Turn Radius

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Turn Radius

Post by Flake » Sun Sep 16, 2012 4:03 am

Trying to work out turn radii for a virtual ATC program here.

Heres a formula you can use:

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(((KNOTS * 0.514444444)^2)/(tan(BANK ANGLE)*9.8))/1852
0.514... is the magic number converting knots to meters/s (1 knot == 0.51444 m/s)
9.8 is the speed of gravity in meters per second per second.
1852 is the ammount of meters to a nautical mile

You can punch this into google to calculate:

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(((%SPEED% * 0.514444444)^2)/(tan %ANGLE% deg*9.8))/1852
Just note that your speed needs to be under 250 if under 10k MSL, and bank less then 30degrees at all times unless it's an emergency expediate.

As a general rule:

120knots, 30 degrees is a 0.363NM turn radius.
240knots, 30 degrees is a 1.454NM turn radius.

To do it backwards to get the radius:

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sqrt(%RADIUS%*1852 * tan (%ANGLE% deg) * 9.8) / 0.5144444444
~141knots, 30 degrees gives a 0.5nm turn radius
~200knots, 30 degrees gives a 1.0nm turn radius

So know the magic numbers to turn at 30 degrees and you're golden! (141 for half nm, 200 for a full nm)
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Re: Turn Radius

Post by Crazypilot » Sun Sep 16, 2012 6:43 am

I am having an incredibly hard time trying to understand your fancy mathematics.
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Re: Turn Radius

Post by Gunny » Sun Sep 16, 2012 1:08 pm

Or get a free E6B flight computer emulator.Here= http://www.skywritersoft.com/Windows/Windows.htm and ported for a Mac here http://sourceforge.net/projects/je6-b/
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Re: Turn Radius

Post by wingzfan99 » Sun Sep 16, 2012 1:57 pm

Thanks for this post, Flake... very helpful.
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Re: Turn Radius

Post by FrenchTOZT » Sun Sep 16, 2012 4:44 pm

I believe Shutter made a map to test an aircraft's turn radius as well.
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Re: Turn Radius

Post by Gunny » Sun Sep 16, 2012 7:46 pm

My apology Flake. :oops:
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Re: Turn Radius

Post by Flake » Sun Sep 16, 2012 9:39 pm

I found this particularly helpful when trying to figure out which outer marker to turn in at and which angle to hold constantly when doing a diamond 360.

I settled on 60 degrees, 300 knots, starting at the 1.5 mile mark. as opposed to the 45 degree version at the 2.5 mile mark. the turn time of 60 degrees is much, much faster.
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Re: Turn Radius

Post by Taskforce 58 » Sun Sep 16, 2012 11:57 pm

It's good to know the math, although I use a E6B app on my ipod touch. :P
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Re: Turn Radius

Post by Flake » Mon Sep 17, 2012 1:41 am

I still feel safer knowing the numbers though.

141knots, 30 degrees is one nautical mile turn radius.
200knots, 30 degrees is two...

I just used the math to get to the end point. if anyone wants to use the math, go ahead.
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Re: Turn Radius

Post by Gunny » Mon Sep 17, 2012 1:57 am

Seriously if anyone is thinking of becoming a real world GA or Commercial pilot knowing the math is a must before playing with the toys.Because some times the toys are just not available.But the math is always there. ;)
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Re: Turn Radius

Post by Shutter » Mon Sep 17, 2012 8:37 pm

FrenchTOZT wrote:I believe Shutter made a map to test an aircraft's turn radius as well.
naw, it's a garbage rate of turn thing, not radius

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Re: Turn Radius

Post by LeCricket84 » Thu Oct 04, 2012 6:45 pm

Huh. Really interesting. It's kind of cool to know how the math works in all of that.

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Re: Turn Radius

Post by Drachenfire » Thu Feb 28, 2013 3:09 am

I love math. Good contribution Flake.

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