How to do multiplication and division problems with E6B?

ZUKO

ZUKO

Well-Known Member
I know its called the rule of 10 but I cant seem to figure it out. I dont believe its anywhere in the instructions. I have been able to figure pretty much everything out but this. Any help would be appreciated.
 
Taken from my jepp E6B manual:

(A scale = outer ring, B scale = inner ring)

Multiplication:
1. Rotate the 'B' scale until the index "10" is directly under the number to be multiplied.
2. Without moving the scales, locate the multiplier on the "B" scale.
3. Look directly over the multiplier and find the answer on the "A" scale.

Ex: 450 fpm for 8 minutes, how much do you climb?
1. Place 450 on A scale directly over 10 on B scale.
2. Find 8 minutes on the B scale and, looking directly over this, find that we would climb 3600 feet in 8 minutes.

Division:
1. Locate the number to be divided on the A scale.
2. Rotate B scale until the divisor is located directly under the number to be divided.
3. Without moving the scales, find the answer on the A scale directly over the index "10"

Ex: An aircraft has to lose 8000 feet in 19 min., what is the rate of descent?
1. Place 8000 on the A scale directly over 19 minutes on the B scale.
2. Look directly over the "10" and find that the aircraft should descend at 420 fpm.
 
ZUKO said:
I know its called the rule of 10 but I cant seem to figure it out. I dont believe its anywhere in the instructions. I have been able to figure pretty much everything out but this. Any help would be appreciated.
Click to expand...

The front of the E-6B is simply a circular slide rule... wait, that probably doesn't help...


If you don't have a manual, take a look at the ASA Manual available online: Air Classics E6-B Flight Computer Instructions

The examples of problems used in the manual focus on rates, where the "Index" is the 60 mark on the middle "ring". For straight multiplication and division, you'll use the "10" mark instead.

As you look at the front side of the computer with the outer and middle rings aligned, you'll see the 10 marks at the top. Turn the movable disc to the right (clockwise) so that the middle 10 points to the 12 on the outer ring. To multiply 12 by any number, you now find that number on the middle ring, and read the answer on the outer ring. For 12 x 11, look for 11 on the middle ring, and you'll see that it aligns with a "tick" mark (the ASA book calls these life marks, or calibration marks) between 13 and 14. Counting those marks you'll see there are 10 between 12 and 13, so each counts for one unit. Directly above 11 on the middle ring is 13.2, but you know the answer has to be larger than 13.2. Being familiar with basic math should lead you to the conclusion that you must multiply 13.2 by 10 to arrive at the correct answer, 132.

In math terms, you should place the Multiplicand (on the outer scale) above the 10 (on the middle scale), and read the Product (on the outer scale) above the Multiplier (on the middle scale).

Multiplicand: 12
Multiplier: 11
Product: 132

Without moving anything, you can read the product for ANY multiplier simply by reading the Product on the scale above it.

12 x 12 ==> read above 12 a number between 14 and 15, specifically 14.4. Again, you need to "move the decimal point" to arrive at the answer, 144.



A few more examples, using the Figures in the ASA book.

Look at Figure 2. ASA uses it as an example of using the Rate Mark, but you'll also notice that the Middle Ring 10 is under the number 20. Since there's not a 2, this is the number you'll need to use if you're trying to multiply by 2. (You get to shift the decimal point...) Look carefully at the relationship between the numbers on the middle scale (the multipliers) and the numbers on the outer scale (the products). Some will look perfectly natural, and others will require a little thought, and shifting of decimals.

Above 40 is 80 - - perfectly natural, could also represent 4 and 8, or 400 and 800.

Above 45 is 90 - - same as above... 4.5 - 9.0, or 450 and 900, etc.

Above 50 is 10 - - requires a shift of decimal point, since you know that 2 x 50 = 100. This could either be 5 and 10, or 50 and 100, or 500 and 1000... each requires the addition of a zero to the end of the product, or moving a decimal to the left in the multiplier... however you want to say it, it's shifting a decimal point.

Above 60 is 12 - - same as above. Anything between the 10 index on the outer ring and the 10 index on the middle ring needs to be handled with care, as the decimal point needs to shift.


Take a look at Figure 3.

The Middle ring 10 is under the outer ring 25. It can represent 25, or 2.5, or 250... and so on. We'll use the computer at this setting to compute the following problems:

25 x 12 = ??
25 x 8 = ??
2.5 x 6 = ??
250 x 150 = ??


The answers are 300, 200, 15, and 3,750 respectively. Did you get those?

Take a look at Figure 6:

The computer is set with the middle 10 aligned under the outer 14.

14 x 7 = ??
140 x 500 = ??
1.4 x 8 = ??

The answers are 98, 70,000, and 11.2.



Now, division is just multiplication, backwards, right?

In math terms, you have a dividend, a divisor, and a quotient. In the equation 200 / 8 = 25,

Dividend: 200
Divisor: 8
Quotient: 25

To use the slide rule, place the Dividend on the outer ring above the divisor on the middle ring, and read the quotient (answer) on the outer ring above the 10 index of the middle ring.

Refer again to Figure 3.

For 40 / 16 = ??, we align the 40 of the outer ring with the 16 on the middle ring, and see that the 10 on the middle ring aligns with 25 on the outer ring. We simply need to determine the correct place for the decimal point. In this case, it's 2.5.


300 / 12 = ??
150 / 60 = ??
200 / 8 = ??


The answers are 25, 2.5, and 25, respectively.







Hope that helps.
 
Thank you both for replying. I printed out this thread and took it with me to learn before my test earlier today. I got an 82 on my test. :rawk:
 
Im sure I got all the multiplication and division correct. What Im sure messed me up some was not the process but the accuracy of some of the tougher problems like density altitude and the wind side. We had to be insanely accurate on this test. If it was multiple choice, I would have gotten near 100.

And it didnt help that I am very bad test taker and was working myself up badly during the start of the test.
 
ZUKO said:
Im sure I got all the multiplication and division correct. What Im sure messed me up some was not the process but the accuracy of some of the tougher problems like density altitude and the wind side. We had to be insanely accurate on this test. If it was multiple choice, I would have gotten near 100.

And it didnt help that I am very bad test taker and was working myself up badly during the start of the test.
Click to expand...
The wind side is understandable. You should be able to get within 1 kt / 1 degree if you are carefull. But how accurate can they expect you to be with density altitude. Each tiny little mark is 1000 freaking feet!!! You can really only get within 500ft on the E6B.
 
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