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Delta IV RocketCam Videos
dmaas writes "High-quality RocketCam videos from the inaugural launch of Boeing's Delta IV rocket have just been made available (in MPEG-1 and Quicktime formats). Of note are the spectacular strap-on solid rocket booster separation, the extension of the second-stage engine nozzle, and the red-hot glow of ablative material in the second-stage engine. (disclaimer: my company prepared these videos for Ecliptic Enterprises, maker of the RocketCam system)" We did RocketCam photos for model rockets a few weeks ago, if you want to compare.
yes! burger!
In Soviet Russia, Rocket takes pictures of you!
Rocket launches YOU!!!!!
These are some of the best arguments against communisim that I have ever heard.
What is RPN?
In the 1920's, Jan Lukasiewicz developed a formal logic system which allowed mathematical expressions to be specified without parentheses by placing the operators before (prefix notation) or after (postfix notation) the operands. For example the (infix notation) expression
(4 + 5) × 6
could be expressed in prefix notation as
× 6 + 4 5 or × + 4 5 6
and could be expressed in postfix notation as
4 5 + 6 × or 6 4 5 + ×
Prefix notation also came to be known as Polish Notation in honor of Lukasiewicz. HP adjusted the postfix notation for a calculator keyboard, added a stack to hold the operands and functions to reorder the stack. HP dubbed the result Reverse Polish Notation (RPN) also in honor of Lukasiewicz.
Why Did/Does HP Use RPN?
In the years that followed, computer scientists realized that RPN or postfix notation was very efficient for computer math. As a postfix expression is scanned from left to right, operands are simply placed into a last-in, first-out (LIFO) stack and operators may be immediately applied to the operands at the bottom of the stack. By contrast, expressions with parentheses and precedence (infix notation) require that operators be delayed until some later point. Thus, the compilers on on almost all modern computers converted statements to RPN for execution. (In fact, some computer manufacturers designed their computers around postfix notation.)
At the time that the HP-35 was introduced, other pocket calculators typically used a partial algebraic model. That meant they could evaluate trivial expressions like 4+5 but couldn't handle anything that involved parentheses or algebraic precedence. The technology of the time didn't allow for full algebraic compilers in pocket calculators.
RPN allowed HP to produce a pocket calculator that could evaluate arbitrary expressions using the available technology. For many, learning a new style of entry was a small price to pay to be able to evaluate arbitrary expressions on a calculator. Once the technology to produce algebraic compilers could fit into a pocket calculator, most RPN users had decided that RPN was more efficient and consistent for the user as well as for the calculator. Also, because subexpressions are evaluated as they are entered, entry errors are more obvious with RPN. On an algebraic calculator, omitting an opening parenthesis, may not lead to a calculation error until much later when an entire subexpression is evaluated.
Another advantage to RPN is consistency between machines. Early algebraic models had differing limits of the complexity of the expressions they could evaluate. For example, TI catalogs from the late 70's listed how many levels of parentheses and pending operations each model could handle. Even today if you begin to use an algebraic calculator, you need to determine just "how algebraic" it really is. For example, some switch to RPN for unary operators (ie 5 SIN rather than SIN(5) or even SIN 5 =), some are still missing parentheses and/or precedence and many can't directly enter an expression like:
4+5
-----
6+7
even though they claim to allow expressions to be entered as they are written.
Learning RPN
If you've recently acquired your first RPN calculator and it didn't come with a manual, this section will get you started. The majority of HP calculators have the version of RPN that is described here.
Special notes for a few models:
HP-9100 and HP-9810
These calculators use a 3 level RPN that is a little different. The most important differences are that the result of two operand functions are left in the Y register and there is never an automatic stack lift. See the RPN versions page and the HP-9100 pages for more information on these models.
HP-28 and HP-48
These models have RPL which is not described here. Fortunately, manuals for these newer model are still easily obtained. The most important difference is that pressing ENTER only places the number in the lowest level of the stack rather than X and Y as on RPN calculators. You can also see the RPN versions page for more information on these models.
Do you remember how you originally learned to do math? Most of us were taught to write down the numbers we wanted to add and then add them like:
25
12
----
37
RPN works the same way. Take your new calculator and key in 25. Press the ENTER key to tell the calculator that you are finished keying this number. Now key in 12 and tell the calculator to add it to the previous number by pressing the + key. The result of 37 will immediately be displayed. Subtraction, multiplication and division all work the same way but with the -, ×, and ÷ keys substituted for the + key. Try it!
This also works for more than two numbers. To multiply the numbers 5, 6 and 7 together press 5 ENTER 6 ×7 × and read the result. Note that you didn't press ENTER after the 2nd and 3rd numbers because the operation key makes it clear that you are finished keying these numbers.
Many functions require only one number. On an RPN calculator, you still enter the number and then press the operation key and see the result. (Many calculators that claim to be algebraic use the same method since it takes less keystrokes than real algebraic syntax.) For example, to compute the sine of 10 press 1 0 SIN and read the result. To compute e5 press 5 ex.
Just remember that RPN calculators perform mathematical operations immediately when you press the operation keys so the number(s) must be entered first. There are no "pending operations" or precedence in RPN calculators. When multiple numbers must be entered in sequence, separate them with the ENTER key.
You now know how to use your calculator in the most basic way. The beauty of RPN is that this model extends to arbitrarily complex expressions without parentheses and precedence rules. To understand this, you'll want to know more about the stack.
RPN uses a stack of registers. Models described here have 4 registers labeled X, Y, Z, and T and show only the X register in the display. As you press the number keys, the number is entered into the X register. When you press ENTER, the number is both completed in the X register and copied to the Y register. The previous contents are moved "up" (Z to T, Y to Z and X to Y) to make room for the new number. See the example below: Initial Stack After 5 After ENTER
T 4 T 3 T 2
Z 3 Z 2 Z 1
Y 2 Y 1 Y 5
X 1 X 5 X 5
Press: 5 ENTER
When the 5 key was pressed, the stack lifted. When enter was pressed, the value in X was copied into Y. Don't worry about the two values pushed out of the T register (4 and then 3) - a four level stack is sufficient even for very complex expressions. The stack was shown preloaded with the numbers 1-4 just to show you how the stack behaves.
Now to add 8 to the 5 already entered, see the example below: Stack from above After 8 After +
T 2 T 2 T 2
Z 1 Z 1 Z 2
Y 5 Y 5 Y 1
X 5 X 8 X 13
Press: 8 +
When the 8 was pressed, it overwrote the 5 in the X register and the + key caused the X and Y registers to be added with the result being placed in X. The rest of the stack dropped to fill the hole caused by two numbers being added to one sum.
Notice that the value of T was copied down to Z. T can be used as a handy constant register. (Last X described below can also be used as a constant register.) For example, if you wanted to compute the growth of $100 deposited in a bank account earning 4%, you could press 1.04 ENTER ENTER ENTER which would fill the stack with 1.04. Then press 100 × to see the amount after the first year. Each additional press of × shows the balance after another year. This can continue indefinitely because the 1.04 in the T register is copied down each time × is pressed. The stack always contains the balance in X and 1.04 in the other three registers.
Another convenient stack trick is to use the × key to square a number. For example, to square 25, just press 25 ENTER ×. This works because after the ENTER both the X and Y registers contain 25.
In the calculations above, you used the X and Y registers of the stack without even thinking about it. Because the stack lifts and drops as needed, you can evaluate much more complicated with the same ease. For example to evaluate:
4+5
-----
6+7
You would press 4 ENTER 5 + 6 ENTER 7 + ÷
Here's how it works: Initial Stack After 4 After ENTER
T 0 T 0 T 0
Z 0 Z 0 Z 0
Y 0 Y 0 Y 4
X 0 X 4 X 4
Press: 4 ENTER 5
After 5 After + After 6
T 0 T 0 T 0
Z 0 Z 0 Z 0
Y 4 Y 0 Y 9
X 5 X 9 X 6
Press: + 6 ENTER
After ENTER After 7 After + After ÷
T 0 T 0 T 0 T 0
Z 9 Z 9 Z 0 Z 0
Y 6 Y 6 Y 9 Y 0
X 6 X 7 X 13 X 0.67
Press: 7 + ÷
Note that you evaluated the expression in the same order you would have by hand.
Pressing most calculator functions leave the stack left in a state where it will automatically lift. The ENTER key (and CLx which clears the X register) leave the stack in state where it won't automatically lift when the next number is entered. In this case, when the next number is entered it will replace the X register. This may sound complicated but it's really simple and intuitive. The ENTER key copies the X register to Y so there is no reason for the stack to automatically lift when you key the next number. You also wouldn't want the stack to lift after a CLx because that would just insert a zero into the stack. You rarely need to think about this - the calculator just does the right thing.
You can easily evaluate more complicated expressions than the one shown above. Just start with the innermost set of parentheses and work outwards as you would to solve the expression with a pencil and paper. For example to evaluate ([(4+5)(2+3)+6]/(8+7))^9 press: 4 ENTER 5 + 2 ENTER 3 + × 6 + 8 ENTER 7 + ÷ 9 yx and read a result of 60716.99. If that's confusing, here it is broken down into steps:
4 ENTER 5 + Add 4 and 5 - one of the innermost terms
2 ENTER 3 + Add 2 and 3 (another inner term)
× 4+5 is in Y and 2+3 is in X so multiply them
6 + Add 6 to the result to complete (4+5)(2+3)+6
8 ENTER 7 + Add 8 and 7 to compute the denominator
÷ Divide into the numerator previously calculated
9 y^x Raise the previous result to the 9th power
This is the same order that you would have solved the expression by hand and the calculator will show the result of each subexpression which helps you catch errors. After a little more practice, RPN will become second nature and you may never want to use an algebraic calculator again.
Stack Manipulation Keys
You can view the stack or change its order by pressing the R to roll the stack contents. The example below shows an example of a roll down: Initial Stack After R dn After 2nd R dn
T 4 T 1 T 2
Z 3 Z 4 Z 1
Y 2 Y 3 Y 4
X 1 X 2 X 3
Press: R dn R dn
Pressing R twice more would return the stack to its initial configuration. You can also exchange the contents of X and Y with the XY key and your calculator may also have a R key. The CLx key will clear the contents of the X register. Some later models have an arrow key like which backspaces individual digits during entry or acts like a CLx at other times.
Last X
Besides the registers above, most HP calculators have a LAST X register which preserves the number that was in X before the last numeric operation. Press the LAST X key to place a copy of the previous contents of X into the X register. You can use LAST X as a constant register or to recover from mistakes.
Here is the same movie, but encoded with an mplayer and xanim compatible codec.
My mission is to win converts for RPN. I will post RPN trolls until slashdot devotes a front page story to the benefits of RPN muhahaha!!! Here's the first troll: ------------------- Choice of calculators important in competition By Dave Bourell Director, Calculator Applications Contest Although there are dozens of different calculators on the market which are suitable for use in the Calculator Applications Contest, contestants should exercise some care in the purchase of their calculator. The calculator should be of the "engineering" type, having the appropriate mathematical functions in addition to being having the capability to add, subtract, multiply, and divide. Further, the calculator must have standard scientific functions including the trigonometric functions (such as sin, cos, tan) and their inverses, and the logarithmic functions (like log, ln, x2, ex, yx). Because questions often involve calculations with , a "pi" key will prove helpful. In addition, the calculator should be from a reliable manufacturer, since a calculator malfunction during a test would spell sure defeat. Finally, the calculator should be affordable. The best calculator for the Calculator Applications Contest is not the most expensive one with lots of features. In fact, some high-end calculators prove to be a liability because they require too many keystrokes and therefore too much time to perform necessary calculations. For example, some expensive calculators have an alphabet and can be programmed to perform a series of operations automatically. To change from the "degrees" mode to the "radians" mode, these calculators require as many as six keystrokes. A calculator with a "deg rad" key that toggles between these modes will be easier to use as will one that can switch between fixed to scientific notation. There are features on the more advanced (and more expensive!) calculators which contestants will not need for the Calculator Applications Contest. Most seasoned coaches agree that the programmability is not required, although it is often useful to have a solution to the quadratic equation on hand. (Program memory must be cleared before the test is taken, so you would need to memorize the program steps and enter them back after the test has started.) Students do not use graphing capabilities of graphing calculators, but UIL does permit graphing calculators on the contest. Some calculators have unit conversion keys that will change a number in "inches" to "meters," for example. These features are useful, but the benefit is not significant, since these calculators do not generally appear at the State Meet. Calculators with these advanced features are still legal for use in the Calculator Applications Contest. Refer to the UIL Constitution and Contest Rules for more information on the types of calculators allowed. Basically, you can use any calculator that does not require auxiliary electric power and is not modified. There are two different types of calculator systems in wide use. These are the RPN type (Reverse Polish Notation) and the algebraic-entry type. Based on recent State Meet surveys, the RPN calculators are much more popular in the contest than algebraic-entry calculators. Hewlett Packard (HP) uses the RPN operating system while all others use the algebraic system. The RPN calculator operates on numbers like you do when you do longhand arithmetic. When you add two numbers, for example, you write the first number, then you write the second number, then you add. If after writing the numbers you decide to multiply, that is possible. Similarly, in an RPN calculator you enter both numbers, then you perform some mathematical operation. The calculation is actually performed when the operation key (+, -, cos, etc.) is pressed, making it unnecessary to have an "=" key. Most RPN calculators have an automatic memory ("stack") feature enabling the calculator to store up to four numbers awaiting a computational command. The algebraic entry calculators, as this name suggests, operate on numbers as you would write an algebraic expression. To write the sum of two numbers, for example, you would write the first number, then write plus (+), then write the second number. The sum would be performed when the equals (=) key or another mathematical operation is indicated. I recommend that you obtain the best calculator you can comfortably afford, for several reasons. For one, you will be using your calculator in non-academic as well as academic activities, in addition to the Calculator Applications Contest, and in these uses you will eventually find many applications for the advanced calculator features. Secondly, the calculator stimulates careful thought and mathematical learning. The better the calculator, the more good exercise the mind receives. Thirdly, a programmable calculator is a handy, inexpensive way to begin learning computer programming, a skill which in the future will be as important as knowing how to drive a car is now. Finally, calculators are fun and their potential for constructive amusement is enormously increased by the programming capability. So get the best calculator you can afford, even if it does not directly benefit you in the Calculator Applications Contest. As discussed above though, too many advanced features may slow down operation which is a real liability on the Calculator Applications Contest, so some compromise may be necessary. We have historically published a survey of the calculators that State Meet contestants bring to compete with at the State Meet. This year, almost everybody brought hp 32S or hp 32SII calculators. In fact, of the 187 calculators registered at the State Meet, only 32 were "non-hp 32S" calculators (17 percent). We do not recommend any particular brand of calculator. Remember, this discussion of calculators is valid only for the Calculator Applications Contest. The other UIL academic contests (i.e., Science) may have different rules regarding calculators. Both RPN and algebraic types of calculators are widely used and both have their advantages in different applications. The UIL will not give advise on specific calculators or even specific types of calculators. Instructors, students and parents must work together to select the best calculator for a given use. Look for a calculator that can add, subtract, multiply, and divide can perform trigonometric funcions such as sin, cos, tan and their inverses can perform logarithmic functions such as log, ln, x2, ex, yx is from a reliable manufacturer; and that is affordable.
RPN... It's a way of life
Did you know that RPN is the preferred entry system of NASA engineers?
RPN... It's a way of life
What does this have to do with a Delta IV booster?
Regardless, you're way off on your "facts." If you're 400m away from a 2,000lb JDAM impact, then you're completely safe. The lethality radius of this weapon is 33.5m -- which is, quite obviously, much less than half a mile.
This booster is funded on military reasons, to be able to deliver nuclear warheads precisely. They unveiled it under the guise of launching satellites.