TOD calcs
Joined: Jul 2002
Posts: 358
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From: australia
The question was how to work out the track miles in order to work out the TOD I think. How do you work out the track miles around the arc in order to get a constant rate of decent to approach height...I have been wondering about this myself and cant answer the question, hopefully one of you folk will.
Cheers
Cheers
Joined: Aug 2001
Posts: 117
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From: Europe
Rule of thumb
Justathought:
My rule of thumb requires 3 steps:
D=(R x A) x 0,018
where
D=Distance on the arc
R=Radius (Distance from Fix)
A=Angle
x 0,018 can easily be resolved: multiply by 2, subtract 10% from the result and divide this result by 100.
Example:
You are flying on the 15 DME arc for 60 degrees:
a) 15 x 60 = 900
b) (900 x 2) - 10% = 1620
c) 1620 : 100 = 16,2NM
Correct distance travelled is 15,708 NM. The error is always 3,13% on the high side, which is acceptable (at least to me).
Hope that answers your question.
My rule of thumb requires 3 steps:
D=(R x A) x 0,018
where
D=Distance on the arc
R=Radius (Distance from Fix)
A=Angle
x 0,018 can easily be resolved: multiply by 2, subtract 10% from the result and divide this result by 100.
Example:
You are flying on the 15 DME arc for 60 degrees:
a) 15 x 60 = 900
b) (900 x 2) - 10% = 1620
c) 1620 : 100 = 16,2NM
Correct distance travelled is 15,708 NM. The error is always 3,13% on the high side, which is acceptable (at least to me).
Hope that answers your question.
Joined: Mar 1999
Posts: 363
Likes: 0
Okey dokey. The easy ballpark figures I use to maintain a 3* GS maneuvering on the initial or intermediate approach phases are as follows;
At average approach speed (140kts) and 800fpm ROD plan on loosing 300-350 feet per NM if you maintain a 3*GS.
Determine height to loose on the arc, ie if initial approach fix is at the beginning of the arc at 5000msl and the final aproach fix is at 2000msl then TOD will be 10 track miles prior to the FAF assuming speed approx 150ish and ROD 800-1000fpm.
Still a variation of the 1 in 3 or 3 in 1 rule so easy to remember.
Based on junior school maths (my comfort level) but if you have to come up with a plan in a flash it works fine for this too!
Re read thread, looks as though I`m prattling on about the wrong thing. Thus prior to applying the 1 in 3 rule you need to apply the 1 in 60 rule. 1* displacement at 60nm=1nm.
0n a 15nm arc each degree equals 1/4 mile so 40*of arc is 10nm straight line from start to finish so add 30% for the arc (that 3 again) gives approx 13nm. That should keep you on the consevtive side with a level off prior to the FAF. Again the 1 in 60
plus 30% is ballpark but relatively easy mental maths.
At average approach speed (140kts) and 800fpm ROD plan on loosing 300-350 feet per NM if you maintain a 3*GS.
Determine height to loose on the arc, ie if initial approach fix is at the beginning of the arc at 5000msl and the final aproach fix is at 2000msl then TOD will be 10 track miles prior to the FAF assuming speed approx 150ish and ROD 800-1000fpm.
Still a variation of the 1 in 3 or 3 in 1 rule so easy to remember.
Based on junior school maths (my comfort level) but if you have to come up with a plan in a flash it works fine for this too!
Re read thread, looks as though I`m prattling on about the wrong thing. Thus prior to applying the 1 in 3 rule you need to apply the 1 in 60 rule. 1* displacement at 60nm=1nm.
0n a 15nm arc each degree equals 1/4 mile so 40*of arc is 10nm straight line from start to finish so add 30% for the arc (that 3 again) gives approx 13nm. That should keep you on the consevtive side with a level off prior to the FAF. Again the 1 in 60
plus 30% is ballpark but relatively easy mental maths.
Last edited by flite idol; 9th June 2004 at 13:58.
Joined: Oct 1997
Posts: 418
Likes: 0
From: Florida
Like Flite Idol *, I'm also a "60-to-1" (or "1-in-60") person myself. Very easy to do in the air, real-time.
Examples of how very simple and user-friendly it is:
10 DME Arc = 1 mile for every 6 degrees of arc, because 60/10 = 6
12 DME Arc = 1 mile for every 5 degrees
15 DME Arc = 1 mile every 4 degrees
20 DME Arc = 1 mile every 3 degrees
etc etc.
You can have those "benchmark figures" stored in your brain for quick recall, and from there, it's very easy to figure (or at least approximate quickly) the number of miles.
For example, a 80-degree journey along the 15 DME arc would be 20 miles (and it only took a brief moment to figure that out, since you already knew that a 15 DME arc gives you 4 degrees per mile, and 4 into 80 = 20).
NB - I don't necessarily add the 30% as mentioned by Flite Idol unless I have a significant headwind -- that extra mileage is a good buffer against unexpected tailwinds in the descent.
Keeps it simple (in line with the KISS principle -- remember that one?
)
Remember also that distances don't have to be figured to the nth decimal in flight. Just make sure you're allowing yourself enough space to get down in time (and not excessively early), but don't waste too many brain-bytes doing complex calculations. If you are on a 13-DME arc, for instance, just use the 12DME figures and adjust a bit. And like N_S_R said re groundspeed, don't forget to consider the overall effect of the winds.
*Flite Idol, how have you been? Still flying with the same company? Hope all is going well with you.
Examples of how very simple and user-friendly it is:
10 DME Arc = 1 mile for every 6 degrees of arc, because 60/10 = 6
12 DME Arc = 1 mile for every 5 degrees
15 DME Arc = 1 mile every 4 degrees
20 DME Arc = 1 mile every 3 degrees
etc etc.
You can have those "benchmark figures" stored in your brain for quick recall, and from there, it's very easy to figure (or at least approximate quickly) the number of miles.
For example, a 80-degree journey along the 15 DME arc would be 20 miles (and it only took a brief moment to figure that out, since you already knew that a 15 DME arc gives you 4 degrees per mile, and 4 into 80 = 20).
NB - I don't necessarily add the 30% as mentioned by Flite Idol unless I have a significant headwind -- that extra mileage is a good buffer against unexpected tailwinds in the descent.
Keeps it simple (in line with the KISS principle -- remember that one?
)Remember also that distances don't have to be figured to the nth decimal in flight. Just make sure you're allowing yourself enough space to get down in time (and not excessively early), but don't waste too many brain-bytes doing complex calculations. If you are on a 13-DME arc, for instance, just use the 12DME figures and adjust a bit. And like N_S_R said re groundspeed, don't forget to consider the overall effect of the winds.
*Flite Idol, how have you been? Still flying with the same company? Hope all is going well with you.
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Posts: n/a
Analog, blowpipes and no magenta:
I use the 1 in 60 , the only thing I will add is that I calculate the track miles from the initial intercept,IE 10 mile arc Airspeed 210, start my turn at a tad over 12 miles, and finish the calc when I roll out on the exit from the ARC,just mentioning not nitt picking.
What ever you are comfortable with and works?.
BUT through the smell of my HOPS, a QUESTION.
PYTHAGORAS::::
We agree 1 in 60 around a 10 mile arc is 60 miles.
I just worked it out with old pythagoras, and there is an error in the 10 mile arc of 2.8 miles, and a 15 mile arc of 4.2 miles , etc etc, could someone tell me why?.
Cheer's.
Crack.
What ever you are comfortable with and works?.
BUT through the smell of my HOPS, a QUESTION.
PYTHAGORAS::::
We agree 1 in 60 around a 10 mile arc is 60 miles.
I just worked it out with old pythagoras, and there is an error in the 10 mile arc of 2.8 miles, and a 15 mile arc of 4.2 miles , etc etc, could someone tell me why?.
Cheer's.
Crack.
Joined: Jan 2001
Posts: 1,692
Likes: 153
From: home
Sorry if I have got the wrong end of the stick, but the 1 in 60 rule is based on three straight sides of the triangle. Certainly enough to give you a ballpark figure which most of our flying calcs are based on. The ARC will always give you a bit more distance than a straight side. The circumference of a circle is 2 x Pi x radius. Pi being 3.14 and quite a few more decimal places. That is why the differnce is 2.8nm. 1 in 60 10 nm = 60nm. With circ calc = 2 x 3.14 x 10= 62.8nm. However as I said not a huge difference, on a 40 degree arc the difference will be less than 0.5 nm. Hope I am barking up the right tree!?!
