× Welcome to the CPL Aerodynamics question and answer forum. Please feel free to post your questions but more importantly also suggest answers for your forum colleagues. Bob himself or one of the other tutors will get to your question as soon as we can.

## Question regarding the angle of bank/ radius of turn.

• Sneh
• Topic Author

### Sneh created the topic: Question regarding the angle of bank/ radius of turn.

Hi everyone,

I understand that if power is increased during a turn while maintaining a constant angle of attack - the rate of turn will decrease and the radius of turn will increase because if the power is increased then the speed will increase as well.
However, I don't under why "If power is increased during a turn while maintaining the stalling angle of attack" the radius of the turn will remain the same, and the rate of turn will increase. Wouldn't the answer to this question be the same as the first one?

I did go through the logic that Bob explained in the Aerodynamics book, but it did not click into my mind.
Can someone please explain the logic of the second question in the simplest way please?

PS these are the question from CPL Aerodynamics on page 9.21 - Q25/26.

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 882

### John.Heddles replied the topic: Question regarding the angle of bank/ radius of turn.

if power is increased during a turn while maintaining a constant angle of attack - the rate of turn will decrease and the radius of turn will increase because if the power is increased then the speed will increase as well.

I don't have Bob's book so I will talk a bit generically.

It gets a little messy as the power increase (actually, we are interested in the thrust increase associated with the power increase) can go towards increasing speed and/or providing for an increase in climb performance if you manage to maintain a constant alpha. I presume that the inference in Bob's text is that the turn is undertaken while maintaining a constant height ? In this case you would expect to see a speed increase. Radius of turn increases at a modestly higher speed while turn rate will reduce due to the larger turn radius.

if power is increased during a turn while maintaining the stalling angle of attack the radius of the turn will remain the same, and the rate of turn will increase.

I suspect that you may have misread/misquoted the text here as the statement doesn't make a lot of physical sense.

Aside - another relevant term you may see is "cornering speed", especially in military parlance. This is where you are simultaneously at the maximum g load permitted and at the stall speed for the gross weight (if you can generate enough thrust to do this - generally only applicable for high performance fast jets) which gives you maximum turn performance for the aircraft. The operative consideration is thrust, rather than power.

At a high alpha (angle of attack) - we are talking stall angle, here - the thrust line provides a measurable component of that thrust towards the centre of the turn. Think back to any military fast jet airshow display you have seen - the jet will be in afterburner to maximise the thrust output. This has the effect of providing an additional force (centripetal force) toward to the centre of the turn which has much the same effect as increasing the wing lift component and you end up with a reduction in turn radius. Recall from elsewhere in your texts that it is the centripetal force which is causing the turn.

A similar observation applies to looping manoeuvres - the jet in A/B at high alpha is able to perform a considerably tighter loop than without A/B for the same conditions. I still well recall an ARDU Mirage display at Ballarat (if my memory is correct) about 40 years or so ago. The pilot came in over the runway at low level and then proceeded to do several loops up into the cloud base and bottoming out at probably only 30-40 feet above the runway - eye opening stuff, indeed !

A similar concept in civil aircraft is the minimum value for the design Va, which is the same intersection on the VG envelope at MTOW. The light aircraft, however, doesn't have anything like enough thrust to manoeuvre at this point. Keep in mind that Va is not driven by this observation, but is a consideration for the design of control surfaces - a very common error in pilot training material where, often, you will see references which, incorrectly, suggest that Va is the speed where the aircraft will always stall before experiencing any structural damage - that may be the case, sometimes, but not always.

So, for the question, presuming you have adequate thrust reserves and are maintaining the speed, you would expect the radius of turn to reduce due to the additional thrust component toward the centre of the turn. This would get you around the turn quicker so the turn rate increases.

I did go through the logic that Bob explained in the Aerodynamics book, but it did not click into my mind. Can someone please explain the logic of the second question in the simplest way please?

You might like to post a scan of just the relevant section of the page in Bob's book so that we are all looking at the same words and then we can discuss.

PS these are the question from CPL Aerodynamics on page 9.21 - Q25/26.

Likewise, if you post a scan of the questions, we are all on the same sheet of music which allows for a better discussion.

Engineering specialist in aircraft performance and weight control.

• Sneh
• Topic Author

### Sneh replied the topic: Question regarding the angle of bank/ radius of turn.

Hi, John here is the screenshots from the book.
##### Attachments:

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 882

### John.Heddles replied the topic: Question regarding the angle of bank/ radius of turn.

The questions are playing with the basic equations for level turning performance without concerning ourselves with the effects of thrust on what is going on. The only "problem" is that we should specify a number of assumptions for accuracy but, for the training purpose, let's put those to one side and just presume that they apply without worrying about them so we don't needlessly confuse the issue with pedantry.

If we consider an increasing bank angle in the turn, the lift force has to increase to maintain the vertical force component necessary to provide for level flight. As we all learnt at an early stage, this means that we need to increase backstick load to increase the angle of attack. Due to thrust limits with small aircraft we rapidly get to the point where the increase in drag sets a bank angle limit for the turn.

For the first question, we can show, via the basic turn equation, that bank angle is related to V^2/radius so, if we increase speed, the radius must increase to keep the angle constant. Similarly, we can show that bank angle is related to speed x turn rate so, if we increase speed, the turn rate must decrease. From your comments, it would appear that you are comfortable with this.

For the second question, I would go down a different path for an explanation and discussion. Rather than confuse the issue for you, just now, it might be better to get Bob to offer further comment, just in case I have missed an assumption or constraint which he may have made.

Engineering specialist in aircraft performance and weight control.

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 882

### John.Heddles replied the topic: Question regarding the angle of bank/ radius of turn.

I've discussed the second question off line with Bob. Turns out that this question should have been culled from the question bank a long time ago but that was missed. Bob will, no doubt, attend to that in due course.

If you start at the stall angle, say in straight and level flight, you will have whatever power (thrust) level might be necessary to make it work. If you increase thrust, you will need to roll into whatever measure of bank with a pitch attitude variation as might be necessary to maintain level flight and the normal equations will apply, as in the previous question. However, the pitch attitude will need to be moderated by consideration of load factor variations. You can progressively increase power until you get to full throttle - which is going to being rather limited in a small aircraft. As you do that you will need to increase the bank angle and vary pitch attitude to maintain level flight. Precisely what happens to the speed is going to be dependent on what the aircraft's characteristics might be.

Because you won't have a necessarily simple speed consequence, as you are getting a significant drag ramp up and a varying thrust vector contribution to the centripetal force, it becomes a bit of rubbing your tummy while patting your head unless you have some details on the aircraft characteristics. That is to say, not a really useful question ... too many ingredients in the pot for a simplistic explanation.

Engineering specialist in aircraft performance and weight control.