of Attack which would cause a stall, the reed “plays” which can be
heard in the cockpit.

Here is a view of where this system is mounted on a Cessna

On some aircrafts, it is a similar principal, however instead of a
reed, it uses a fin which at critical AoA pushes a micro-switch which
activates a buzzer/horn inside the cockpit.

Here is the assembly on a Beech 18

Large commercial aircraft typically rely on either Angle of Attack (AoA) Vanes or Differential Pitot Tubes  to supply input to flight computers for the purpose of calculating AoA.

Source

Review:

A lot of important stuff regarding aerodynamics in this post. Here’s a summary of the post:

Boundary Layer concept  — >  Why do aircrafts stall ? — >  How to get out of one  — > How are stalls detected ?

That’s all folks!

Hope you enjoyed today’s post and learnt something new.

Have a good one !

This post covers the fundamental principles from which the subsequent posts queued up for this weekend are derived from. Stay tuned.. It is gonna be wild ride.

P.S: If you study at UCDavis, feel free to ping me !

## When you are in the combat zone, agility of a fighter jet is of…

When you are in the combat zone, agility of a fighter jet is of utmost importance. But as an engineer, if you have already fiddled around with the wing structure your next option would be to fiddle around with the direction of the thrust.

## Thrust Vectoring

Thrust vectoring is primarily used for directional control in rockets and jets. And one achieves this by manipulating the direction of thrust .

This generates the necessary moments (and forces) that enable the directional control of the aircraft.

An aircraft traditionally has three “degrees of freedom” in aerodynamic
maneuverability; pitch, yaw and roll. **

The number of “dimensions” of
thrust vectoring relates directly to how many degrees of freedom can be
manipulated using only the vectored engine thrust.

Therefore, 2D
vectoring allows control over two degrees of freedom (typically pitch
plus either roll or yaw) while 3D controls all three.

## Lockheed Martin F35B

The F-35B short takeoff/vertical landing (STOVL) variant is the world’s first supersonic STOVL stealth aircraft.

It achieves STOVL by swiveling its engine 90 degrees and directing its thrust downward during take off/lvertical landing mode.

In the following gif you can witness the transition from a 90 degree tilted engine towards a forward thrust engine during flying.

Unlike other variants of the Lockheed Martin F-35 the F-35B has no landing hook. And as a result, witnessing its landing is rather pretty special.

But nevertheless, this is one of those posts which addresses a topic that has been a the
gold mine for research. If this sort of thing fascinated you, there have been a lot of research conducted by NASA do check them out.

Have a great day!

** Aviation 101 : Pitch Roll and Yaw