# Single Propeller load asymmetry in turns?

#### WrathofAtlantis

Single Propeller load asymmetry in turns

Does this have a formula, and what is the current Flight Physics consensus of the effect of this on turns?

G.

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#### russ_watters

Mentor
Single Propeller load asymmetry in turns

Does this have a formula, and what is the current Flight Physics consensus of the effect of this on turns?
Could you be more specific please. I think you are referring to the tendency of a single engine propeller plane to "want" to turn left. But what, exactly, you are trying to model about it I can't tell. Regardless, suffice to say, this is a complicated effect and there is likely no single formula to describe it.

#### berkeman

Mentor
Welcome to the PF.

Can you say more about your question and give some examples please? What type of aircraft? (Cessna or P-51 or ?) What types of turns? What speeds?

:

#### WrathofAtlantis

I am basically talking about low wing WWII fighters in sustained speed 3.2 G level turns, which implies maximum prop load (around 3000 lbs full power, full low speed sustained level turning load on about 100 square feet I'm told, or roughly 30 pounds of thrust per square feet).

Turning implies slower air on the inside turn half (or more) of the prop disc, which implies a greater blade front vacuum on the inner turn disc side. This implies more inside turn disc half thrust, which in turn implies a slanting of the thrust axis towards the outside of the turn, in addition to off-centering the thrust center towards the inside turn side.

This curving air cannot be replicated by slanting the air in a wind tunnel, since that does not replicate the slower inside turn air. Given the leverage of a 100 square foot plus disc surface, the effect must be significant compared to a four square foot jet plume... I figure 1 pound per square foot per degree (for typical 7 degrees max sustained) would easily yield 700 pounds of continuous extra asymmetrical thrust, slanting the thrust axis towards the outside of the turn.

This has nothing to do with low-speed torque, yaw, or the higher speed slip stream spiral. It is strictly the issue of making a broad flat surface follow a curve... Contrary to those other effects, I have never found anything concerning the airflow speed asymmetry... The effect is obviously there for many reasons, including WWII prop pilots lowering throttles long before the merge, and lowering power even further after being in continuous slow speed turns on the deck. When a turning contest became prolonged and on the deck, the contest often seemed to be who could lower the power the most to gain the faster sustained turn rate (in multiple consecutive 360s)...

WoA

#### berkeman

Mentor
Very interesting question! Do you have access to fluid dynamics and aerodynamic modeling software? Paging @boneh3ad for a better response than I can provide...

#### anorlunda

Mentor
Gold Member
I am basically talking about low wing WWII fighters in sustained speed 3.2 G level turns,
I agree, interesting question.

Can you translate 3.2G level turn into inside/outside speed differences at the prop tips?

For example, if the plane was traveling at 300 knots before the turn, the prop tips might be 295 and 305 knots during the turn.

#### WrathofAtlantis

Unfortunately no, I do not have software, and I really should have at least calculated the tip speed difference, in all the time since I started to assemble the elements of this observation...

My interest in this effect originates entirely out of my very extensive readings of WWII combat accounts (including masses of combat reports), where the effect appears to emanate from several disparate angles.

To begin with, one thing that is required to "conceal" this effect is a forward displacement of the CL, but only in circumstances where the prop is heavily loaded: This is because no pilot ever complained that high power at low speed makes the backward stick effort greater (certainly not on low wing monoplanes)...: Quite the contrary: One test pilot, Eric Brown, hints at some sort of forward CL displacement, one that seems to be fully ahead of the CG (quote: "tendency to nose up" while in turns only, this on a very nose-heavy type), and this only below 220 mph and only in turns: This disposition would make sense if the propeller was the source...: For a given power, the prop would be more heavily loaded in a horizontal turn and at a lower speed. More speed or more vertical motion (downward), would unload the prop, and presumably reduce the corresponding CL forward displacement effect.

The importance of this is major, because if the prop's resistance to turning is indeed "concealed" by the forward displacement of the CL at high prop loads (in proportion to the pilot's input to make the turn), this means this "concealment" is at an enormous leverage disadvantage compared to the lenght of the nose... An 8 foot nose with a 1 foot CL displacement would be an 8:1 ratio, meaning 700 lbs requires 5600 lbs of unknown extra lift (I suspect wing bending was never measured on WWII prop fighters, at least not while in sustained horizontal turns). But on another type, a 4 inch CL displacement with a 10 foot nose would mean a 30:1 ratio, or 21 000 pounds of extra unknown lift at the CL's forward position, for this to totally conceal the prop's resistance to the pilot's stick effort...

These above numbers would allow bridging the gap between a 48 lbs/sqfoot FW-190A and a 32 lbs/sqfoot Spitfire Mk IX, giving a lower actual wingloading to a seemingly near 50% heavier wingload...: Actual accounts concluded the Spitfire is vastly superior in high speed turns but inferior in low speed sustained turns compared to the FW-190A: The opposite one would expect if the prop/nose length is ignored...

This theory of mine came from another observation: In addition to lowering the throttle seemingly producing faster sustained turns, and the Spit/FW-190 conundrum, WWII airframes that were converted from longer inline to shorter-nosed radials experienced vast increases in handling quality (Ki-61 to Ki-100, LaGG 3 to La 5) despite hundreds of pounds of extra weight... The reverse path, Radial to inline (FW-190A to D-9) caused significant worsening of the turning ability...

If all this is true, the hardest part is not estimating the prop load asymmetry value, but how much and where the CL gets the force to match the prop, to make all forces zero...: Therefore, calculating the prop asymmetry force is where this should start, since it is far easier to do than understanding the odd trick the CL is performing to match it...

WoA

#### russ_watters

Mentor
Sorry, but I'm just not seeing how the issue you are describing is functionally different from P-factor, and also would like to point out that a 3.2 g turn is 70 degrees angle of bank, so the plane is pitching into the turn more than it is yawing. Some analysis:

Google tells me the P-51 has an 11' diameter propeller and a minimum turn radius of 531' at 270mph and an 18.5 degree stall aoa. So the difference between inside and outside of the turn for the propeller tip is 2% of the turn radius. At 270mph, that's 5.4mph.

I think the minimum radius turn happens just below stall aoa. An 18 degree aoa yields a differential of 31% or 83mph. Note, that this is exactly aligned with the pitch axis and the thrust differential aligned with the yaw axis (not the turn axis).

So that's why I don't think this is something much talked about. Note that the speed differential between the inside and outside wings is of course many times larger and therefore is considered/discussed much.

That's said, I think I do get the difference you are referring to: the P-factor causes a pitching plane to yaw, so it or a similar effect would cause a yawing plane to pitch.

#### cjl

It seems very unlikely to me that the propeller is making 700 pounds of vertical force due to a couple percent speed difference between the top and bottom of the disk. In fact, it seems very unlikely to me that the propeller is making any amount of vertical force due to this effect. Maybe I'm visualizing it wrong, but my initial impression is that this will slightly offset the effective thrust location, as if the thrust were coming from a point slightly above center on the prop rather than at the center, but the thrust vector overall will still be in the direction of flight. Counteracting this would require far less of a forward lift shift on the wing than you're calculating above.

I also would tend to suspect the angled inflow will have a much larger effect. A low-speed, high-g turn implies high AoA (probably 10-12 degrees). This means that from the aircraft's perspective, in a high-g turn, the flow is coming from below the plane. This will cause a force upwards on the nose of the airplane as the propeller turns the flow (since the wash behind the prop will be closer to in line with the plane). This would tend to agree with your reduction of stick force for low speed turns, since a higher speed turn would involve a lower angle of attack for the same load factor.

(It will also cause a yawing moment due to a difference in angle of attack between ascending and descending blades, but all of this is, as russ stated, just P factor)

#### hmmm27

When a turning contest became prolonged and on the deck, the contest often seemed to be who could lower the power the most to gain the faster sustained turn rate (in multiple consecutive 360s)...
They're messing about with precession. I don't suppose you've a video link ? That sounds interesting (and hilarious) to watch.

(assumption: "on the deck" meaning "on the ground/ship's deck", not "at a very low altitude")

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#### cjl

They're messing about with precession. I don't suppose you've a video link ? That sounds interesting (and hilarious) to watch.

(assumption: "on the deck" meaning "on the ground/ship's deck", not "at a very low altitude")
I'm pretty sure WrathofAtlantis is talking about low altitude sustained turns, not just spinning around on the ground (though that does create a hilarious mental image)

#### OCR

I'm pretty sure WrathofAtlantis is talking about low altitude sustained turns. . .

I'll go along with that. . . .

. . .spinning around on the ground (though that does create a hilarious mental image)

Pilots usually don't see it that way, maybe, a distressing mental image ? .

Ground loop. . .

.

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#### WrathofAtlantis

"Sorry, but I'm just not seeing how the issue you are describing is functionally different from P-factor, and also would like to point out that a 3.2 g turn is 70 degrees angle of bank, so the plane is pitching into the turn more than it is yawing. "
Well, pitching is precisely my main concern... The effect I describe is nearly the exact opposite of the P-factor, which claims the thrust is increased on the outside turn portion of the disc (this because, on the outside, the blades are angled [by the AoA] to move forward, while, on the inside turn portion, the blades are moving backwards).

This may well happen in pitch, in theory (the yawing is, of course very real, and explains the preference to one side of some types), but the effect is, in pitch, completely obliterated by the increase of inner disc thrust due to the curvature of the air.

The P effect in my view only really exists in yaw: Just like a wheel turning it pushes the nose to one side... But this is from the lateral drag of turning the blades, and this is separate from their longitunal load.

The fact the P effect is assumed to be also dominant in pitch is a reflection of the inability of wind tunnels to replicate curving air... Naturally, they would consider as dominant something that works without air curvature...

Slanted air at an angle, and curving air, are simply not the same...

If the P-factor was dominant in pitch, that is, other than yaw to the turning direction, the propeller would assist a 70 degree bank turn, so more power would increase the sustained turn rate... This is exactly the opposite to what was widely observable to WWII pilots... They would try to increase the low speed sustained turn rate by maintaining the lowest power possible, in multiple consecutive 360s, at slow speeds and at ground level. Karhila: "If the opponent lowered power, I would lower it even more [reducing speed, but reducing the radius even more]. 160 mph seemed to be the optimal sustained turn speed."

160 mph is far lower than the minimum sustained speed radius of turn, at full power, for the 1500 hp (and 406 mph capable!) Me-109G, which is likely around 220 mph, perhaps higher at WEP. This means power, up to a point, is definitely adverse to the sustained low speed turn rate, contrary to what is currently assumed...: Apparently a higher sustained turn rate exists as low as 55 mph above landing speed...

"Some analysis:

Google tells me the P-51 has an 11' diameter propeller and a minimum turn radius of 531' at 270mph and an 18.5 degree stall aoa. So the difference between inside and outside of the turn for the propeller tip is 2% of the turn radius. At 270mph, that's 5.4mph.
"
I think that is for 7 Gs... The minimum speed to reach 6 G was found by the SETP (in 1989) to be 276 mph, in a slight downward spiral. It seems from their wording that, without a downward spiral, the minimum for 6 Gs was closer to 300 mph...

They do not explicitly say the figure was higher without diving, but it is implied by the phrase "Corner Speed (6G) on all 4 types was found to be very close to their maximum level speed at METO." This METO speed at 10 000 ft. was 320 mph for the P-51...

The reason the P-51 flight manual claims a minimum 255 mph (flaps up), for 6 Gs horizontally , could be that all the manual G values were achieved with dive pull-outs, which unloaded the prop... (21 mph higher than 255, in a nose-down spiral, is the best the SETP could do, so they were unable to match flight manual figures)

This is not really central to my thesis, but you definitely sense the real puzzlement of the SETP towards the poor ability of these WWII aircrafts to reach high Gs at "useable" middle range speeds... This is because, in reality, you have to go really fast for the prop to become less loaded enough to allow even touching 6 Gs...

This is why anyone who has read a ot of WWII combat accounts knows values like 6 Gs are really of little relevance to actual fighting...: 3.2 or 3.4 Gs sustained is where the real meat of the matter lies. The P-51 was rather an exception to this, being exceptionably able to reach high Gs (6-7) at moderately high speeds (350-400 mph), hence the use of G-suits, but even then, the SETP in 1989, being used to jet testing, found the P-51 unimpressive...: "An interceptor type aircraft of limited turning ability": Because, in the mind of a jet pilot, turning really boils down to quite high Gs... Even the high G-gifted P-51 found jet jockeys near impossible to please...

With jets, Gs beyond 4-5 are far more easily achievable, and far more sustainable for far longer, because they are not impeded by increasing prop asymmetry as the turn tightens, and speed decays, while power is kept up.

"So that's why I don't think this is something much talked about. Note that the speed differential between the inside and outside wings is of course many times larger and therefore is considered/discussed much."
If the bank angle is 70 degrees, I don't see how the wing speed turn difference is all that much larger than the span of the prop disc width... Pilots could increase the bank angle further by riding the turn on deflected ailerons... Even for sustained turns, turning can become largely a pitch issue, with fairly moderate wingtip speed difference, while still with a full prop diameter, nearly perpendicular to the trajectory...

"That's said, I think I do get the difference you are referring to: the P-factor causes a pitching plane to yaw, so it or a similar effect would cause a yawing plane to pitch."
Yet the whole point of my theory is that the prop resists pitching...

The assumption that P has authority in pitch is likely caused by something else: By the changes in the CL position, when the CL is subjected to high prop loads, and this from a long nose leverage: If the CL moves forward, it can "hide" the prop's real pitch-averse behaviour, but at a gigantic cost in extra needed lift, given the minuscule leverage available to the displaced Center of Lift, all of eight to ten feet behind the prop...

Where does the CL get this huge extra lift is where the current error resides, but measuring wing bending, while actually turning horizontally at full prop load (which was obviously never done on low wing WWII prop types), would immediately reveal this extra wing load (imposed by the prop resisting pitching)...

As to the difference of 5.4 mph in prop tip speed, it will tell us little about the actual cost of tilting the prop, if we don't know how much the wings are actually suffering through bending: It is possibly only the extra (over assumed math value) bending measured in the wings that will tell us exactly how much the prop is actually fighting them...

WoA

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#### WrathofAtlantis

It seems very unlikely to me that the propeller is making 700 pounds of vertical force due to a couple percent speed difference between the top and bottom of the disk. In fact, it seems very unlikely to me that the propeller is making any amount of vertical force due to this effect. Maybe I'm visualizing it wrong, but my initial impression is that this will slightly offset the effective thrust location, as if the thrust were coming from a point slightly above center on the prop rather than at the center, but the thrust vector overall will still be in the direction of flight. Counteracting this would require far less of a forward lift shift on the wing than you're calculating above.
If the thrust center is above the center of the prop, then the thrust is no longer in the direction of flight...

The reason you think 700 pounds is unreasonable (I do not quite claim a fully vertical force), is because you do not take into account the leverage implied by the surface involved: One pound per square foot per degree, over 100 square feet, is not an unreasonable total to add to the -actual- 30 pounds per square foot initial load...

The other huge factor is that this extra load, from the slower air, is concentrated towards the inner turn disc edge, which means the distribution is concentrated for maximizing the leverage in resisting the turn...

I also would tend to suspect the angled inflow will have a much larger effect. A low-speed, high-g turn implies high AoA (probably 10-12 degrees). This means that from the aircraft's perspective, in a high-g turn, the flow is coming from below the plane. This will cause a force upwards on the nose of the airplane as the propeller turns the flow (since the wash behind the prop will be closer to in line with the plane). This would tend to agree with your reduction of stick force for low speed turns, since a higher speed turn would involve a lower angle of attack for the same load factor.
True, and some of that might even explain why fatter radial engine noses do so much better at low speeds, despite a higher wing loading, or that a slight stick reversal occurs in the FW-190's case. But it would not explain why the 190 also benefits from lowered power in sustained low speed turns. Or, even beyond that in the P-51's case, why some 8th AF pilots used full coarse prop pitch in 200 mph sustained speed level turns, on top of downthrottling, to get the prop blades to stall, thus lowering the disc load even further than downthrottling: This seems like an attempt to get some extra lateral P-factor yaw, at the expense of the disc load in pitch...

High G turns, at low speeds, are very difficult to make, when the prop is heavily loaded by the low speed itself... Low speed tends to mean a high prop pitch load... This is what WWII pilots found out: The prop load is fighting you, so you want to lower power to turn better... This is why the SETP were later quite surprised, in 1989, when the minimum for 6G on the P-51 was found to be around 300 mph at METO, or at least 276 mph when spiralling down, since they had no clue they needed to drop the power... If they wanted to turn better at a lower speed... I think they even assumed METO was too little power for them to match the flight manual(!)... And they had no clue, because jets do turn better with more power, and the P-51's flight manual G values were -likely- achieved with prop-unloading dive pull-outs.

WoA

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#### cjl

If the thrust center is above the center of the prop, then the thrust is no longer in the direction of flight...
No, and this is (I suspect) part of the reason for your misunderstanding. Changing the effective location of the force does not change its direction. Instead, it is equivalent to applying both a force and a moment to the center of the prop disk, and importantly, this moment does not change depending on how far forward or aft you are. It is dependent purely on the location, vertically, at which the effective thrust force is acting.

Regardless, the entirety of the force is still acting entirely parallel to the aircraft.

The reason you think 700 pounds is unreasonable (I do not quite claim a fully vertical force), is because you do not take into account the leverage implied by the surface involved: One pound per square foot per degree, over 100 square feet, is not an unreasonable total to add to the -actual- 30 pounds per square foot initial load...
The reason that I think it's unreasonable is because there's no reason, fundamentally, why having a velocity gradient across the inflow would cause *any* vertical force, much less an amount that is a significant fraction of the thrust force. Yes, it's amazing how force over area can add up, but you still need some fundamental reason why the force would exist in the first place.

The other huge factor is that this extra load, from the slower air, is concentrated towards the inner turn disc edge, which means the distribution is concentrated for maximizing the leverage in resisting the turn...
This can all be accounted for easily enough by just modeling the thrust as coming from slightly above center on the prop disk. Also, keep in mind that the total difference in inflow here is on the order of a couple percent. It's not going to create major changes in the flow patterns.

True, and some of that might even explain why fatter radial engine noses do so much better at low speeds, despite a higher wing loading, or that a slight stick reversal occurs in the FW-190's case. But it would not explain why the 190 also benefits from lowered power in sustained low speed turns. Or, even beyond that in the P-51's case, why some 8th AF pilots used full coarse prop pitch in 200 mph sustained speed level turns, on top of downthrottling, to get the prop blades to stall, thus lowering the disc load even further than downthrottling: This seems like an attempt to get some extra lateral P-factor yaw, at the expense of the disc load in pitch...

High G turns, at low speeds, are very difficult to make, when the prop is heavily loaded by the low speed itself... Low speed tends to mean a high prop pitch load... This is what WWII pilots found out: The prop load is fighting you, so you want to lower power to turn better... This is why the SETP were later quite surprised, in 1989, when the minimum for 6G on the P-51 was found to be around 300 mph at METO, or at least 276 mph when spiralling down, since they had no clue they needed to drop the power... If they wanted to turn better at a lower speed... I think they even assumed METO was too little power for them to match the flight manual(!)... And they had no clue, because jets do turn better with more power, and the P-51's flight manual G values were -likely- achieved with prop-unloading dive pull-outs.

WoA
I'll have to think some more about what the dynamics of a prop plane at low speed and high G would be. However, I'm pretty confident in stating that the effect you're hypothesizing here wouldn't do it.

#### WrathofAtlantis

No, and this is (I suspect) part of the reason for your misunderstanding. Changing the effective location of the force does not change its direction. Instead, it is equivalent to applying both a force and a moment to the center of the prop disk, and importantly, this moment does not change depending on how far forward or aft you are. It is dependent purely on the location, vertically, at which the effective thrust force is acting.

Regardless, the entirety of the force is still acting entirely parallel to the aircraft.
But for a given angle of attack, does the propeller not rise higher to the trajectory if the nose is longer?

For a given amount of increased lift, it is pretty evident the longer nose lifts the Center of Thrust higher above the trajectory...

The reason that I think it's unreasonable is because there's no reason, fundamentally, why having a velocity gradient across the inflow would cause *any* vertical force, much less an amount that is a significant fraction of the thrust force. Yes, it's amazing how force over area can add up, but you still need some fundamental reason why the force would exist in the first place.
It does not have to be a vertical force, at the nose, to resist a vertical downward input by the pilot, at the tail.

You want to prevent a rotation using the CL as axis: It doesn't matter, in a rotation, how the resistance is oriented: If you concede the resistance exists, and is in a contrary direction to the rotation, the rotation is impeded, regardless of the angle...

If the prop/thrust axis is above the CL, then a downforce at the tail is in a rotation opposite to the thrust direction on that rotating axis. That answers why this impediment exists.

I don't suppose you will argue a straight force cannot impede a rotation?

The only real question to me is, why does the pilot not feel this impediment? When turning begins, the added prop load offsets the thrust center inside the turn, the added drag from the added height of the thrust (vs the Center of Drag) causes the CL to move forward (why is not at all clear to me, but it has to), and this changes the CL's action from a near-neutral to a clear nose-up effort, as it moves in front of the CG, immediately, as the impediment of the prop thrust taxes the wings.

The rotating axis then becomes a point between the CG (rear) and the CL (now in front). The aircraft is not unstable, or too tail heavy, because the now rearward CG is held up by the opposing tension between the wings and the prop.

Prop is a nose down moment, due to offset longitunal drag, held up by the -now- nose-light biaised wings.

The CL's effort increases in proportion to the turn's sharpness, just as the prop's center of thrust height increases proportionally with same. This means, to maintain the angle of attack, that the CL draws extra lift to defeat the ever increasing drag caused by the increasingly low position of the Center of Drag, relative to the rising Center of Thrust. Normally that low Center of Drag position would cause the rear of the aircraft to rise up, while the nose tilts down, but the outward momentum of the turn (helped by the now rearward CG) prevents this, so the wings are forced to bear the cost of this inefficiency.

The pilot is unaware of the huge loads his aircraft is bearing, but a 10:1 or 30:1 CL displacement lever to nose length ratio does impose an extra (as of yet unmeasured, with full prop load at least) bending from the wings.

This can all be accounted for easily enough by just modeling the thrust as coming from slightly above center on the prop disk. Also, keep in mind that the total difference in inflow here is on the order of a couple percent. It's not going to create major changes in the flow patterns.

I'll have to think some more about what the dynamics of a prop plane at low speed and high G would be. However, I'm pretty confident in stating that the effect you're hypothesizing here wouldn't do it.
Bear in mind that the one pound per degree is an average over 100 square feet, where maximum thrust is already around 3000 pounds... The effort would in reality be distributed increasingly heavily towards the end of a 5 foot right angle lever... Depending on how square are the propeller blade ends, it could be 300 pounds on the last 10 square feet near the circle's apex alone, 30 pounds per square feet, still only around 4.3 pounds per degree for the 7 degrees of sustained speed turning. That's 300 pounds being held at the end of a four foot lever, since 4 foot would be roughly in the center of that specified concentration ...

Current calculations are assumed to be very much the same for a 4 square foot jet plume or a 100 square foot prop: That just seems very unlikely to me...

WoA

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#### WrathofAtlantis

I do understand now a radius of 1000 feet is just too large for a 10 foot prop to produce more than a 1% thrust imbalance...

The inside turn thrust increase would amount only to 1 percent at 3G-200 mph, due to the percentage of the prop width to the turn radius, as a ratio... (I am not interested in higher G unsustained speed figures, as they are not that relevant to actual WWII dogfighting, or the observed use of downthrottling)... To work, the theory needs at least a 10 percent prop thrust imbalance, to bridge the wingloading gap observed to be bridged, or exceeded, between vastly different types.

The 10% prop thrust imbalance exists, but the missing 9 percent are likely: 6 percent from accelerated air behind the outside disc half, plus 3 percent from the resulting slowdown in speed overloading the top disc half: Mainly a reduction of thrust on the outside turn prop half, rather than solely an increase on the inside turn half ... This accelerated airflow behind the outside disc half could be caused by the extra lenght of an inline nose lifting, through the Angle of Attack, the underside of the prop's slipstream ABOVE a low-set wing, thus curving and accelerating the airflow behind the outer prop half more than a shorter nose woud do.

There is actually a strong clue that there is accelerated airflow, inside the prop, in low speed 3G turns at 200 mph...: Several different pilots reported using full coarse prop pitch, at low speeds, to increase the sustained speed turn rate at 200 mph (while reducing power in concert wih this)... And this appears only with a long nose inline type, the P-51.

WoA

"Single Propeller load asymmetry in turns?"

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