Max Rate turn vs. Min Radius Turn

[Simon150]

A question posed during my course.....

Is a Maximum Rate turn the same as a Minimum Radius turn...if not, why not?

I have an idea on the Max Rate Turn (which I think is different from a Max Rate Level Turn) but I have no idea how you would go about conducting a Min Radius Turn (if it is indeed different).

[ReverseFlight]

This is an interesting one - I haven't seen it this way before. Let me try and have a stab at it.

A rate 1 turn is expressed as 3 degrees per second or 2 minutes to go around 360 degrees. We normally think that any increase in airspeed causes the rate of turn to decrease, but that's assuming you're holding a constant angle of bank. In order for the aircraft to finish a larger circle in the same 2 minutes, it would need to fly faster (assuming it has the power) but by increasing its angle of bank, it can still achieve a rate one turn in the outer circle (within the same 2 minutes). The result is : the rate of turn is not affected by the radius of turn due to the change in bank angle.

A minimum radius turn is not related to time at all - it's a measurement of spatial distance. The aircraft would slow down to just before the stall and keep on as much bank as it can. It is trying to make to smallest circular smoke trail in the sky but he can take as long as he likes to do that. Conclusion : radius of turn varies directly with (square of) airspeed but inversely with bank angle.

[Whopity]

A max rate turn is flown at the buffet producing maximum lift with minimum airspeed and the smallest radius that you can fly the aeroplane. However; turn is a change of heading which is also the definition of Yaw, rotation about the vertical axis. A Stall turn has a smaller radius of turn than a max rate turn.

[Simon150]

Whopity.

Not my understanding.....

A true Max rate turn is flown at the minimum speed needed to achive the limiting airframe load factor. You need to be flying at sufficient speed to pull maximum G without stalling, but no faster - which is around Va. I believe the maths supports this.
Typically, I understand that this requires a descent as there is unsually insufficient power in your usual training aircraft to maintain the limiting load factor in a level turn.

Regarding a minimum radius turn, thats where I most confused, although I don´t think it can be just ´slowest speed nessesary´as theoretically, the slowest you can go is just above the stall and put any reasonable bank on at that speed and you drop out of the sky. You must surely need to fly at a speed that allows you to fly at a reasonable angle of bank.....otherwise you are not going to turn.

[ReverseFlight]

Simon150, looks like you're talking about practical flying. I mistook yours is a pure theory course.

Agree with your analysis - in order to pull a max rate turn, the stall speed is much higher and Va is close to the mark for the average training aircraft anyway. I also note you are referring to a max rate turn rather than a max rate level turn, so the descent does the trick.

In a min radius turn, you're going to have the same problem because you need to build up speed to avoid the stall in the turn.

Is there really a practical difference between max rate turn and min radius turn then ?

[Whopity]

You need to be flying at sufficient speed to pull maximum G without stallingThats what I said, you fly at the buffet, where you achieve max lift, and minimum speed without stalling.
Have a look at this Aircraft Turn Information Calculator (http://www.csgnetwork.com/aircraftturninfocalc.html) you can play with speeds and bank angle to see what radius of turn you can achieve.

[DB6]

A max rate turn is not flown at the minimum, but the maximum possible speed. Basically you need the maximum possble lift, inclined at the maximum possible angle, to give you the maximum turning rate. To wax technical for a second, Lift = C.1/2 Rho. V squared. S (C is lift coeff, Rho is air density, V is speed, S is wing area). S is fixed (ignoring things like flaps) so you need max lift, speed and air density. So the max rate of turn is achieved low down at max power and max lift - on the light buffet. Because you're on the buffet the speed is fairly low as there is so much induced drag, but it is the max possible with the power available, not the minimum.
Don't have the gubbins for a min radius turn but I would imagine it's flown at a lower speed, using flaps etc.
Simon 150, normally a 'max rate turn' is accepted as being a max rate level turn. A true max rate turn is flown at the airframe g limit, which in most aircraft will mean descending as they don't have enough power to sustain max g in level flight.

[Simon150]

Thanks all....looks like we have reached agreement on the max possible rate turn. Its a turn at maximum possible G at Va (more or less) and probably would include a desent to maintain speed.

I believe that once you are G limited (i.e. at Va) then any additional speed reduces the rate of turn? So the turn must be flown at the minimum speed capable of allowing the airframe limiting load factor to be achieved (about Va)...but no more.....right?

I have been kindly provided with a link to a website which says that a maximum rate turn is also the same as a minimum radius turn (baring fancy stall/canyon turns etc). The author would seem to be an authority on the subject. However, he also states that practically the low speed flaps out option is nearly as effective and much safer.

Airplane Upset Recovery Training: Advisory & Consulting Group • View topic - Turn Capability (http://www.upsetrecovery.com/forum/viewtopic.php?f=5&p=60)

I think the exam question has been answered as 'yes - they are the same', with the caveat that it's a theorectical answer to a theorectical question. In practice although you might have a bash at a max rate turn at altitude with an aircraft fitted with an accelerometer, trying a true min radius turn in anger (avoiding stuff low down) is probably not a good idea. The flaps out, slow speed second best option is almost as good and much safer!

Thanks everybody!

[Islander2]

I think the exam question has been answered as 'yes - they are the same' ..................... the flaps out, slow speed second best option is almost as good and much safer!Well, I disagree strongly with both those statements. It's an interesting and quite complex subject on which many of the standard aerodynamics and mechanics of flight texts disagree.

However, it can be shown mathematically that, for level flight, the speed for maximum rate is higher than the speed for minimum radius and, at least in the days of the JP, that is exactly what the RAF used to teach (minimum radius being the low point on the radius/TAS graph for a particular altitude, and maximum rate being the point where a tangent from the origin just touches the curve).

And I am appalled at the suggestion that a maximum performance manoeuvre be carried out with the flaps down to improve safety. On many aeroplanes, the design limit load factor is significantly lower with the flaps lowered; as an example, the A36 Bonanza I fly is designed to withstand +4.4g with the flaps up, but only +3.0 with them down.

[Simon150]

Islander2, sounds like you have the interest and experience to make a useful contribution here. I am glad you disagree.....lets see if we can sort out the truth then...

Please don´t be appaled by anything on PPRUNE - its so easy to fly off the handle and type something on a computer to a faceless piece of text that you wouldn´t dream of doing if you were talking to the same person in real life. Most aruments and abuse on otherwise really interesting threads start with people being appaled and other people taking offence and then down the spiral it goes.

Again, please don´t be appaled, and if you are interested I suggest you read the link to which I was refering before getting to stressed about max rate flaps down turns!

The aerobat I fly is limited to plus 6 clean and plus 2 with flaps down. The gentleman in the thread is only saying that a slow speed turn with flaps down - (which would of course be well within the limiting G with flaps down - basic airmanship!) only gives a slightly larger radius of turn than a clean high G manoever at a correspondily higher airspeed. He does provide the maths to back this up.

So what would be your answer to the question then if they are not the same? Do you agree with the max rate at Va because that seems to be universally accepted as far as I can figure. The way to fly a min radius turn is the one we seem to be getting our knickers twisted with!

You seem to have the answer for the JP if you happen to have a radius vs. TAS graph available. Although they are clearly different, the low point on the curve, and the point of tangency will be pretty close together so although the speed to fly may not be identical, it sounds like they will be pretty close.

Cheers

Simon

p.s. we are talking theory here and not nessesarily 'level flight' if that makes any difference?

[Charlie Foxtrot India]

Another angle: (excuse pun)

Rate of turn is degrees per second.

Radius of turn can be relative to the ground eg if you configure slow safe cruise and turn at about 45 degrees angle of bank into wind, you can do a 180 without covering much, or any, ground. For the same reason at low level or in a valley you should always turn into wind, reduces the radius of turn in terms of distance travelled as well as reducing the liklihood of getting disorientated.

[Islander2]

Although they are clearly different, the low point on the curve, and the point of tangency will be pretty close together so although the speed to fly may not be identical, it sounds like they will be pretty close.Actually, no, they're not that close at all. In any event, you'd sought a 'theoretical answer to a theoretical question'; it's probably not helpful to then dismiss the theory by arguing that, for practical purposes, the answers are pretty close!

The aerobat I fly is limited to plus 6 clean and plus 2 with flaps down. The gentleman in the thread is only saying that a slow speed turn with flaps down - (which would of course be well within the limiting G with flaps down - basic airmanship!) only gives a slightly larger radius of turn than a clean high G manoever at a correspondily higher airspeed. Basic airmanship, eh? Let's examine that more closely.

I don't have an Aerobat POH to hand, but assuming the 1g stall speed to be around 50 KCAS clean and 45 KCAS with flaps fully deployed, then a Va turn nibbling at the stall at the design limit load factor would be flown at circa:
a) 80deg bank angle and 122 KCAS (r=225ft; ROT=53deg/sec) clean; or
b) 60deg bank angle and 64 KCAS (r=208ft; ROT=30deg/sec) with flaps down.

But the reason for using flaps, apparently, was to provide a safety margin. So let's assume we fly at a load factor of 1.75 rather than 2. In that case, the turn would be flown at circa:
c) 55deg bank angle and 60 KCAS (r=219ft; ROT=26deg/sec) with flaps down.

(Edited to observe that I've made no assumption about level flight here, which would necessitate the more complex consideration of power available; obviously, in the flaps raised scenario - option a above - the high induced drag means level flight couldn't be sustained in an Aerobat at that speed)

So which do you think is better airmanship? 80deg bank/122KCAS, or 55deg bank/60KCAS?

Before you reach a conclusion, consider what might happen in circumstances where things don't go according to plan and the nose drops. In case a), the speed at which some primary structure may fail upon application of full control deflection (design ultimate load factor exceeded) is circa 150KCAS. In case c), it's a mere 78 KCAS! How many pilots would have an appreciation that full control deflection in an Aerobat could possibly cause structural failure at speeds as low as 78kts?

Please don´t be appaled by anything on PPRuNe Advising that a maximum performance manoeuvre be flown with flaps down for safety reasons is both wrong and highly dangerous. You may not like my use of the word 'appalled', but I'm confident it's appropriate.

[Brian Abraham]

Is a Maximum Rate turn the same as a Minimum Radius turn
Yes is the short answer, and it occurs when flown at Va pulling the max allowable "g". Fighter pilots are more than a little interested in this for obvious reasons, except they often refer to it as "corner speed" or Vc, that relating to the speeds position on the aircrafts V-n diagram. A look at may clarify http://www.flightlab.net/pdf/8_Maneuvering.pdf

[rapiddescent]

Interesting discussion.

I can tell you for sure that a min radius turn isn't always the same as a MRT.

Yes, you can fly 'configured' and therefore fly a very small radius of turn, but not very tactical is it?

Fighter guys do use the term 'corner speed' as the speed at which you are flying at max rate of turn.

From this point, you can bleed airspeed (by pulling harder into the buffet) and reduce your 'radius'. Some aircraft cannot do this effectively, however, the hornet has the ability to continue to enter heavy buffet and not stall conventionally.

The min radius is best flown at a slower speed than the max rate turn. A simple look at any Em diagram will depict this.

[BEagle]

For a level min radius turn, CL sin AOB needs to be the maximum. This means at buffet nibble at the AOB corresponding to the maximum permitted value for the aeroplane, or if that cannot be achieved due to lack of available thrust, at the AOB corresponding to the maximum sustainable +GZ.

For a max rate turn, TAS x CL sin AOB needs to be the maximum. Plot R against TAS assuming unlimited thrust and the min radius turn speed is the TAS corrsponding to the 'bottom' of the U-shaped curve, whereas the max rate turn TAS is obtained from the tangent drawn from the origin to the curve - this will correspond to a TAS greater than that for minimum radius.

If CLmax does not change appreciably with TAS and the turn rate is limited by the max sustainable level flight +GZ value, the turn graph will not have a turning point corresonding to a theoretical minimum, hence the tangent will meet the curve at its lowest point and the TAS for minimum radius and maximum rate will be the same.

In conclusion:

Theoretically, a max rate turn will require a TAS greater than that for a min radius turn. However, in practice this is only acheivable in high performance aircraft. Low performance light aircraft have very limited thrust and +GZ limits, so for such aircraft the TAS for max rate and min radius are the same.

Ignore any of the nonsense about using flaps in puddlejumpers - the +GZ limit and drag rise would render this impossible. Even in the Hunter at the limits of a max rate turn, dropping 23deg flap would only give you a momentary advantage - perhaps just enough to get the kill.

[Brian Abraham]

Low performance light aircraft have very limited thrust and +GZ limits, so for such aircraft the TAS for max rate and min radius are the same.
With the limited thrust available I'm guessing the average lighty would be unable to make a sustained level turn at Va and pull max "g". Question, would the answer then be max power coupled with the max sustainable angle of bank?

Edited to add: Beagle and rapiddescent, we mere mortals are on a lower plane than you chaps and can only stand and lust after your machinery. What a Hornet and the like are capable of don't relate to the civil text books.

[BEagle]

In something like the Bulldog, which had a +4.75 g limit, the corresponding theoretical level AOB would be 79.7 deg. But it could not sustain a level turn at CLmax and 80 deg AoB.

You need to be as low and as light as possible on the buffet nibble with full power. But above all you need to be taught how to do this safely - and NOT in a non-aerobatic light aicraft.

For the max rate possible turn, you would need to reach the sustained level max rate turn, then allow a descent to build up until you reach +4.75 g on the buffet nibble. I only tried this a couple of times in the Bulldog - it is very difficult and quite tiring. Never try it unless you have received training.

Speed is immaterial - you fly on the buffet nibble with full power. AoA is indicated by the light buffet.

To digress, 'MLTs' (medium level turns) in the Gnat were considered so demanding that there was a safety limit on the number of sorties you were allowed to fly that day. Full power, roll to about 90 deg AoB, pull to 5g then squeeze to 6. All the while looking over your shoulder to tell the instructor how many fingers he was holding up........ The Gnat couldn't sustain a 6g level turn, but the Valley Hunter 'GT6' could sustain a 6g climbing turn at low level!

[Simon150]

Islander2 - some really interesting points. The low structural failure speed applies to all C152s as both the aerobat and common-all garden variants have the same limiting load factor flaps down, its only clean where the aerobat can pull more G so the comment applies to all C152s!

"Actually, no, they're not that close at all. In any event, you'd sought a 'theoretical answer to a theoretical question'; it's probably not helpful to then dismiss the theory by arguing that, for practical purposes, the answers are pretty close!"

Not trying to dismiss the theory....just understand why the consensus in the industry seems to be that they are the same thing.

"Basic airmanship, eh? Let's examine that more closely."

Sorry - that comment just applied to not exceeding the limit loads in the flight configuration (flaps up/down etc) which I am sure you agree is basic airmanship.

"Advising that a maximum performance manoeuvre be flown with flaps down for safety reasons is both wrong and highly dangerous. You may not like my use of the word 'appalled', but I'm confident it's appropriate. "

Just to clarify.....I started the thread by asking the question which pretty much means that I know zero about the subject and am not in a position to advise anybody anything. Refering to the referenced article I think the point the guy was making was that the low speed option was supposed to NOT be a maximum performance manoever, and thats where the margin came from. I think his choice of example speeds and bank angles may be inappropriate (especially for our example a/c) as your maths demonstrates but if your going to be appaled by anybody, please be appaled at him as he should in a position to know better!

Islander 2 - Cheers - so its a no, they are different from you.

Brian Abraham - Cheers - so its a yes they are the same from you.

rapiddescent - Cheers - its a definate no from you, but presumably an 'EM' diagram is 'Energy Management' - again, didn't get one of those with the C-152 POH.

BEagle - your explaination agrees with the detail provided by Islander2 against his JP experience :O, but in line with BAs point, it's not sustainable in the aircraft I am being quized on (C-152). As discussed earlier in the thread (getting quite a long way back now) I should re-itterate that we were looking at the maximum possible rate turn and not the maximum possible rate LEVEL turn.

For a light aircraft, I think its been accepted (I am sure I will corrected if wrong) that the absolute max rate turn is flown on the buffet at the lowest speed capable of generating the limit load.

BEagle - just noticed your last post appear and noticed that you included the issues with needing to desend. Really interesting about the Gnat and Hunter by the way, especially since the 152 I fly is limited to 6G the same as your aircraft! I won't be trying this out in a hurry - don't worry.

"Speed is immaterial - you fly on the buffet nibble with full power. AoA is indicated by the light buffet."

Is this true? I understand that you let the speed build on the buffet until you reach limiting G, but presumably then you hold that speed. Maintaining (say) +6G in a turn and letting the airspeed increase will reduce the rate of turn won't it?

In summary, I think we all agree on the maximum rate turn more or less (minimum speed to achieve limiting G and pulling to the buffet), but despite all the discussion, there is still a huge division of opinion on how to fly a minimum radius turn (apart from those who have access to advanced performance data - EM and TAS/Radius diagrams) and it seems that these are based on level turns only as well!

I suppose at some point I could do the maths for a min radius turn. It can't be that hard can it?

On a practical note (in a theorectical discussion - sorry), Charlie Foxtrot India has an excellent point that the wind would pretty much dominate any manoever in real life and would probably more than offset any advantage by turning at Vthis or Vthat.

Oh....and how do you get those little blue quote boxes to come up????

[Islander2]

if your going to be appaled by anybody, please be appaled at him as he should in a position to know better!Simon150, my profuse apologies if I've unfairly attributed the 'flaps down' advice to you. It was contained in your summing up, and I couldn't find any reference to it in the forum link you provided (quite possibly down to my web incompetence, which is hardly unusual!).

Oh....and how do you get those little blue quote boxes to come up????Copy, paste and highlight ... then the far right icon on the post toolbar is your friend (square quote box containing some pseudo text).

[bowly]

Aaaaaah, the single circle versus 2 circle decision! Alternatively, go vertical and pray.

[BEagle]

I'd be utterly astonished if the Cessna 152 had a +6g normal limit. I last flew the Cessna 150 about 40 years ago and recall that the ultimate load limit (the point at which it fell apart) was around that value. 6.6 g, was it?

Flying at CLmax (buffet nibble), full power and at the normal G limit will give the max turn rate / min turn radius in a light aeroplane; anything else will reduce performance. But trying to sustain more than about +4 g without training and a g-suit will probably induce g-loc and possible death.

[Simon150]

Prepare to be utterly butterly astonished........

Cessna 152 - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Cessna_152)

Look under 'variants' - specifically the 'aerobat' version

Wikipedia is hardly conclusive but its the best I can find at short notice. I know for sure 'cause its placarded in G-BHEN (the aircraft I usually fly) and stated quite clearly in the POH - not that I have been anywhere near that!

As I understand, to be categorised as aerobatic under FAA certification requirements, the aircraft must be capable of +6, -3 limit (not ultimate) loads....so it is.

:ok:

[djpil]

The official astonishing data is in the TCDS. (http://150cessna.tripod.com/3a19.pdf)

[BEagle]

Thanks for that..... :eek:!! I remember the +4.4 g limit for the things I flew, with a fail limit of 150%, equating to +6.6 g.

I would very strongly dissuade anyone from trying to fly a sustained +6 g descending max rate turn on the buffet nibble in a Cessna 'Aerobat' though!

Even if the aircraft could manage it, the pilot would probably lose consciousness quite quickly. Not something you would want to happen in a descending max rate turn.....:\

Beagle and rapiddescent, we mere mortals are on a lower plane than you chaps

Nope - we're all equals!

[Brian Abraham]

Beagle and rapiddescent, we mere mortals are on a lower plane than you chaps
Nope - we're all equals!
Our plane maxs out at 10,000, yours is/was somewhat higher. :p
The text book answer (Australia - civil) is/was min radius/max rate to be flown at Va and max "g", but recognising that power to sustain would in all likely hood not be available.
Beags, you are quite right in that your 150 had a g limit less than 6, the Aerobat version was beefed up for the aerobatic role.

[ithinkso]

My lad,

they are one and the same.

its really very simple. all your answers are contained int he lift formula.

best wishes

[ithinkso]

The max rate/ min radius is to be considered in level fligth only.

Rate of turm is indirectly proportional to airspeed, and directly proportional to angle of bank. That is simply put, the higher you airspeed the lower is you rate of turn, and the higher your angle of bank, the higher your rate of turn.

Radius of turn is directly proportional to airspeed and indirectly proportional to angle of bank. Put simply once again, the higher your airpseed, the larger is your radius of turn and the higher your angle of bank, the lower your radius of turn.

In order to achieve your lowest airspeed, in level flight, you must be configured with gear up, and full flap. You must then roll into the turn and apply full power,(to lower your stall speed further). Remember he stall anlge is the same for your configuration. When you are immediately at the critical angle, and holding it, in level flight, you will then be at max rate and min radius.

It is all very elementary, but can be made as complex as you want, the basic facts however, are always right!!

best wishes.

[Islander2]

When you are immediately at the critical angle, and holding it, in level flight, you will then be at max rate and min radius.

It is all very elementary, but can be made as complex as you want, the basic facts however, are always right!!Except, ithinkso, those aren't the basic facts!

Rate of turn is, as you say, a function of AOB/V.

But radius of turn, contrary to what you say, is a function of V^2/AOB.

In consequence, as has already been explained by BEagle and myself, the speed for maximum rate of turn is higher than the speed for minimum radius. And it's not possible to have a sensible discussion on this topic without considering limit load factors and also power available. Which makes it not quite so elementary.

[Big Pistons Forever]

If you absolutely positively want to turn 180 degrees in the minimum distance you have to do a hammerhead.

[BEagle]

Or either Immelman, or just roll inverted and pull through!

[sycamore]

Beags,but which one uses least airspace ?:)

[ithinkso]

Lads, it is ever so elementary.

Limit turns, are dependent on the particular aircraft. A higher g loading does not mean a higher rate of turn. At least thats what I was taught thanks to Her Majesty. First rule, If you want to out turn someone my boy, min speed, max bank, max power, sit in stall buffet.

On a more practical note for you boys who havent flown an aircraft that goes faster than 700kts, full flap, min speed, max bank, and max g up the point of stall. Max rate and Min Radius are one and the same. Check your books.

The basics are the same, the rules dont change, keep it simple and you will never go wrong!

Best of Luck!! And keep trying!!

[Islander2]

Max rate and Min Radius are one and the same. Check your books.(my bold) Alright, try the Royal Air Force's FTP/002/2 'Aerodynamics and Aircraft Performance':

"The speed for maximum rate of turn is that which corresponds, on the minimum radius of turn graph, to the point where a tangent from the origin just touches the minimum radius curve. Fig 3 shows that, at any given altitude, this speed is higher than the speed for minimum radius."

Lads, it is ever so elementary .... Best of Luck!! And keep trying!Patronizing airs aren't always underpinned by knowledge!

Edited to correct for finger trouble: somewhat obviously, minimum radius of turn graph was mis-written as minimum rate of turn graph. Apparently, that makes me "a clown". Ah well, c'est la vie!

[ithinkso]

Check your books again my lad, you should perhaps check context.Yes they are my lad.

ps: I think you may have the wrong graph. It may have changed on the last 40 years, but I wouldn't think so!

pps: I have never seen a "minimum rate of turn" graph????

You clown!

[Islander2]

Check your books again my ladOK, which one now? 'I Spy Aeroplanes'?

You clown!
You have such a way with words!

[sycamore]

Point of interest for a European jet trainer,SL,wt 8000lbs,maxpwr/wt ratio .47; max ROT @8g 300kts =28.5deg/sec,radius 320 mtrs,instantaneous at load limit.
Sustained ROT @2.8G, 160 kts,rate of turn18 deg/sec,radius 275 mtrs,level.Any subsequent reduction in speed will reduce G/bank angle/ROT TO 1/0/0, with subsequent increase in radius..Chart doesn`t give any benefit for flaps,but it will decrease radius slightly..

[ithinkso]

The use of full flap generally only applies to light trainers, as with most high performance machines, the extension of flap will lower the max g limit, generally by about 40%.. We used full flap for the manouvere in the P3.(Orion). The Canberra was clean for the manouvere.

[Oktas8]

Simon 150 - you mentioned doing the maths. Some time ago I did just that for a "typical light aircraft", assuming a limiting g of 4.4g clean and 2.2g with flap down. The graphs illustrating the results were most illuminating for me. In particular, max rate (level turn of course) is indisputably achieved at full power clean. But if you want min radius, it doesn't make much difference whether flaps are up or down. I have found that fact useful for scenario based training.

If you like, I'll PM you the spreadsheet with graphs attached. (If I can attach files to a PM that is - if not, send me an email address.)

[Islander2]

The use of full flap generally only applies to light trainers, as with most high performance machines, the extension of flap will lower the max g limit, generally by about 40%.idon'tthinkso, you may find it helpful to read previous posts before committing to yet another wrong position:

a) post #9 referred to a 32% reduction in max g limit with flap lowered in a Beech Bonanza; and

b) post #23 linked to the data for the Cessna 150/152 family, showing the Aerobat to have a 42% reduction in max g limit with flap lowered.

So we can reasonably conclude that the extension of flap in maximum performance manoeuvres isn't particularly good advice for either GA aeroplanes or high performance machines!

And, since you're so insistent that we check our books in order to come around to your "it is ever so elementary" yet incorrect assessment, here's a couple for you to go to bed with:

i) Aerodynamics for Naval Aviators by H.H.Hurt, which is the aerodynamics text for US Navy aviators, and which takes seven pages to explain the complexities of maximum performance tactical turning, in the process considering lift limits, strength limits and power limits and

ii) Flightwise (Volume 2 - Aircraft Stability & Control) by Chris Carpenter, who was Head of Aerodynamics at the Royal Air Force College Cranwell in the 1980s, which takes nine pages to deal with the same complexities.

Hardly 'elementary'!

If I could give you a steer (unlikely, I know, from one of 'you boys who haven't flown an aircraft that goes faster than 700kts'), I would point yet again to your incorrect paraphrasing of the relevant formulae. The fact is that turn radius is a function of V^2/tanAoB and turn rate is a function of tanAoB/V. It is mathematically impossible for V=minimum radius to be the same as V=max rate! This is covered more than adequately in the two texts quoted above but, should your preference be for a more academically-rigorous book, I would point you in the direction of Introduction to Flight by John D Anderson.

[Say again s l o w l y]

So, you're coming to a dead end in a valley and an immelman isn't sensible. What do you do and why?

[waren9]

A min radius turn of course! Its not important how long it takes you to get round, is it?

[Say again s l o w l y]

Exactly, so why all the arguing?
Oh I forget, this is the internet!

[hugh flung_dung]

If an Immelman isn't sensible I would do a stall turn or, more likely, a wingover -wassallthefussabout? ;)

HFD

[AC103]

Apologies for digging up a old thread though it seems to be the most relevant.
I am trying to better understand the physics around max rate vs min radius turns. This is how I understand it currently:

Turn rate increases directly proportional to a decrease in TAS or an increase in radial G. Usually at Va and C/L Max or limiting characteristic approaching C/L Max. Note that Va is an IAS not TAS

Turn radius decreases proportional to the square of a decrease in TAS and directly proportional to an increase in radial G. It is usually somewhat slower that Va and at a lower G loading than max rate due to the square relationship with TAS while only proportional relationship to G Loading.

Now I look at two examples:

1. F16 26,000lbs Sea Level: (See Turn Performance chart below)
- Min Radius Turn: R1473ft, 13°/s @ 0.3M (198kt) AoB 67.1° 2.6G
- Max Rate Turn: R1756ft, 22°/s @ 0.6M (397kt) AoB 82.9° 8G

2. Theoretical Aerobatic a/c Vs 60kt, 8G, Va=170kt Sea Level:
- Min Radius Turn: R322ft, 51°/s @ 170kt AoB 82.9° 8G
- Max Rate Turn: R322ft, 51°/s @ 170kt AoB 82.9° 8G
- 2.6G for Ref. to F16 Min Radius Turn: R347ft, 27°/s @ 96kt AoB 67.1° 2.6G

Calculators:
Aircraft Turn Information Calculator (http://www.csgnetwork.com/aircraftturninfocalc.html)
Aviation Calculator (http://www.hochwarth.com/misc/AviationCalculator.html)

Why does my theoretical aerobatic aircraft have the same Max Rate as Min Radius turn, while the F16 seems to fit my intuitive understanding better?
What am I missing folks?

Cheers!
https://cimg2.ibsrv.net/gimg/pprune.org-vbulletin/1009x991/tp_d7b0de336867888058219544e5897c28e0cc824f.png

F16 26000lbs DF 100 Sea Level

[BillieBob]

I had this question on my A2(A) with CFS many years ago. I give the same answer now that I gave then - "who the f***k cares?" I got the A2(A) by the way.

[AC103]

"who the f***k cares?" I got the A2(A) by the way.
..FOLK..(?)

Anyone here flown F16s or Hornets? Is the Max Rate / Min Radius spread down to comprehensibility and Reynolds numbers at higher speeds / wing loadings?

[Genghis the Engineer]

Flown F16s or F/A-18s, no. Flown (back seat) FJ, and studied combat performance, yes.

Max rate and min radius are both primarily down - in any continuous turn - to available excess thrust in a fast jet, particularly at lower altitudes. Higher up you can turn potential energy into continuous turn rate - but clearly will lose height doing so.

Instantaneous are down to the stall margins - but almost always there's not enough thrust to sustain what the wing can, indefinitely.

G

[AC103]

Flown F16s or F/A-18s, no. Flown (back seat) FJ, and studied combat performance, yes.

Max rate and min radius are both primarily down - in any continuous turn - to available excess thrust in a fast jet, particularly at lower altitudes. Higher up you can turn potential energy into continuous turn rate - but clearly will lose height doing so.

Instantaneous are down to the stall margins - but almost always there's not enough thrust to sustain what the wing can, indefinitely.

G

Cheers for chiming in. Looking at the Turn Performance graph it seems like the left edge of the dog house is AoA limited (Cat 1?) so equivalent to an theoretical critical angle? It also looks like potential energy required to maintain the turn is taken into account and overlayed on the carpet plot with potential energy loss/gain represented as Ps in feet per second so Min Radius looks like it occurs at ~-100fps and Max Rate at ~-1100fps? Guessing you would have to go back to the climb data to determine if the turn is sustainable.

So back to square one? It looks like that even with potential energy accounted there is still a huge spread between Max Rate and Min Radius... 8G vs 2.6G
Guaranteed I am missing something here. Just not sure what it is or even if I have already said it...

[ASRAAMTOO]

We seem to agree that a maximum rate turn is achieved when maximum lift is achieved at the aircraft load limit. Practically speaking pulling light buffet at the aircraft's limiting 'g'. Only very high performance aircraft will be able to sustain this in level flight without the speed decreasing and if the speed decreases then the light buffet will no longer achieve limiting 'g', hence a need to descend and sustain the speed.

Theoretically the best radius of turn will be achieved at the slowest speed and the highest load factor, in other words if an aircraft could fly a high 'g' turn at low airspeed. Most (all?) aircraft are unable to do this so a compromise is required.

I'm not clever enough to post a graph but essentially Rate of turn is proportional to VSquared/load factor and Radius of turn is proportional to load factor/V.

So in an F16 there will be a large gap between best rate and best radius speeds and in a C150 there will be a small gap. There will however STILL be a gap!

[AC103]

essentially Rate of turn is proportional to VSquared/load factor and Radius of turn is proportional to load factor/V.

Thanks A, Isn't it radius that has the squared relationship to velocity?

Could it be due to compressabiilty at the Mach numbers involved? ie. Compressibility = heat = greater kinematic viscosity = lower Reynolds number than expected for the increased velocity = lower C/L max at lower AoA for the airfoil?
ie If we assume the the F16 is at a Critical Angle Cat 1 at 198kt below doing 2.6G for min radius then 8/2.6 = 3.07 times increase in load factor at max rate/load factor so multiply by 1.61 to get the 8G Critical Cat 1 AoA velocity and we get 347kt where as the sea level plot shows it is tilted way back at 398knt doing 8G at its Cat 1 AoA.

Is Cat 1 not a fixed AoA but varies with velocity?
Why does the dog house tilt back like that? It seems to get more tilted at higher altitude Turn Performance plots as well. See 30,000ft below.

On to something here or still missing the bull?

https://cimg3.ibsrv.net/gimg/pprune.org-vbulletin/1279x863/tp_30k_3ff53e6cb9be36df41292794d24e1174f0902f04.png

30,000 ft

[AC103]

OK so it looks like Cat 1 for the F16 is NOT a fixed AoA but starts off at 25.2° at 1G then tapers off to 20.4° at 7.3G, I am guessing to prevent departures from max roll commands at high
AoA.

Anyone know of an aircraft without any such trickery or automatic lift devices or thrust vectoring with an actual definable stall break that has turn performance charts prepared for it? I am guessing not if the reason they are prepared in the first place is due to these aircraft sufficiently departing from the simplified POF formulas...

So are we back accepting that Max Rate = Min Radius as per the calculators and believing that stall speed increases to the square root of the increase in load factor even out to 8-10G?


https://cimg5.ibsrv.net/gimg/pprune.org-vbulletin/781x517/cat1_5a8e5a4428ac710ef52a99008b0dc5f875dcfccb.png.

Cat 1

[ASRAAMTOO]

[QUOTE=AC103;10309534]Thanks A, Isn't it radius that has the squared relationship to velocity?

AC, your second graph in blue has radius as straight lines so I'll stick with my original guess. As regards limiting AOA its possibly structural rather than giving a margin prior to departure. A certain fast jet with which I am familiar will produce vortices strong enough to remove the RWR aerial if AOA is exceeded at higher speeds despite being below the aircraft 'g' limit

[AC103]

Islander stated it pretty well but seems to come to the same conclusion as me. (wrongly by the looks so far) In fact we were looking through the Hurt text at the aeroclub yesterday trying to figure this out in which those very formula seem to prove us wrong.


i) Aerodynamics for Naval Aviators by H.H.Hurt, which is the aerodynamics text for US Navy aviators, and which takes seven pages to explain the complexities of maximum performance tactical turning, in the process considering lift limits, strength limits and power limits.

Turn radius is a function of V²/tanAoB and turn rate is a function of tanAoB/V. It is mathematically impossible for V=minimum radius to be the same as V=max rate!

ASRAAMTOO, you raise a very good point though! Radius lines on a Rate over Speed chart are straight... So there must be a squared relationship lurking somewhere that cancels out the V² in the radius formula? Thinking about it.. well of course there is.. it is the fact that we are using stall speed for each load factor (equivalent to AoB) as the very V and assuming that stall speed increases √G There you go!

Back to the Theoretical Aerobatic a/c Vs 60kt, 8G, Va=170kt Sea Level:
- Min Radius Turn: R322ft, 51°/s @ 170kt AoB 82.9° 8G
- Max Rate Turn: R322ft, 51°/s @ 170kt AoB 82.9° 8G
- 2.6G for Ref. to F16 Min Radius Turn: R347ft, 27°/s @ 96kt AoB 67.1° 2.6G


Now if you have boat loads of power/thrust and a shallow drop on the back side of the C/L curve maybe you can reduce your radius by fudging your V flying back of the bucket. But something tells me that if you are going to pick your spot on the C/L curve for radius that rate would also tighten up to match it so long as you can still maintain your load factor... Ps=0
Here is the Mustang for an aircraft devoid of trickery and a definable stall break. Green is combat flaps and Blue is clean. Notice how the radius lines still intersect at higher rates/velocity/load factors.

So is that the answer then? Max rate velocity = Min radius velocity at a given load factor or position on the C/L curve? Anyone disagree?

https://cimg9.ibsrv.net/gimg/pprune.org-vbulletin/628x453/p51_ac549e0fc583620f114844cce54ba4eb162922a3.png

P51

[AC103]

Time for a practical application:
If we agree that Min Radius = Max Rate then you have just recovered from a flat spin and are now pointing strait at the ground at 80kts and 500ft AGL, do you:

1. Keep power at idle, pull to the buffet and then limit load at Va
2. Apply full power, pull to buffet then power off at Va and hold limit load
3. Only apply full power if you know that you will not reach Va in a 90° pull out from 80kts and so will hit the tightest radius fastest without being load limited in at any point.
4. Do not apply any power because although the radius may be wider on the buffet initially the rate is slower which means you spend more time in the pull out without gravity negatively impacting lift required.

[ASRAAMTOO]

Time for a practical application:
If we agree that Min Radius = Max Rate then you have just recovered from a flat spin and are now pointing strait at the ground at 80kts and 500ft AGL, do you:

1. Keep power at idle, pull to the buffet and then limit load at Va
2. Apply full power, pull to buffet then power off at Va and hold limit load
3. Only apply full power if you know that you will not reach Va in a 90° pull out from 80kts and so will hit the tightest radius fastest without being load limited in at any point.
4. Do not apply any power because although the radius may be wider on the buffet initially the rate is slower which means you spend more time in the pull out without gravity negatively impacting lift required.


Still not convinced I'm afraid, although I am prepared to accept that for most G/A aircraft they will be similar. For your latest challenge don't forget option 5.

5. Deploy high lift devices and pull to limiting 'g' for said devices

Indeed we could split this into a couple of sub-options involving the use of power as per your original!