Radius for turn Formulae
Guest
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John Farley,
I was curious to see why your V squared/10G formula works. I would have liked to use it on a C172, except I can't find the G meter.
So I tabulated theoretical and JF methods in the range 5 to 85 degrees bank, 100 to 450 knots, and calculated the differences.
Here are three cases
AoB 20, 1.064g, 200kt. Theoretical r 9743 ft, JF r 3759 ft.
AoB 40, 1.305g, 300kt. Theoretical r 9509 ft, JF r 6894 ft.
AoB 60, 2g, 150kt. Theoretical r 1152 ft, JF r 1125 ft.
For us mortals who get really worried above 60 AoB, your formula is not so good. At 30 AoB, your error is 43% the WRONG way.
The two methods break even a little over 60 degrees, then the JF approach is 11% safe at 80 degrees (5.76g), and 12.4% safe at 85. So we can see where you used to play.
Lastly, why is your formula so good in the 60+ range ?
(Dan Winterland, I promise I will go fishing immediately I have posted this).
Answer: The cosine of an angle asymptotically approaches 1/tan of the same angle as the angle approaches 90. And the g load is related to cos(AoB); the turn radius to tan(AoB)
Gone fishin.
ET
I was curious to see why your V squared/10G formula works. I would have liked to use it on a C172, except I can't find the G meter.
So I tabulated theoretical and JF methods in the range 5 to 85 degrees bank, 100 to 450 knots, and calculated the differences.
Here are three cases
AoB 20, 1.064g, 200kt. Theoretical r 9743 ft, JF r 3759 ft.
AoB 40, 1.305g, 300kt. Theoretical r 9509 ft, JF r 6894 ft.
AoB 60, 2g, 150kt. Theoretical r 1152 ft, JF r 1125 ft.
For us mortals who get really worried above 60 AoB, your formula is not so good. At 30 AoB, your error is 43% the WRONG way.
The two methods break even a little over 60 degrees, then the JF approach is 11% safe at 80 degrees (5.76g), and 12.4% safe at 85. So we can see where you used to play.
Lastly, why is your formula so good in the 60+ range ?
(Dan Winterland, I promise I will go fishing immediately I have posted this).
Answer: The cosine of an angle asymptotically approaches 1/tan of the same angle as the angle approaches 90. And the g load is related to cos(AoB); the turn radius to tan(AoB)
Gone fishin.
ET
Guest
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I can't help suspecting that when JF was using that particular formula he wasn't making turns with less than 60° of bank, or as slow as 150 knots all that often.
You may not know his name down under, and I hope John will forgive me blowing his trumpet for him. JF is a very distinguished test pilot, with a 20 year record of test flying British jet fighters (when we used to build them unaided) - and inevitably as a company pilot, displaying them as well.
This of-course assumes that he is who he says he is on Pprune, but I am happily convinced that that is the case.
G
You may not know his name down under, and I hope John will forgive me blowing his trumpet for him. JF is a very distinguished test pilot, with a 20 year record of test flying British jet fighters (when we used to build them unaided) - and inevitably as a company pilot, displaying them as well.
This of-course assumes that he is who he says he is on Pprune, but I am happily convinced that that is the case.
G
Guest
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EchoTango
You said:
Answer: The cosine of an angle asymptotically approaches 1/tan of the same angle as the angle approaches 90. And the g load is related to cos(AoB); the turn radius to tan(AoB)
However:
According to me g = 1/Cos AoB
Does that affect the price of fish when you are upside down?
BTW Hope you had a good holiday in the sun Ed
Regards
JF
You said:
Answer: The cosine of an angle asymptotically approaches 1/tan of the same angle as the angle approaches 90. And the g load is related to cos(AoB); the turn radius to tan(AoB)
However:
According to me g = 1/Cos AoB
Does that affect the price of fish when you are upside down?
BTW Hope you had a good holiday in the sun Ed
Regards
JF
Guest
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Despite my flippant comment earlier in this thread, this is something we have to use doing the job I do - Air to Air Refeulling. We often have to set up RVs calculating the radius of turn to ensure we roll out exactly one NM ahead of the customer. However, a lot of this info is already calculated and tabulated.
When these tables aren't valid, do also have a natty gadget called a 'Turn Radius Nomogram' which is a graph with various parameters (Alt, IAS, g, Radius etc.) which does all this for us. I tried to copy it at put it in this thread, but failed on the technical side.
If anyone wants a copy, mail me with your snail mail address and I will send you one.
When these tables aren't valid, do also have a natty gadget called a 'Turn Radius Nomogram' which is a graph with various parameters (Alt, IAS, g, Radius etc.) which does all this for us. I tried to copy it at put it in this thread, but failed on the technical side.
If anyone wants a copy, mail me with your snail mail address and I will send you one.
Guest
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John Farley,
You are quite right. We have terrible problems down here knowing when to replace functions with their inverses when applying formulae out of english books. The local zoo had a similar problem when they brought out some pommie bats. Poor buggers wore their teeth out in a couple of months trying to hang on in the bat cave.
I was looking at something else with the cos; 1/tan thing.
JF's formula for r is V/10G, where G = 1/cos(a) (V in knots, r in ft)
The theoretical r is (V * 6080/3600)squared / 32.2 tan(a)
So the fractional error in the JF formula is (JF radius - Theoretical radius) / (Theoretical radius)
That error function reduces to
1 - (cos(a)/10) / (2.852 / 32.2 tan(a))
And as a approaches 90, cos(a) / tan(a) approaches 1. That was the cos; 1/tan matter I noted.
So as a approaches 90 degrees, the error approaches 1 - ( 0.1 / .08857), or 12.9%. That is the 13% limit you originally cited.
Dan Winterland
JF's formula is within 13% of correct in the range 51 to 90 degrees bank. It is spot on at 62.5.
Its a very good method if you are low, fast and busy showing off, or engaged in a tactical exercise. Like in JF's old playground.
Don't think it would suit you. Sounds like your nomogram and tables will be hard to beat in your case.
John, Had a great Xmas. Thank you.
ET
You are quite right. We have terrible problems down here knowing when to replace functions with their inverses when applying formulae out of english books. The local zoo had a similar problem when they brought out some pommie bats. Poor buggers wore their teeth out in a couple of months trying to hang on in the bat cave.
I was looking at something else with the cos; 1/tan thing.
JF's formula for r is V/10G, where G = 1/cos(a) (V in knots, r in ft)
The theoretical r is (V * 6080/3600)squared / 32.2 tan(a)
So the fractional error in the JF formula is (JF radius - Theoretical radius) / (Theoretical radius)
That error function reduces to
1 - (cos(a)/10) / (2.852 / 32.2 tan(a))
And as a approaches 90, cos(a) / tan(a) approaches 1. That was the cos; 1/tan matter I noted.
So as a approaches 90 degrees, the error approaches 1 - ( 0.1 / .08857), or 12.9%. That is the 13% limit you originally cited.
Dan Winterland
JF's formula is within 13% of correct in the range 51 to 90 degrees bank. It is spot on at 62.5.
Its a very good method if you are low, fast and busy showing off, or engaged in a tactical exercise. Like in JF's old playground.
Don't think it would suit you. Sounds like your nomogram and tables will be hard to beat in your case.
John, Had a great Xmas. Thank you.
ET
Guest
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TAS squared over g tan theta is a jolly useful formula! When I used to fly triangular aeroplanes, I really couldn't be @r$ed to draw a different track for different speeds at low level. The hole in the end of a standard RAF nav rule was always used for drawing the turns and I just varied the angle of bank to stay on track at different speeds!
It also enabled me to produce ALL the turn ranges for various AAR RV procedures for ATP56A back in 1991; didn't cost HM a cent as there was no such thing as GEMS back then! I evolved (and still have) the generic expressions for all RVs, although I could only solve the RV C by an iterative process. So if we suddenly decide to change any parameters (AoB, TAS split, roll-out range) then I can recalculate the turn ranges very quickly. But this time HM'll have to pay me for my troubles!!
It also enabled me to produce ALL the turn ranges for various AAR RV procedures for ATP56A back in 1991; didn't cost HM a cent as there was no such thing as GEMS back then! I evolved (and still have) the generic expressions for all RVs, although I could only solve the RV C by an iterative process. So if we suddenly decide to change any parameters (AoB, TAS split, roll-out range) then I can recalculate the turn ranges very quickly. But this time HM'll have to pay me for my troubles!!
Guest
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what a forum ... what an amount of expertise ...
could'nt some of you gurus have a look at my topic 'V2 .....'
still longing for the answer that hits it on the head ...
thanx in advance
LF
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Let there be cold beers on a hot day !!!
could'nt some of you gurus have a look at my topic 'V2 .....'
still longing for the answer that hits it on the head ...
thanx in advance
LF
------------------
Let there be cold beers on a hot day !!!
