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Max Rate turn vs. Min Radius Turn

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Max Rate turn vs. Min Radius Turn

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Old 16th Jan 2009, 10:30
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Max Rate turn vs. Min Radius Turn

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).
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Old 16th Jan 2009, 11:38
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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.
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Old 16th Jan 2009, 12:19
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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.
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Old 16th Jan 2009, 12:47
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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.
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Old 16th Jan 2009, 22:31
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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 ?
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Old 17th Jan 2009, 08:39
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You need to be flying at sufficient speed to pull maximum G without stalling
Thats 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 you can play with speeds and bank angle to see what radius of turn you can achieve.
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Old 17th Jan 2009, 08:48
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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.
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Old 17th Jan 2009, 10:42
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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

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!
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Old 17th Jan 2009, 15:55
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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.

Last edited by Islander2; 17th Jan 2009 at 16:08.
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Old 17th Jan 2009, 18:22
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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?

Last edited by Simon150; 17th Jan 2009 at 18:41.
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Old 17th Jan 2009, 23:20
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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.
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Old 17th Jan 2009, 23:26
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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.

Last edited by Islander2; 18th Jan 2009 at 00:52.
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Old 18th Jan 2009, 06:25
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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
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Old 18th Jan 2009, 06:40
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MRT

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.
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Old 18th Jan 2009, 11:01
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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.
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Old 18th Jan 2009, 14:24
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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.

Last edited by Brian Abraham; 18th Jan 2009 at 14:42.
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Old 18th Jan 2009, 16:55
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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!
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Old 18th Jan 2009, 18:04
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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 , 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????
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Old 18th Jan 2009, 19:04
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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).
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Old 18th Jan 2009, 19:50
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Aaaaaah, the single circle versus 2 circle decision! Alternatively, go vertical and pray.
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