PDA

View Full Version : Distance to fly an arc

Oxford1G
2nd Apr 2001, 20:05
If you had to fly a DME arc, ie at 15nm,through 90 degrees, does any one have a simple rule of thumb to calculate the distance flown?

Bored Cheese
2nd Apr 2001, 20:21
Calculate the total circumference of the circle using pi. Divide as required. i.e in this case by 4. There's your answer. I realise that you already know this but quite honestly once you have done it a few times in the air it's fairly easy.
I think that your question is good because you are obviously thinking about the vertical profile of your approach routing. Your future Captains will appreciate flying with a colleague who doesn't have to level out for 12 miles during a DME ARC procedure because he was only thinking about the lateral plot.

HugMonster
2nd Apr 2001, 20:22
The circumference of a circle is 2πr where r is the radius and π is 3.14159265358979323846264338327950288419716 (approximately). :)

Therefore, if you are going to fly through 20 degrees of arc on a 12 dme arc, you will fly (2π x 12 x 20)/360 = 4.2 nm approx.

The formula can be simplified to (radius x arc)/60.

In your example, the distance flown is 22.5 miles. Using a closer approximation for π, we get 23.561946 nm, but the first is probably good enough for government work! :)

Oxford1G
2nd Apr 2001, 22:16
Thanks very much.

Vmu
2nd Apr 2001, 23:07
Arc flying for dummies:

HugMonsters simplified formula can be simplified even more by memorizing two numbers; 6 and 3.
Flying a 10-mile arc you will cover a mile for each 6 radials.
Flying a 20-mile arc you will cover a mile for each 3 radials.

Example:
30 degrees to go on a 10-mile arc: 30/6=5nm to go.
30 degrees to go on a 20-mile arc: 30/3=10nm to go.

For other arc's you can interpolate using these two numbers

------------------
"Recovery was marginal..."

Oxford1G
3rd Apr 2001, 12:32
VMU, Thanks very much, just what i needed.

yowie
4th Apr 2001, 09:28
How about the good ol 1:60 rule.
As exampled earlier,12nm arc through 20deg=4 track miles(20/5=12).Try a 15nm arc through say 100deg (100/4=25nm).
Sorry guys,knw how to do it,cant explain myself very well,but it works really well and quick to work out in your head!!

najib
4th Apr 2001, 14:58
Just multiply the arc (radius) by 6 (2n=2*3.14), you will get circumfrence distance (that is distance for the entire circle if you were to fly the complete circle). Now if you are to fly 60 degrees: 60 degrees is 1/6 (16%) of a 360 degrees circle ( 60/360 ). So if u are flying 15 Nm. arc for 60 degrees total distance flown is 14 miles.
(DME ARC*6)* factor of 360 degrees (degrees to fly/360)
I hope it's not too complicated; a bit of arithmetic fluency really helps.

HugMonster
4th Apr 2001, 21:50
najib, arc is not the same as radius.

You've also very successfully managed to complicate a very simple calculation.

Why multiply the radius by 6, divide by 360 and multiply again by the arc angle?

You get the same result radius x arc / 60.

e.g. 10 dme arc (circle radius 10 miles) - 30 degrees of arc.

10x30=300

300/60=5

Easy, no?

MasterGreen
5th Apr 2001, 03:36
Very Good HugMonster. 5 stars and a lollipop. Nice to see we got there in the end.

MG

najib
6th Apr 2001, 10:11
Hey, I was attempting the query from a conceptual point of view. So if one forgets which number to divide by, then he/she can derive. Some people are good in remembering the formula and some are good in understanding the theory. Anyway, as long as oxfordg1 is happy, we are happy!

cromañon
6th Apr 2001, 20:07
check this one. It is simple and precise

if you fly a 60º arc yu are flying the arc distance hence a 90º arc you will be flying 1.5 times the arc.

got it?

if u dont let me know and with a few more examples i am sure u will get it.

se ya

COWPAT
7th Apr 2001, 17:57
Just use LNAV, VNAV and an Autopilot whilst having a cup of coffee!

Cmdr Data
7th Apr 2001, 21:44
1 in 60 rule, like others have said.
If you are on the 20 dme arc and have to fly 45 deg, 20 is 1/3rd of 60, so 1/3rd of 45 deg is 15. Hey presto: 15nm.

ITCZ
10th Apr 2001, 18:01
Arc discussed on Dunnunda Thumb Rules thread, inter alia. From that discussion... one in sixty works well.

On a sixty mile arc, you change bearing one degree per mile flown.

30DME arc, two degrees per mile,
20DME, three per mile
15DME, four per mile
12DME, five per mile
10DME, six per mile
9DME, seven per mile
8DME, eight per mile
7DME, nine per mile
6DME, ten per mile
Less than 5DME, write a complaint to the issuing agency, because it is too small.

Anything in between, interpolate because you will be bloody close.

Also note that if your RMI is marked in 5 degree increments, each mark on a 12DME arc represents a mile flown/to fly. If you are incorporating a descent profile like 3nm per 1000 feet to lose, that is 1000 feet per three divisions on a 12DME arc.

With numeric skills like that, you think my countrymen could do something about the aussie dollar. &lt;sigh&gt;.

[This message has been edited by ITCZ (edited 10 April 2001).]

BIK_116.80
16th Apr 2001, 03:21
HugMonster,

From memory, I am pleased to confirm that your approximation of pi is correct.

Again from memory, I can offer the next few decimal places, which are "9399".

Look it up and tell me I am wrong.