Mach .75

[Map Rousch]

Asan aircraft moves through the air, the air molecules near theaircraft are disturbed and move around the aircraft. If the aircraft passesat a low speed, typically less than 250 mph, the densityof the air remains constant. But for higher speeds, some of theenergy of the aircraft goes into compressing the air and locallychanging the density of the air. This compressibilityeffect alters the amount of resulting force on the aircraft.The effect becomes more important as speed increases. Near and beyondthe speed of sound, about 330 m/s or 760mph, small disturbances in the flow are transmittedto other locationsisentropically or with constant entropy.But a sharp disturbance generates ashock wave that affects both the lift and drag of an aircraft.

Theratioof the speed of the aircraft to the speedof sound in the gas determines the magnitude of many of the compressibilityeffects. Because of theimportance of this speed ratio, aerodynamicists have designated itwith a special parameter called the Mach number in honor ofErnst Mach, a late 19th century physicist who studied gasdynamics. The Mach number M allows us to define flight regimes in whichcompressibility effects vary.

The Mach number appears as asimilarity parameterin many of the equations forcompressible flows,shock waves,andexpansions.When wind tunnel testing, you must closely match the Mach number betweenthe experiment and flight conditions.It is completely incorrect to measure a dragcoefficient at some low speed (say 200 mph) and apply that dragcoefficient at twice the speed of sound (approximately 1400 mph, Mach= 2.0). The compressibility of the air alters the importantphysics between these two cases.

The Mach number depends on the speed of sound in the gas andthe speed of sound depends on the type of gas andthe temperature of the gas. The speed of sound varies fromplanet to planet. On Earth,the atmosphere is composed ofmostly diatomic nitrogen and oxygen, and the temperaturedepends on the altitude in a rather complex way.Scientists and engineers have created amathematical model of the atmosphere to helpthem account for the changing effects of temperature with altitude.Mars also has an atmosphere composed ofmostly carbon dioxide. There is a similarmathematical model of the Martian atmosphere.We have created anatmospheric calculatorto let you study the variation of sound speed with planet andaltitude.

Here's another JavaScript program to calculate speed of sound and Mach numberfor different planets, altitudes, and speed. You can use this calculatorto determine the Mach number of a aircraft at a given speed and altitudeon Earth or Mars.

Other problems may occur while running the applet due to it being outdated. Until it is updated, we have provided a substitute link for calculating the mach number. The application can be found HERE.

To change input values, click on the input box (black on white),backspace over the input value, type in your new value, andhit the Enter key on the keyboard (this sends your new value to the program).You will see the output boxes (yellow on black)change value. You can use either English or Metric units and you can input either the Mach numberor the speed by using the menu buttons. Just click on the menu button and click on yourselection.If you are an experienced user of this calculator, you can use asleek versionof the program which loads faster on your computer and does not include these instructions.You can also download your own copy of the program to run off-line by clicking on this button:

However, in OS X, Mach is linked with other kernel componentsinto a single kernel address space. This is primarily for performance;it is much faster to make a direct call between linked componentsthan it is to send messages or do remote procedure calls (RPC) betweenseparate tasks. This modular structure results in a more robustand extensible system than a monolithic kernel would allow, withoutthe performance penalty of a pure microkernel.

At the trap level, the interface to most Mach abstractionsconsists of messages sent to and from kernel ports representingthose objects. The trap-level interfaces (such as mach_msg_overwrite_trap)and message formats are themselves abstracted in normal usage bythe Mach Interface Generator (MIG).MIG is used to compile procedural interfaces to the message-basedAPIs, based on descriptions of those APIs.

OS X processes and POSIXthreads (pthreads)are implemented on top of Mach tasks and threads, respectively.A thread is a point of control flow in a task. A task exists to provideresources for the threads it contains. This split is made to providefor parallelism and resource sharing.

is a collectionof system resources. These resources, with the exception of theaddress space, are referenced by ports. These resources may be sharedwith other tasks if rights to the ports are so distributed.

A task is a fairly expensive entity. It exists to be a collectionof resources. All of the threads in a task share everything. Twotasks share nothing without an explicit action (although the actionis often simple) and some resources (such as port receive rights) cannotbe shared between two tasks at all.

A thread is a fairly lightweight entity. It is fairly cheapto create and has low overhead to operate. This is true becausea thread has little state information (mostly its register state). Itsowning task bears the burdenof resource management. On a multiprocessor computer, it is possiblefor multiple threads in a task to execute in parallel. Even whenparallelism is not the goal, multiple threads have an advantagein that each threadcan use a synchronous programming style, instead of attempting asynchronousprogramming with a single thread attempting to provide multipleservices.

A threadis the basic computational entity. A thread belongs to one and onlyone task that defines its virtual address space. To affect the structureof the address space or to reference any resource other than theaddress space, the thread must execute a special trap instructionthat causes the kernel to perform operations on behalf of the threador to send a message to some agent on behalf of the thread. In general,these traps manipulate resources associated with the task containingthe thread. Requests can be made of the kernel to manipulate theseentities: to create them, delete them, and affect their state.

In most cases, the resource that is accessed by the port (thatis, named by it) is referred to as an object. Most objects namedby a port have a single receiver and (potentially) multiple senders.That is, there is exactly one receive port, and at least one sendingport, for a typical object such as a message queue.

The service to be provided by an object is determined by themanager that receives the request sent to the object. It followsthat the kernel is the receiver for ports associated with kernel-providedobjects and that the receiver for ports associated with task-provided objectsis the task providing those objects.

For ports that name task-provided objects, it is possibleto change the receiver of requests for that port to a differenttask, for example by passing the port to that task in a message. Asingle task may have multiple ports that refer to resources it supports.For that matter, any given entity can have multiple ports that representit, each implying different sets of permissible operations. Forexample, many objects have a name port anda controlport (sometimes called the privileged port).Access to the control port allows the object to be manipulated;access to the name port simply names the object so that you canobtain information about it or perform other non-privileged operationsagainst it.

One type of object referred to by a port is a port set.As the name suggests, a port set is a set of port rights that canbe treated as a single unit when receiving a message or event fromany of the members of the set. Port sets permit one thread to waiton a number of message and event sources, for example in work loops.

Traditionally in Mach, the communication channel denoted bya port was always a queue of messages.However, OS X supports additional types of communication channels, andthese new types of IPC object are also represented by ports andport rights. See the section Interprocess Communication (IPC),for more details about messages and other IPC types.

Ports and port rights do not have systemwide names that allowarbitrary ports or rights to be manipulated directly. Ports canbe manipulated by a task only if the task has a port right in itsport namespace. A port right is specified by a port name, an integerindex into a 32-bit portnamespace. Each task has associated with it a single port namespace.

Tasks acquire port rights when another task explicitly insertsthem into its namespace, when they receive rights in messages, bycreating objects that return a right to the object, and via Machcalls for certain special ports (mach_thread_self, mach_task_self,and mach_reply_port.)

As with most modern operating systems, Mach provides addressingto large, sparse, virtual address spaces. Runtime access is madevia virtual addresses that may not correspond to locations in physicalmemory at the initial time of the attempted access. Mach is responsiblefor taking a requested virtual address and assigning it a correspondinglocation in physical memory. It does so through demand paging.

The default pager handles nonpersistent memory, known as anonymousmemory. Anonymous memory is zero-initialized, and it existsonly during the life of a task. The vnode pager maps files intomemory objects. Mach exports an interface to memory objects to allowtheir contents to be contributed by user-mode tasks. This interfaceis known as the External Memory Management Interface, or EMMI.

The memory management subsystem exports virtual memory handlesknown as named entries or namedmemory entries. Like most kernel resources, these aredenoted by ports. Having a named memory entry handle allows theowner to map the underlying virtual memory object or to pass theright to map the underlying object to others. Mapping a named entryin two different tasks results in a shared memory window betweenthe two tasks, thus providing a flexible method for establishingshared memory.

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