Formula for Radius of Turn [Archive]

Microburst2002

3rd Oct 2009, 07:46

It all depends on what units you use for V and for g.
If you use knots and NM per squared hour you get radius in nm.
If you use meters per second and 9.8 meters per squared second, the radius is in meters.

9.8 m/s^2 = 9.8 x 3600 x 3600 / 1852 = 68578.83369 NM per squared hour

For a 250 kt with a 25º bank angle:

r= 250^2/68578.83369 x tan 25º= 1.954 NM

If you use NM/min, g = 9.8 x 3600 / 1852 = 19.04967603 NM/min^2
tan 25º= 0.466307658
tan 30º= 0.577350269
g x tan 25º = 8.883009818
g x tan 30º = 10.99833558

So if you find your speed (GS) in NM/min you can use, as a rule of thumb, that speed squared and divided by ten. This figure is approximately your radius of turn for a typical 25º-30º bank angle turn.

examples:

180 kt, 3 nm/min, 0.9 nm radius
300 kt, 5 nm/min, 2.5 nm radius
420 kt, 7 nm/min, 4.9 nm radius

I use it to join, or exit, DME arcs and it works really well. It is useful too when you have to initiate a turn to intercept a radial, or to intercept the LOC if you have distance and a bearing pointer. Sometimes if you wait until the CDI moves it is too late already. No need for the FMS!

mustafagander

3rd Oct 2009, 08:42

So you see that 10% ground speed in knots is good enough and dead easy to calculate when there's plenty of other stuff screaming for brain space. :ok:

9.G

3rd Oct 2009, 11:20

mustafagander, my calculation says it's 1% not 10% unless I've had too much of 12 years old Chivas. :}

mcdhu

3rd Oct 2009, 19:28

Careful chaps!!

Surely the 1% equals the DIAMETER of the turn - at least, that's the way it's worked for me for a few decades!

Cheers
mcdhu

28L

3rd Oct 2009, 20:07

Aviationluver,
Wikipaedia is correct, as is Microburst. You just have to be consistent with the units.
I.e. if you want metres for the radius you must use metres per second for v and metres per second squared for g.
If you want the radius in Nautical Miles you must use Nm per second (!) for v and Nm per second squared (!!) for g.
If you really have to use Kts for speed (Nm per hour) then you'll also have to use Nm per hours squared for g (!!!)
As I say, you MUST be consistent with the units in the formula.
Good luck :ok:

Genghis the Engineer

4th Oct 2009, 07:29

As 28L said.

Use TAS (not IAS) for V, in m/s

g=9.81 m/s/s

r will then be in m

Or if you like old imperial units, use TAS in fps, and g in f/s/s, and you'll get an answer in ft.

G

Skunkworks

4th Oct 2009, 08:35

standard rate (360 degree) turn at 180KTAS --> 6nm (11 112m) in 2min.

circumference (circle) = 2 x Pi x radius

11 112 = 2 x 3.14 x r

r = 1769m

ITCZ

4th Oct 2009, 08:54

Does anyone have the formula for radius of turn for an airplane (with everything in metric units)???
If you want the answer, not the formula, try this..
Aircraft Turn Information Calculator (http://www.csgnetwork.com/aircraftturninfocalc.html)

Careful when you use the term Standard Rate. Your AIP may state that turns be made at Standard Rate (= 2min) or 25 deg AoB, whichever is lesser. It says "whichever is lesser" because 2min turn ≠ 25 AoB turn.

Skunkworks' formula works when variable is timing = 2min.

Wiki formula works when the variable is AoB.

They may be equal under certain conditions, but not always.

The following may be helpful... from "Aviation Formulary V1.24" by Ed Williams

Metric? Just work out a factor!

Turns and pivotal altitude

In a steady turn, in no wind, with bank angle, b at an airspeed v

tan(b)= v^2/(R g)
v= w R

where g is the acceleration due to gravity, R is the radius of turn and w is
the rate of turn.

Pivotal altitude h_p is given by

h = v^2/g

With R in feet, v in knots, b in degrees and w in degrees/sec (inconsistent
units!), numerical constants are introduced:

R =v^2/(11.23*tan(0.01745*b))

(Example) At 100 knots, with a 45 degree bank, the radius of turn is
100^2/(11.23*tan(0.01745*45))= 891 feet.

The rate of turn w is given by:

w = 96.7*v/R

(Example) = 96.7*100/891= 10.9 degs/sec

The bank angle b_s for a standard rate turn is given by:

b_s = 57.3*atan(v/362.1)

(Example) for 100 knots, b_s = 57.3*atan(100/362.1) = 15.4 degrees
A useful rule-of-thumb, accurate to ~1 degree for speeds up to 250
knots, is b_s= v/7 (v in knots).

The pivotal altitude is given by:

h_p = v^2/11.23

(Example) At 100 knots groundspeed the pivotal altitude is 100^2/11.23 = 890
feet.

BOAC

4th Oct 2009, 11:02

How's about for pilots we keep it simple? We ALWAYS turn procedurally at Rate 1, don't we?:rolleyes: FORGET angle of bank.

Basic rotational algebra tell us that R=v(TAS)/'omega'(Rate of turn) where omega = radians per whatever (not degrees/???).

Rate 1 is PI*60 radians per hour. So, if you choose to work in nm (who on earth would want to use something else...:)), at 240kts TAS:-

R(nm)=240/3.142xxx*60 =1.27nm - close enough for government work Even easier is TAS/180. That I could handle in the cockpit. Most of the above is just TOO much:) [I never could roll out on a radial, anyway...............]

:

Keith.Williams.

4th Oct 2009, 15:47

For JAR exams use

R in meters = (0.51 x TAS) ^2 / g (tan bank ang)

Where TAS is in knots and the 0.51 converts this into m/sec.

Or use 0.515 if you want to be a bit more accurate.

Remember to multiply the TAS by 0.51 before you square it. The mathematically challenged often square the TAS then multiply by 0.51. This does not work!

flybywire380

4th Oct 2009, 17:34

Careful chaps!!

Surely the 1% equals the DIAMETER of the turn - at least, that's the way it's worked for me for a few decades!

Cheers
mcdhu

I would agree with mcdhu.

Microburst2002

4th Oct 2009, 17:48

Hi BOAC

Rate one turns can be done at low speeds (for airliners) but at high speeds we would exceed the 30º bank angle. In these occasions we have to calculate in a different manner. And in some airplanes there is not bat and ball
anymore.
I remember when I had a sim test for an airline in a 727 simulator. We had to do the "B figure", I don´t know if in UK you are familiar with it. Well it is like a series of racetracks and procedure turns, which legs have to be timed. Turns are supposed to be made at 3º/sec.
During the procedure we had to use three speeds: hi, med, low. 300 kt, 250 kt, 200 kt.
Timing was impossible, of course, so it was impossible to make a good B figure! The sim was a complete wreck, so it was a nightmare...

cheers

mm43

4th Oct 2009, 18:41

The same spreadsheet formula using 180/PI() for MicroSoft and RADIANS for Open Office:-

=ROUNDUP(POWER(TAS,2)/((TAN(AoB/(180/PI())))*68625),3) MicroSoft EXCEL
=ROUNDUP(POWER(TAS;2)/((TAN(RADIANS(AoB)))*68625);3) Open Office CALC

TAS = KNOTS
AoB = DEGREES

RESULT = Turn Radius in Nautical Miles

Example TAS 240KTS AoB 25 degrees = 1.8NM (radius)

and if you REALLY want to use metric units, enter TAS in KMH and divide answer by 1.852, e.g.

=ROUNDUP(POWER(TASkmh,2)/((TAN(AoB/(180/PI())))*68625),3)/1.852

NOTE: BOAC's "back of the fag packet" method gives about the same result!

mm43

BOAC

4th Oct 2009, 22:29

We ALWAYS turn procedurally at Rate 1, don't we? - Microburst - you telling me you are flying procedures at 300kts:eek:/ That's how you hit cumulo granitus. If you are talking about cruise speeds - why are you bothered about 'radius of turn'?

Artisan

5th Oct 2009, 00:35

If you want to join a DME arc or intercept a LLZ course etc, the following method has worked well for me;

1. For a rate one turn, use a Bank Angle of =(TAS/10)+7 (Degrees)
2. Turn radius for a rate one turn is approx = 0.9% of G/S (Nm)

Note the use of Ground Speed rather than airspeed, if you are interested in your ground track.

ITCZ

5th Oct 2009, 14:43

How's about for pilots we keep it simple?
I would violently agree with you, if it were for use by pilots in the cockpit, with a groundspeed > 0kt!

But our friend did not specify in his original post, whether he sought a rule of thumb for inflight use, or a formula for his latest iPhone or Excel spreadsheet project.

The clue for me was that he posted in TechLog (bing!), a geometric expression (bing bing!), but could someone help this USA resident with one that used metric units (bing bing bing!). Us rule-of-thumb pilots only work on a tan when we are on a tropical layover, and metric when forced to fly through foreign airspace!

If our friend is doing some research, or aims to produce some kind of calculator (javascript, iPhone, spreadsheet or otherwise) then why use a Rule of Thumb when a floating point arithmetic gadget is doing the computations? That's sloppy.

If our friend is attempting to work out his radius or diameter of turn to write an Ops manual or a Procedure, then likewise, why not use a formula and apply factors for wind and varying pilot skill?

If our friend is looking for a rule of thumb to see how wide he will fly in a holding pattern he is assigned tomorrow, then formula? Forgetaboudit! Use a rule of thumb as above.

We ALWAYS turn procedurally at Rate 1, don't we? FORGET angle of bank

No, that is not correct.

I am permitted to turn at 30ºAoB, it is normal for the category of aircraft, and do so when circling.

"Procedurally"?

I am instructed to turn at the lesser of Rate 1 or 25ºAoB in departure and approach procedures. "The lesser of", because Rate 1 and 25ºAoB are rarely coincident.

I am instructed to make turns at 15ºAoB in an EOSID procedure.

My aircraft AFGS commands 25ºAoB turns <=FL200 and 20ºAoB turns >FL200 if GCP selected. If in full autoflight, the Honeywell Pegasus FMS commands a far lower AoB if at high TAS/high altitude.

Less "procedurally"... If I'm avoiding Wx that is a fair distance ahead, I might choose to turn at only 5º or 10º AoB by use of the AoB limiter on my GCP.

So no, "we" pilots don't "always" turn at Rate 1 "procedurally". Plenty of exceptions to that rule.

Thats where a Rate of Turn calculator based on AoB might come in handy for those pilots and others that design procedures.:ok:

This IS techlog, is it not?

BOAC

5th Oct 2009, 16:00

Well, ITCZ, I suppose it depends on how anally retentive any particular pilot wishes to be? a.l. already has the equation and his answer (see Genghis the Engineer's post) if he wishes 8 decimal point precision in metric bits.

Your post yesterday was more than sufficient to cure a.l. of insomnia. :)

If I wished to avoid weather at 5 or 10 AoB I would probably use the 'TLAR' rule of thumb.:ok:

I trust you spotted the carefully hidden :rolleyes: in my previous post?

mustafagander

7th Oct 2009, 06:50

A bit late to apologise for getting it wrong, but I did, didn't I?

1% works fine, 10% is a bit generous :}

I use it for turning onto DME arcs etc.

I must re read my posts!!

john_tullamarine

7th Oct 2009, 12:26

This chart may be of use to some. It was knocked up many years ago for a mate who ran an I/F procedural trainer school and wanted several charts to simplify briefings. He's long out of the workforce and I have no continuing interest in copyright so I've deidentified it and you are welcome to use it if it is of any value to you.

As I recall it made life in the Link Trainer a bit easier but, as we all know, rule of thumb and watching the needles tends to be the go in the air.

I note that a few posters have been at pains to show concern about consistency of units.

That's all fine but, at the end of the day, you can use whatever units you choose just so long as you do the conversion calculations to make the equations correct ... I think that speeds in megafurlongs/fortnight or deci-lightyears/weekend would be rather cute ... but, somehow, I don't think that will take off ...
http://img.photobucket.com/albums/v318/john_tullamarine/album%20002/TurnperformancenilID.jpg

Old Smokey

7th Oct 2009, 13:47

I've never seen so much discussion over what should be a relatively straight-forward matter:ugh:

The application of the various simplifications (e.g. 1% of TAS) is good in practice. Perhaps the original poster needed something more accurate, as may be required when working out OEI Escape Routes etc.

The two formulae given below apply 2 different constants, one for entry speed in Knots, the other for entry speed in Km/Hr.

If Entry speed is in Knots :-

R = TAS^2 X .02698711 / Tan AoB

If Entry speed is in Km/Hr :-

R = TAS^2 X .00786818 / Tan AoB

Example : TAS = 200 Kt (370.4 Km/Hr) at Bank angle 25 degrees.

R = 200^2 X .02698711 / Tan 25 = 2314.96 M....... OR

R = 370.4^2 X .00786818 / Tan 25 = 2314.96 M

If you want the answer in Km, divide by 1000:ok:

Anghammarad

7th Oct 2009, 14:20

Loke Old Smokey said

R = TAS^2 X .02698711 / Tan AoB

or

R= TAS^2/(37*tan AoB)

which is more or less the same.

Will give you the radius of the turn in meters.

john_tullamarine

8th Oct 2009, 11:18

For those of us who have an engineering or similar background, unit conversion is routine bread and butter stuff. For those who are not comfortable with such antics, you might like to see how it is done -

The sequence requires that you keep rigorous track of the variables, constants and units .. which I have separated below to make it a bit easier to follow.

Explanation -

Using speed, V, in kts, g in ft/sec^2 and I want the answer to be radius in nm. You might just as easily have started with some other units - makes no difference to the technique.

To change units, we use the "trick" of multiplying by unity ("1") which doesn't change the value of an expression. We can extend this by noting that dividing something by itself is "1" eg 4/4 = 1. The secret, then, lies in further extending this to account for different units which represent the same quantity. So, for instance, we can say that 1nm/1nm = 1 which is the same as saying that 1nm/6080ft = 1. (or you might chose to use 6076.131 as the conversion - depends on what reference you look up). This then allows us to cancel out unwanted units and we just carry the resulting numbers into the main calculation. This last bit is very important and the source of much error when folk start learning about unit conversions.

At the second line we need to get rid of the hour, second, and feet units. To make it easier to follow we can do it in two stages.

To get rid of the hours and seconds, we note that

1 hour = 60 x 60 seconds = 3600 seconds

as we have to get rid of hours^2 and seconds^2 (whatever those units might represent physically is not a concern) we can square the conversion units to come up with

1 hour^2 = 3600^2 seconds^2 which gives the unity expression

1/3600^2 with units hr^2/sec^2. Whether you put the hours or seconds on the top line is determined by the original equation. In this case we want to get rid of hr^2 on the bottom and sec^2 on the top so it makes sense to insert hr^2/sec^2 as in the graphic.

To get rid of feet, we note that

1 nm = 6080 feet (or some similar conversion value) so the unity expression is

1 = 6080/1 with units ft/nm as we need to cancel out ft on the bottom in the original expression

Notice that I now end up with nm as the only unit on the RHS of the equation and this is what I needed. Note also that I have taken the conversion units (3600^2 and 6080) into the constants expression so that I don't lose track of them.

If we do the arithmetic to simplify the numbers we get 0.0000145694 as the conversion constant. As that is a dreadful number to work with, I prefer to replace it by the reciprocal on the bottom line. All this means is I note that

1/2 = 0.5/1, so

0.0000145694/1 = 1/68637

To convert to metres, we note that

1 = 1852/1 with units m/nm so that we can cancel out the nm and to get to Old Smokey's version we do the reciprocal trick.

Note that the small difference in constants is a consequence of which values go into the intermediate steps. It may be important to the academic purist but, functionally, the end result is sufficiently similar not to worry too much about it .. all depends on the reference table from which you pick your conversion constants.

http://img.photobucket.com/albums/v318/john_tullamarine/album%20002/Graphic1.jpg

Old Smokey

12th Oct 2009, 11:54

Jeez J_T, multiplication is much more fun than division! Just ask any rabbit (or poodle) :ok:

Now to work out a formula for Pugilistic Animus' asymptotic turn.:)

Pugilistic Animus

15th Oct 2009, 22:09

You nerds :8

john_tullamarine

15th Oct 2009, 23:03

You nerds

C'mon, now .. don't be like that .... OS and I can't help ourselves.

Pugilistic Animus

15th Oct 2009, 23:31

J_T despite my humor I think it's nice to see folks [in the technical fraternity] who still know what they are doing and what they talking about and don't consider pedantry at all; I have received innumerable educational benefits from you all :ok: from a humble student of the art,...

May you find marry a gorgeous AND experienced computer to write your polar plots:}

john_tullamarine

16th Oct 2009, 00:07

May you find marry a gorgeous AND experienced computer to write your polar plots

love it ...

MD83FO

31st Aug 2013, 09:57

is there an IOS application that covers these kind of formulas?
like sort of an advanced E6B

thanks

john_tullamarine

31st Aug 2013, 10:10

.. at the risk of making myself look a bit of a goose ... what's an IOS ?

MD83FO

31st Aug 2013, 10:21

ha ha, sorry John, its iPhone Operating System for us the lazy guys.

john_tullamarine

31st Aug 2013, 10:41

ah .. par for the course for us old pharts ...

BARKINGMAD

2nd Sep 2013, 17:46

In the halcyon days when Bett Windsor's Flying Club (aka the RAF) flew real aeroplanes, without all these clever wiggly amps and gigabytes to help, we were issued with a small card/piece of paper which if I recall correctly had three/four lines of figures on it.

Angle of bank was one, TAS was another, radius of turn was the third and possibly "g" force was the fourth.

All one had to do was to put a straight edge along 2 of the values and read off the other(s) where the edge intersected the line of values.

All this tan theta and mental maths was obviously too hard for the top guns of the period and it sounds like a prime example of KEEP IT SIMPLE.

Has the K I S S principle been abandoned forever in favour of geeks and shiny touchscreens?

To the OP, I appreciate this cribsheet is not a formula but it seemed to be worth that fine institutions efforts to educate their pilot and navs.

Can any ex RAF/FAA exiles out there recall the nomogram and put what's left of my mind at ease, please?! :)

Green Guard

3rd Sep 2013, 10:53

φ is a Bank °

Turn Radius (r) in NM = TAS^2 / 68649 / tg φ °
Turn Radius (r) in sec=TAS / 19.07 / tg φ °

for calculatons on mobile phone calculator

Radius in NM for (φ 30°) = TAS*TAS /39683
(φ 15°) = TAS*TAS/ 18382
(φ 10°) = TAS*TAS/ 12107

for calculations from one's "top of head"

TAS 199 kt φ30 r=1 NM
φ16 r=2 NM
φ11 r=3 NM

Radius in SECONDS (φ 28°) ~ TAS / 10
(φ 15°) ~ TAS / 5
(φ 10°) ~3 xTAS /10

Turning Point= Radius (NM or KM) * tg (( next CRS – present CRS) /2) ;)

djpil

3rd Sep 2013, 11:35

we were issued with a small card/piece of paper which if I recall correctly had three/four lines of figures on it
http://www.tscm.com/maneuver.pdf is one source

Lightning Mate

3rd Sep 2013, 11:44

There is of course a very accurate formula to get the answer.

flyboyike

3rd Sep 2013, 13:50

Holy Guacamole, they're even resorting to using Greek letters now!

underfire

3rd Sep 2013, 17:46

What is the context of the OP need for turn radius?

R= NM

Figure your true airspeed TAS, tailwind component TW, and FAA std bank angle of 18 degrees;

R= (V KTAS + V KTW)^2 * 0.0000449

Non-standard bank angle;

R= [(V KTAS + V KTW)^2 * (1.4589*10^-5)] / tan(desired bank angle)

Given a turn, what is your bank angle;

Bank Angle= tan^-1 {[(V KTAS + V KTW)^2 * (1.4589*10^-5)] / R}

cruisercruiser

8th Nov 2013, 12:00

Desert185

8th Nov 2013, 16:34

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). :ok:

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. :D

Oktas8

8th Nov 2013, 21:32

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

9th Nov 2013, 00:55

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

9th Nov 2013, 12:13

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

9th Nov 2013, 13:48

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

9th Nov 2013, 16:10

OK,

The calcs in post #38 are from 8260.52.

Jetpipe.

9th Nov 2013, 18:47

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 :p just kidding! I won't mention the wind factor... :8

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. :ok:

Wally Mk2

9th Nov 2013, 23:06

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

westhawk

10th Nov 2013, 01:11

Where are all the pilots gone though?

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

Pontius's Copilot

10th Nov 2013, 19:11

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

10th Nov 2013, 21:44

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

11th Nov 2013, 02:24

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

11th Nov 2013, 13:27

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

11th Nov 2013, 15:12

A Squared

11th Nov 2013, 15:25

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

11th Nov 2013, 18:55

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

11th Nov 2013, 20:57

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

11th Nov 2013, 22:05

Where are all the pilots gone though?

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

bubbers44

11th Nov 2013, 22:25

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

12th Nov 2013, 04:46

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... :)

bubbers44

12th Nov 2013, 09:42

The only time a formula is helpful is in a descent. We made it a game to reduce smoothly to idle power at altitude and calculate our winds and weight to not power up until 1,000 ft. Speed brakes were not allowed, just slight AS changes. My first airline in 737's we didn't even have a GS readout and we still could do it. You can't get much smoother than that.

Yancey Slide

12th Nov 2013, 13:38

"In reading through this thread, I certainly hope that active commercial pilots have not been providing responses. http://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/censored.gif"

Are you looking for 'chandelle'?

aditya104

12th Nov 2013, 18:43

This thread has had lots of accurate formulas and calculations submitted. Here is another one. This time it is an excel calculator for radius of turn. Not too sure if it can serve any one's practical needs. If you find any mistake, let me know and I will fix it. :)

http://i.imgur.com/tmOBNVt.png (https://mega.nz/#!khpgGTQb!J1rS3lYecDG9thjKbqWfvgObDRhecAlO6x0O4RtIUPM)

Download file through your browser (https://mega.nz/#!khpgGTQb!J1rS3lYecDG9thjKbqWfvgObDRhecAlO6x0O4RtIUPM)

The following two rule of thumbs from this thread, I found, are easy to use. :ok:
For a rate one turn, use a Bank Angle of =(TAS/10)+7 (Degrees)
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. :ok:

john_tullamarine

12th Nov 2013, 19:33

We made it a game to reduce smoothly to idle power at altitude and calculate our winds and weight to not power up until 1,000 ft

Even more fun (freighter ops) was to climb to whatever maximum height one calculated .. nose over (without any cruise) for the descent .. and then as you have indicated ...

Used to be the highlight on Sunday morning paper runs HBA-LST on the Electra ..

underfire

12th Nov 2013, 21:05

aditya,

You have not factored in winds

bubbers44

12th Nov 2013, 23:48

90% of the time we could do the idle descent to 1,000ft but different winds would sometimes make you lose the game if they changed a lot through the lower altitudes. We always knew the winds would diminish but didn't know how much. We had a lot of one hr flights to the Bay Area so needed something to challenge us and not get bored.

john_tullamarine

13th Nov 2013, 00:09

but different winds would sometimes make you lose the game if they changed a lot through the lower altitudes

.. but we got very good at recalculating mental profiles every mile or so and running ± 5-10 knots on the descent to adjust for wind ... rarely did anyone lose the plot entirely. Mind you, ATC sometimes would make things harder than necessary ..

And, invariably, this was all done raw data and no FMS.

bubbers44

13th Nov 2013, 01:13

We had B737's with no GS readout so used DME and watch to figure GS. We were happy if the autopilot worked. Guess that is why I don't understand automation dependency by some posters. We never needed it and the aircraft flying today are no harder than our old planes to fly. Only the new pilots seem to sometimes have a problem if automation fails.

Rotorman

15th Sep 2016, 20:22

A simple explanation :

Circumference of a circle = 2 x pi x R

If the TAS = 120 kts/ h, then aircraft is travelling at 2 nm per min.

A rate 1 turn~ 360 degrees in 2 min.

So 2 x pi x R= 4 nm

Therefore R= 4/ (2 x pi)= 2/pi=2/3.14=0.63 nm

which is roughly TAS/200

underfire

15th Sep 2016, 23:52

Aditya, Are you still working on this?

It would help if you had input for KIAS, altitude, and tailwind components. This would make it more flexible using for the KTAS calculation.
Turn radius parameters always begin with a fix at the beginning of the turn, you can then add the wind component with angle. This will be used to determine the max bank angle, not simply bank angle. Winds have significant effect on bank angle.
FAA/ICAO calculations use a 50kt tailwind that follows the ac through the turn, so it simply adds 50 kts to the entire path. Other proprietary software uses the wind component, usually to advantage in the max bank angle determination.