Tag Archives: aeroplane

Altitude and Flight Level

The term elevation refers to the position of a point or an object on the ground above a fixed reference point, usually mean sea level. The term altitude refers to the position of a point or object in the air above a fixed reference point.

But defining altitude can be difficult, and so when altitude is referred to, the reference point must always be explicitly defined. Altitude is normally measured above mean sea level (AMSL) or above ground level (AGL). For example, if an aeroplane flew over the peak of Mount Everest, its altitude could be referred to as either 38 000 ft AMSL or 9000 ft AGL, because the peak of Everest has an elevation of 29 000 ft.

For aircraft it is difficult to measure altitude. You might think that GPS could provide this information, but GPS is designed for positioning on the surface of the Earth and isn’t very good at measuring altitude.

Pilots have always used atmospheric pressure to measure altitude. As an aircraft moves further upwards into the air, there is less air above it pushing down on it and the pressure decreases. This decrease is predictable and easy to calculate:

p_h = p_0 \left( 1- \frac{\gamma h}{T_0} \right)^{\frac{gM}{R\gamma}}

where p_h is the pressure at height hp_0 is the standard atmospheric pressure of 1013.25 hPa\gamma is the rate at which temperature decreases with altitude (the temperature lapse rate); T_0 is the standard temperature; g is the gravitational field strength; M is the molar mass of dry air; and R is the molar gas constant.


Aeroplanes do not fly at a set altitude. Rather they fly at a given flight level, which – although it sounds like a height – is actually a pressure. When a pilot flies at a flight level of 32 000 ft (FL320) they are actually flying at a constant pressure of 275 hPa, and may actually be far above or far below this altitude, depending on the local weather (and therefore pressure) conditions. If they enter an area of particularly high or low pressure they will have to ascend or descend correspondingly.

Using flight levels helps to prevent collisions between aircraft: in the UK aircraft flying on headings between 000° and 089° (north to east) they flight at odd numbered flight levels (FL310, FL330, etc); flying between 090° and 179° (east to south) at odd numbered flight levels plus 500 ft (FL315, FL335); flying between 180° and 269° (south to west) at even numbered flight levels (FL320, FL340); and flying between 270° and 359° (west to north) at even numbered flight levels plus 500 ft (FL325, FL 345). In other parts of the world different flight level rules are used.

The Kármán Line

The Kármán Line, at 100 kilometres above sea level, is commonly taken to be the boundary between Earth’s atmosphere and space. But why?

An aircraft generates lift by moving through air.

L=\frac{1}{2} AC_L \rho v^2

where L is the lift generated, A is the wing area, C_L is the lift coefficient, \rho is the density of air, and v is speed through the air.


Data from NASA MSIS E-90 atmosphere model. Note that density is plotted on a logarithmic scale and (absolute) temperature on a linear scale.

The density of air changes with elevation (altitude is height above ground, elevation is height above sea level). Therefore, keeping all other factors the same (which would be the case for an aircraft, which cannot change the area of its wings or its lift coefficient), as the air becomes less dense an aircraft must increase its speed to stay airborne. A Boeing 747-400 has a wing area (planform) of 541.2 square metres and a lift coefficient of around 0.5. Assuming that it flies empty, with a mass of 178?800 kilograms (weight 1?754?000 N), the speed it will need to fly to generate the required lift changes rapidly as the air becomes thinner. (At an elevation of 200?km a 747-400 would have to fly at nearly twenty thousand times the speed of sound.)


Speed required at elevation for a Boeing 747-400.

The cruising speed of a 747-400 is about Mach 0.85 or 290 metres per second, which limits the 747-400 to an elevation of around 16 km. (In reality it flies much lower, around 12?km, for safety and fuel consumption reasons.) The record elevation for sustained horizontal flight by a ground-launched aircraft is 36?240 m by a MiG-25M, which was, at the time, one of the fastest military aircraft with a top speed of Mach 2.83.

The Kármán Line, at an elevation of 100?km, is the point at which the atmosphere is so thin (more than a million times thinner than air at sea level) that an aircraft would have to be moving at a speed faster than it could orbit in order to stay in the air. Thus, it is the greatest altitude at which an aircraft could fly in a straight line rather than following the curvature of the Earth.



As you can see from the graph above, for our Boeing 747-400, the Kármán Line is around 61?km, rather than the full one hundred kilometres, because the 747-400 is not the most aerodynamic of aircraft, designed for bulk passenger carrying and cost-efficiency rather than performance.

Pylon Turns and Long Line Loitering

A pylon turn is a manoeuvre in which an aeroplane flies in a circle, banked with one wing pointed towards a fixed point on the ground.

Pylon turns were originally used in air racing, and are used extensively by military aircraft, as it allows them to easily and accurately direct fire onto targets on the ground for a long period of time.


In the photograph above an AC-130 Spectre gunship is executing a pylon turn. The aircraft’s GAU-2/A miniguns and L/60 Bofors cannon are visible on the aircraft’s left-hand side, pointing towards the centre of the pylon turn.


An AC-47 Spooky gunship executing a pylon turn whilst directing tracer fire against a target on the ground.

The physics of a pylon turn depend on the bank angle, the speed of the aircraft and the aircraft’s altitude, but these are intrinsically linked. You can pick two, but the third is then fixed: a pylon turn can only occur at a certain bank angle for a given speed and altitude; or at a certain speed for a given bank angle and altitude; or at a certain altitude for a given bank angle and speed.

A pylon turn also allows for a procedure called long-line loitering, in which a container can be lowered to the ground from a moving aircraft, remaining stationary on the ground in the process. This enables delivery and retrieval of material without the aircraft having to land.


Patent drawings from US patent US3724817 A. Click to enlarge.

A drag cone (a small parachute) helps to pull the line into a loop, keeping it relatively stationary and allowing the far end of the line to drop to the ground. This technique has been used to retrieve personnel and even to deliver mail.


The plane that shot itself down

The Grumman F-11 Tiger was the US Navy’s first supersonic fighter jet. It came equipped with four Colt Mark-12 cannons that fired 20mm projectiles at more than 1000 metres per second.

Grumman F-11 Tiger, serial number 138620

In September 1956 Thomas W. Attridge, a Grumman test pilot, was flying Tiger #620 in a test flight over the Atlantic Ocean; part of this test flight was to test-fire the Tiger’s cannons. At 20 000 feet Attridge entered a shallow 20° dive and at an altitude of 13 000 feet fired a 70-round burst from one of the cannons. He then activated the Tiger’s afterburners and entered a steeper dive, firing a 55-round burst from the cannon at 7000 feet to empty the cannon’s gun belt.

At this point three of the rounds that he had fired at the higher altitude, which had been slowed by air resistance and which had curved towards the Earth under the effect of gravity, struck the aeroplane’s windshield, nose cone and one of the engine intakes. With reduced engine power available Attridge was unable to return to Grumman’s Long Island airfield and when the engine finally died he was forced to crash land, 800 metres short of the runway.

Despite the unused fuel catching fire, and unfired ammunition from the other cannons “cooking off“, Attridge survived with only a broken leg and three damaged vertebrae; had the cannons been armed with explosive rounds, as would normally be the case, it is unlikely that he would have survived. Attridge later went on to become the project manager for LM-3, the first Apollo Lunar Module to be rated for human spaceflight, which was used as part of the Apollo 9 mission.

In 1973 another Grumman test pilot, Pete Purvis, also shot down his own plane,* this time  with a dummy AIM-7E Sparrow III air-to-air missile that pitched upwards after being released from its hardpoint and struck the wing of the F-14 Tomcat that Purvis was flying. Both Purvis and his Weapons Systems Officer ejected safely.

via Futility Closet

* Source: The Day I Shot Myself Down by Pete Purvis. Purvis also worked on the Fulton Skyhook recovery system.

Whole aeroplane parachutes

Some pilots wear parachutes when they fly, in case they have to bail out of a malfunctioning aircraft. But what if you wanted the aeroplane itself to bail out?

Unlike parachutes for humans, whole aeroplane parachutes are deployed balistically; they are “fired” out of their containers by solid-fuel rockets, rather than pulled by air resistance.

A vertical launch whole plane parachute mounted on an aeroplane’s roof. The thin black container contains the solid-fuel rocket that will pull the parachute out of the white container.