Sonic booms and Mach cones

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When an object moves through the air it pushes the air in front of it away, creating a pressure wave. This pressure wave travels away from the object at the speed of sound. If the object itself is travelling at the speed of sound then these pressure waves build up on top of each other to create a shock wave, or sonic boom.

On the left, an object travelling at Mach 0.7. On the right, an object travelling at Mach 1.0.

One of the most common misconceptions about sonic booms is that they occur only as an object accelerates beyond Mach 1.0 (through the “sound barrier”) and not during supersonic flight. This is not the case. A sonic boom is continuously created as long as an object is travelling faster than the speed of sound, and this sonic boom trails behind the object, creating a Mach cone.

mach-cone

The shape of this Mach cone depends on the speed of the object, and the faster an object is, the narrower its Mach cone. For a supersonic or hypersonic object these cones can become very narrow and thus when the sonic boom from a high-speed aircraft reaches the ground the aircraft in question has already passed by and can be quite a distance away.

The angle of the Mach cone (μ) between the shock wave and the horizontal is simple to calculate from the object’s Mach number (M).

mach-angle-equation

For an F-22 Raptor travelling at its maximum speed of Mach 1.82 the angle of the Mach cone formed is 33.3°. If the Raptor was flying at an altitude of one hundred metres then it would always be sixty-five metres away (horizontally, in the direction of travel) from where its sonic boom was detected and 120 metres in a straight line from the point of impact. At a distance of 120 metres a person on the ground is hearing (or rather, feeling) the sonic boom 350 milliseconds after it is emitted, assuming the speed of sound is 340 metres per second.

By looking at Schlieren photographs, which can image differences in gas density, we can see the shockwave created, find the Mach cone angle, and from that calculate the speed of an object moving through the gas.

bullet-mach-cone

In the photograph above the Mach cone angle is 28° and therefore the bullet must have been travelling at Mach 2.1 or 720 metres per second (assuming the speed of sound is 340 m/s).

The fission-fragment rocket

Travelling to very distant objects in space such as stars and exoplanets will require very large amounts of thrust to drive rockets to very high speeds in order that we can travel there in a reasonable amount of time. Conventional chemical rockets are unsuitable for this purpose as the thrust they provide is limited by the amount of fuel that they can carry. So far we have only travelled as far as the Moon, and that’s a mere 380 000 kilometres away.

An artist’s impression of a possible FFR design. The large grey fins are for cooling and the crew habitat or payload area is at the far end, pointing away.

The fission fragment rocket (FFR) is a theoretical engine design that uses the products of nuclear fission (“fission fragments“) to generate thrust. These fission fragments cannot normally escape from the fuel, but in an FFR this is designed to be not only possible but likely. A number of different designs have been proposed, but perhaps the most promising is the “Dusty Plasma Rocket” proposed* by Rodney Clark and Robert Sheldon.

In Clark and Sheldon’s dusty plasma rocket the fuel is a magnetically- and electrostatically-confined plasma containing tiny grains of radioactive fuel, each no more than one hundred nanometres in diameter. As the fuel fissions, the fission fragments are steered either to collection electrodes to generate electrical power, or out the back of the engine to generate thrust.

A schematic of Clark and Sheldon’s dusty plasma rocket. Fission fragments are ejected to the left to produce thrust, and on the right are collected by electrodes for electrical power. Also shown are the RF coils (red dots) used to heat the plasma and the containment field generator (orange) required to keep the dust cloud in place. The beryllium oxide or lithium hydride moderator is shown in light green.

Although the mass of the fission fragments is very small, they exit at speeds of a few percent the speed of light and are therefore able to generate a significant thrust force. An FFR “burning” one hundredth of one gram of fuel per second and ejecting those fragments at five percent of the speed of light would still be able to generate a force of 150 newtons and Clark and Sheldon calculate that their dusty plasma rocket would be able to generate a specific impulse (ISP) of 1.5 million seconds. Specific impulse is a measure of the efficiency of a rocket engine and compares the force generated with the mass of propellant used per unit time, and for comparison purposes each of the Space Shuttle Main Engines had an ISP of between 360 and 450 seconds (as ISP varies with altitude). An FFR therefore offers a huge improvement in efficiency over standard chemical rockets.

Perhaps the most interesting aspect of the fission fragment rocket is that unlike other proposed long-distance rocket designs such as matter-antimatter reactors, it is well within current technological capabilities: we could begin building an FFR tomorrow. Clark and Sheldon calculate that a ten-year mission to the Sun’s gravitational lens point, 550 astronomical units (82.2 trillion metres) from Earth would require only 180 kg of nuclear fuel and a 350 megawatt reactor, both of which are well within current design parameters.

* Rodney Clark and Robert Sheldon, “Dusty Plasma Based Fission Fragment Nuclear Reactor”, 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (2005). PDF Link.

 

Blood types

What is it that makes blood types different from each other?

The existence of blood types* is down to the presence of antigens (“antibody generators”) on the surface of red blood cells and antibodies in the blood’s plasma. Someone with Type A blood has A-type antigens on their red blood cells and anti-B antibodies in their plasma. Someone with Type B blood has B-type antigens on their red blood cells and anti-A antibodies in their plasma. Those with Type AB blood have both A- and B-type antigens on their red blood cells and no antibodies in their plasma; whereas someone with Type O blood has no antigens on their red blood cells but both anti-A and anti-B antibodies in their plasma.

If, for example, someone with Type A blood is given a transfusion of Type B blood the anti-B antibodies in their system will attach themselves to the Type-B red blood cells, labelling them for destruction by white blood cell phagocytes. This can lead to an acute hemolytic reaction in which the red blood cell count drops to a dangerously low level and the blood is no longer able to carry enough oxygen to support life. This reaction can vary between patients, with some patients dying very soon after receiving a small amount of the wrong type of blood and some not dying after receiving relatively large amounts.

Can receive … Someone with Type …
A B AB O
A ✔ ✔
B ✔ ✔
AB ✔
O ✔ ✔ ✔ ✔

People with Type AB blood are universal recipients and can receive blood of any type, as their plasma does not contain anti-A or anti-B antibodies. Those with Type O blood are universal donors and can donate blood to anyone, as their red blood cells do not have any antigens on their surfaces.

Across the world, Type AB blood is rarest with only 5.5% of the population being Type AB. Type O blood is the most common (40.8%) and Type A is more common (31.8%) than Type B (22.0%). That said, blood types vary enormously between different countries and races: all Bororo people are Type O, nearly half (48%) of Norwegians are Type A and 32% of Indians are Type B.

* For the purposes of simplicity, this post ignores the effect of the Rh (Rhesus) factor that leads to, for example, the difference between A+ or A− blood.

Norman Borlaug

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Norman Borlaug probably saved more lives than anyone who has ever lived (some estimates put the number of lives saved at over one billion) but chances are you’ve never heard of him, despite the fact that he won the Nobel Peace Prize for his work and is one of only six people ever to have won the Nobel Prize, the Presidential Medal of Freedom and the Congressional Gold Medal. Borlaug was an agronomist (that is, he studied the use of plants for food and fuel) who is often referred to as the Father of the Green Revolution; a period of time from the 1940s to 1970s in which the production of food by agriculture increased markedly.

Borlaug worked with wheat, and developed high-yield disease-resistant varieties and led the introduction of these varieties, coupled with modern production methods like irrigation and the use of pesticides, into Mexico, Pakistan and India. In India alone wheat yield went from nine million tonnes in the 1960s to seventy million tonnes in the 1990s. Similar efforts with rice followed (in some cases increasing the yield tenfold) and these efforts are thought to have saved more than one billion people from starvation, with the average person in the developing world now receiving 25% more energy from food than before the Green Revolution.

Osteoporosis

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Osteoporosis is a disease that causes the density of bones to decrease. Normally bones are constantly being remodelled – some of the bone is broken down (resorped) and new bone grows in its place. In a normal person about ten percent of bone at any one time is undergoing this process. If there is a different in the rate of the two processes, with resorption occurring faster than growth, then osteoporosis will develop.

The two micrograph images below, from the Wellcome Collection, demonstrate the difference very clearly.

Normal Bone

Osteoporotic Bone

The holes in bones are required so that nutrients can get to the bones and also to give bones some “give” so that they are not too brittle; it’s important for bones to be able to bend a small amount to absorb shocks.