Formula for Radius of Turn

[Desert185]

I've been slowing down. Let me know when to roll in when you guys agree.

The variable that challenges the whole process in the flight levels when doing science is the changing groundspeed during the turn. The often dramatically changing radius of turn frequently calls for proper tongue placement and eye squint in order to rollout on the desired track. Automation? No workee. Be a pilot and use the turn knob, with an eye on the MFD wind vectors (if available).

I'm sure there is a formula, but I don't lug around an enormous brain. Keep it light; keep it simple (thank you old-school bush pilot Oren Hudson) works for me. Having a headwind on the base leg for the turn on helps, too.

[Oktas8]

The variable that challenges the whole process in the flight levels when doing science is the changing groundspeed during the turn.

I don't think that this has anything at all to do with mental arithmetic in flight; this thread is more to do with aircraft & procedure design, by engineers. However...

Accounting for wind is most easily done, not by changing groundspeed, but by simple calculations of constant TAS in a turn, and (separately) the time that the aircraft is affected by a constant wind.

So, if an aircraft does a 180° turn in a 60kt wind at rate 1, forget changing groundspeed. Instead, calculate radius in nil wind, then move the aircraft 1nm downwind at the end of the turn.

PANS-Ops Doc 8168 (instrument procedure design) has many beautiful diagrams illustrating this principle.

[mikkojuha]

Basics

Answer to the original question: D is about 1,06/100 of your speed, of course same amounts, knts, kms, meters/day, what ever... when the turn is basic = 3 dec/1 sec.

r is half of the D = 0,56/100

All this is very basic maths you must know before you can get PL, at least in Finland. Travelling speed X your turn takes 2 mins, so you travel during the turn X/30, the D is then X/30x3,14 and r is half of that.

So, using 1 % of your speed you get the diameter of your turn. If you like to be more accurate, you can add to the result 6 % and you are quite near of the absolute truth.

[A Squared]

Originally Posted by cruisercruiser

Hi,

I was told in training as a general rule of thumb, 1% of G/S for 25-30 degree AOB for a 90 degree turn.

For example joining a DME arc at 90 deg with a G/S of 200kt, you need to initiate the turn 2nm before the arc so as not to overshoot the arc.

Of course we don't always join the DME arc at 90deg. Say if you join at 45deg, you need only 1nm in the above example.

Same applies for QDR intercepts if you are told to fly over a VOR to intercept a radial outbound.

That's a good way of estimating the lead for intercepting an arc, but it's not a very good way of estimating turning radius in an established turn. The rule of thumb allows for rolling in and out of the bank. The radius of an established turn with the same bank will be somewhat smaller than that. IOW, if you calculated precisely what your radius of turn would be ay X airspeed and y bank, and began your 90 degree turn to an arc at precisely that distance, you'd fly thru the arc by a fair amount.

[FLEXPWR]

aviationluver, are you only looking for a formula to be used with a calculator, or a method to quickly get a result in flight?

Formulas and calculators will obviously give near-perfect figures, the question may be, on the practical side: can you use them in flight in a dynamic environment?

As previously posted, 1% TAS (or GS depending on your needs) is a good rule of thumb, provided the aircraft maintains a rate-one turn.

Beyond 180KTAS, maintaining a rate-one turn is not an option for commercial (carrying pax) aircraft. Most flight directors limit the bank angle to 25 or 30 degrees. In these higher speeds situations, the 1% calc will not fit.

But you can find the turn radius for higher speeds based on the Mach number, or the speed in miles-per-minute:

Say M0.7 or 7 miles-per-minute (MPM), just subtract 2 and you get the radius in NM. This is really close to a formula used with a calculator, and you can use it instantly while in flight without losing focus on what you're doing (flying I guess?).

This is described in "M3: the Mile, the Mach, the Minute", mental math for aviators, with the correponding formulas.

Note that it does not take into account the time (and thus distance) travelled during the intiation of the turn, from level flight to 25 or 30 degree bank.

[underfire]

OK,

The calcs in post #38 are from 8260.52.

[Jetpipe.]

I saw some serious computations a few posts behind.. If you are trying to be so accurate with the turning Radius I guess you should include the change of the gravity force (g) with altitude..

g=g’[r/(r+h)]² and then put it in the R=V²/g tanφ

g: gravity at height
g’: standard gravity 9.81m/sec
r: earth mean radius
h: height in meters


which should be somewhat negligible at lower altitudes but hey, you guys started it just kidding! I won't mention the wind factor...

The 1%*GS*½ is the best rule of thumb ever for RATE 1 turns up to 250kts so thats what I m keeping from this thread.

[Wally Mk2]

Wow I'm impressed with the level of knowledge here by some
Where are all the pilots gone though?

[westhawk]

Where are all the pilots gone though?

Many are probably gone flying.
After all somebody has to put theory into practice!

[Pontius's Copilot]

How about keeping it VERY simple ...

1/3 x ground speed (n.m./minute) = radius in n.m. at Rate 1

Do the metric conversion yourself, I do my flying in nautical miles!

[Flybartfcp]

Even more simple…

From my Air Force days to the day, I use Groundspeed per minute - 2, for a 30º bank, 90 degree turn.

Speed 240 = 4nm/min-2= 2 Nm before

[bubbers44]

In light aircraft if you cared about radius of turn in a blind canyon and had to do a 180 either do a split S to get out or a wingover or hammerhead stall and there is no radius. Airliners never fly up canyons so why do we care what the radius of turn is unless we are just bored? Are we bored?

[roulishollandais]

bubbers44,
The glacier pilot Henri Giraud+ used the hammerhead facing the cliff : No problem with 180° turns, and so beautiful ! Good exemple of what I'm calling basic gestural process (BGP) *. (You did it since 50 years).
Landing climbing the slope and taking off descending the slope (both eventually downwind) were others BGP Giraud taught to his best friends, that Air Force refused to do during a long time, crashing some aircrafts in "Les Deux Alpes" (altitude 2000m) and jalous of Giraud flying like birds without "butterfly" *

French Civil Aviation autorised the two last to allow Ziegler's family to build their Air Alpes airline, but never the safe 180°! Many pilots died like idiots spining in turn trying to keep short radius in altitude or hitting the mountain having no more enough room. No Sop , no reckoning could help, only BGP

*definition of BGP and butterfly in thread NTSB update on Asiana 214 #121,123

[Desert185]

bubbers

I live and fly in the mountains, and have flown and taught search and rescue. We never advocate any course reversal other than a steep turn, slow and with flaps. Its the most survivable reversal.

A good hammerhead requires energy. When flying in the canyons, it is common to fly slower than cruise speed to reduce turn radius, which limits hammerhead capability.

[A Squared]

Originally Posted by Desert185

I live and fly in the mountains, and have flown and taught search and rescue. We never advocate any course reversal other than a steep turn, slow and with flaps. Its the most survivable reversal.

A good hammerhead requires energy. When flying in the canyons, it is common to fly slower than cruise speed to reduce turn radius, which limits hammerhead capability.

Yeah, that's pretty much my take on it. By the time you've let the situation develop to the point where a course reversal in a confined area is critical, you're almost certainly not going to have the energy to do a hammerhead. This just isn't the sort of situation that suddenly pops up in front of you while you're tooling along at cruise speed. And at least in my part of the world, there's also usually bad weather involved, which is why you were down in the valleys to begin with. Below the terrain in marginal visual conditions is not a great time for aerobatics.

[roulishollandais]

it is common to fly slower than cruise speed

In altitude True airspeed and turn radius are greater than it seems showing IAS. That is the biggest danger when the ceiling decreases blocking the path and doing the valley smaler. Temptation gets great to increase the bank. If you have low visibility you see the obstacle later and you want to finish the turn. And engine has less power too. That is the typical mountain crash.
But hammerhead must be masterized and well trained. Bubbers44 who is aerobatics instructor is better than I to developp.

[bubbers44]

I agree if you are flying low and slow my two options would not work but having no time to calculate radius of turn or estimate radius required before your escape I would hug the downwind side of the canyon and make sure speed would not put me into the other side using flaps if necessary to make the turn as tight as required and banking to what ever was required without stalling.

Of course you first climb to use the altitude to use lift to turn,not maintain altitude and get to what ever speed is required to do your 180.

[underfire]

Where are all the pilots gone though?

In reading through this thread, I certainly hope that active commercial pilots have not been providing responses.

[bubbers44]

Tell me one time in aviation history when knowing any of these formulas has affected safety of flight. I think never is the answer.

[Oktas8]

There are a few formulae here which help greatly in providing accurate and smooth flight under the IFR.

Does "accurate & smooth" count towards "safety of flight" Bubbers? I hope so, or a lot of my time has been wasted over the past dozen years...