Without using a calculator (trig functions):

Does anyone know the quick mental-formula for determining the heading required to proceed from one point in space to another point in space when navigating off a single VOR?

Example:

What heading is required to go directly from the 090 radial 20 DME fix - to the 180 radial 70 DME fix?

I am at a total loss...?

Scale it out on the wind side of an E6B. Don't have on with me

GF

The method we used to teach on aircraft equipped with RMIs was to use per your example the 180/70 as the full face of the instrument and the 90/20 as a smaller proportional leg-now draw an imaginary line or use a straight edge(paper) between the two points, now slide that line to the center of the instrument and there is your heading. Refine repeatedly as you steer to the point.

No RMI? You can do the same thing on the back of a whiz wheel(the wind side)- set current heading, mark 180/70 and 90/20 in proportion and then note the heading from the current position to the desired position, slide the line to the center of the wheel. Refine solution as you continue to steer to the point.

Or use trig to find the angle, the heading required is 196 degrees.

First, square the dimensions of the two known sides

20*20 = 400
70*70 = 4900

They total 5300, take the square root of that to get 72.8 nm between the two points.

Now, divide 20/72.8 and use a calculator to find the sin -1 of the resulting dividend, which is rounded to 16 degrees. Add 16 degrees to 180 degrees to find the necessary course change to reach the 180/70.

Easy, peasy

GF

GF is correct on the trig part, he used the Pythagorean Theorem to determine the length of the "hypotenuse", plus use of the unit circle for the trig angle, which assumes right angles are formed between the two legs. In this case the 90 and the 180 legs form a right angle, how convenient, so we can find arc tan (20/70) = ~16, so you would need to head 180 + 16 = 196 which he got. It is a simple trig relationship, it only works when the legs form right angles. Trig is based on the unit circle.

But I suspect you are trying to find a practical formula which is usable in the airplane without a calculator. Most pilots would simply do an intercept to the 180 and fly it outbound to the 70 DME fix. There are rules for deciding what intercepts to use based on DME values, let me get my sheet out for that. In this case I would use a 45 for this intercept, since it is so far away from the VOR. I can post those rules if I can find my sheet (yeah, I should know them!).

I too, am at a total loss, but for a different reason.

Please tell me when in real life you will need this.

Galaxy, I got exhausted just reading that....

Jungle, can you explain your method a little more? Putting the dots on the wind side "proportionally", what marks are we using?

In the meantime, I read up on this and learned there is another course correction function in the E6-B (see the instruction book) on the slide rule side. First grab a beer, then put the number of miles off course (in our case 20) on the outer dial, and the distance you want to go to re-intercept under that (in our in case 70 miles). Then you find the rate arrow is, and voila- the intercept angle you need is shown there (16-17 degrees in our case). Add that to whatever heading you are presently on, and fly that to re-intercept the course. Again, this works because there is a right angle between the two courses which allows trig relations via the unit circle.

I was cruising around Kansas at night recently and wanted to use the slide rule on an E6B and did not have one with me, wanted to do a simple rate calculation as headwinds were robbing cruising range and it looked like I might be impinging on my fuel reserves. Unfortunately the only E6B I had was on my pilot watch, and my eyesight has gotten so poor up close I can't read it any more, it was too small. So I resolved to carry my old ASA E6B used for teaching. People always frown on proven tools like the E6B whiz wheel, but they are truly useful.

Set your heading on the wheel, visualise the center of the wheel as the VOR/DME, now using the same scale mark 180/70 and 90/20-draw a line beteen those two points, move that line to the center of the wheel while maintaining the same angle(think parallel rulers)and it will point to your desired heading.

The marks just need to be proportional, seven units for seventy and two for twenty, just as you would mark windspeeds except now you are marking distance.

Cubdriver, believe it or not I had to pull out the old E6B just a few months ago for the first time in 25 years or so-an unplanned hold had temporarily befuddled the FMS and I needed a simple time/speed/distance calculation the FMS just could not see.

This is the classic "fix to fix" we all hated in UPT. It can be done in the aircraft without an E6B. I'm going to change the fix just a bit to make things easier (fly from 180/80 to the 090/20)

The easiest way I've been able to describe this process is to look at your RMI or HSI as a smaller "god's eye" view of the actual situation. The middle of the HSI/RMI represents the VOR station.

The tail of the needle at the outer ring of the HSI/RMI card represents the more distant (from the station) fix, in this case the 180/80. In this example it also represents your current location in the "world" of the HSI. You now must "eyeball" a proportionate location for the other fix on the 090 radial on the HSI. Since the outside ring of the HSI or RMI (where the tail of the needle is) represents 80 DME, then the 090/20 (1/4 of 80 DME) would be 1/4 of the distance from the middle of the HSI on the 090 radial.

You can now visualize both fixes on the face of the HSI. Where you are and where you want to go. You turn to make the imaginary course between those two points appear vertically on your HSI. This would be your no wind heading from your current position to the new fix.

I don't know if I helped or just made the situation worse. All I can say is thank goodness for GPS.