Debunking Glider Spoiler Turns Causing Spin Thinking

On Wednesday, June 17, 2015 at 6:14:09 AM UTC-7, wrote:
"Now if you suppose that it's the lift part which is opposed to the weight, then L/D would influence g-load. But this is just not how physics works on this planet.*"

A key point is that g-load is really just an expression of force. That's all it is. It is the vector sum of all the real forces acting on the aircraft, except gravity. Then we divide by weight to get a dimensionless expression.

When we talk about g-load, we really aren't saying anything that we couldn't express just as well by talking about the actual aerodynamic and thrust forces generated by the aircraft.

In a glider, where there is no engine, the g-load is the vector sum of all the aerodynamic forces generated by the glider. In coordinated flight, this would simply be the vector sum of lift and drag.

When we say that g-load affects stall speed, we really should say that the lift-wise component of the g-load vector affects stall speed. Not the total g-loading vector. But all we're really saying is that the magnitude of the lift vector affects stall speed. No extra information or content is added by bringing the concept of "g-loading" into the discussion.

The L/D ratio affects the magnitude of the lift vector, and also affects stall speed. In a powered climb, the T/W ratio affects the magnitude of the lift vector, and also affects stall speed. As per the tables I posted on June 4, and yesterday.

S

You discuss the "lift G-load" as if it was a thing in itself. It is not, it is a mathematical construct of several derived values. When the load on the wing changes many other things change - and perhaps the lift also increases. Let us suppose you are in an unaccelerated glide and a magic wand causes the glider's weight to double. After some time and control input, you return to an unaccelerated glide at the same speed. You will discover that the angle of attack has doubled, the induced drag has quadrupled, the angle of the resultant forces on the wing spar has changed, as has the bending moment. And the L/D is reduced.

As a second thought experiment, I fly my glider at 40 knots, it gets an L/D about 40. I then increase the speed to 80 knots, and still get an L/D of 40. But: the angle of attack is reduced by 75%, the induced drag on the wing reduced even more, the parasitic drag of the fuselage increased by 4x, the angle of the resultant forces on the wing spar changed again. My L/D and "lift G-load" are identical, but nothing else on the glider is. At 40 knots I am very close to stall, at 80 no where near it.

As a third thought experiment, I will take the resultant aerodynamic force on my wing, and split into two vectors: one at 30 degrees above the angle of attack which I will call Lift, one at 120 degrees above the angle of attack which I will call Drag. This is every bit as natural and valid as your Lift and Drag, which are similarly arbitrarily defined. When I am in a high drag configuration and my glide ratio is 2:1, I discover that Lift has disappeared completely. My Lift G-load is 0. Yet I am still in steady state flight, and there is still 1G bending load on the spar.

You cannot take an arbitrary mathematical construct, deal with it in isolation, and draw any momentous (or perhaps even any valid) conclusions.

My admittedly incomplete understanding of the effect of weight on L/D is that increasing weight does not change the
L / D but will change the IAS required.

I suppose if you require the airspeed pre and post weight increase to be unchanged, the L / D will vary, but this is usually not the way we exploit the usefulness of added weight, as far as I know anyway.

Re the recent post above from jfitch--

Thanks for your continued engagement. There are some interesting and fundamental ideas at play here. Here are some thoughts-- you might want to read all the way to the end before responding to anything, as I've come around somewhat closer to your viewpoint. This is REALLY LONG, but I think there are some interesting points here.

I agree that L and D can be argued to be arbitrary constructs. As can Cl (lift coefficient) and Cd (drag coefficient). But that doesn't mean they are un-useful. A given value of L and a given value of D will result in a given net aerodynamic force vector. (Assuming for the moment that we are talking about coordinated flight in an unpowered glider.) L and D are useful because they are tools to allow us to specify a net aerodynamic force vector. But other coordinate systems could serve the same purpose.

Let's think more fundamentally about what determines stall speed. Stall speed is just whatever airspeed you happen to have at some particular moment, when you place the wing at the stall angle-of-attack. It could be a very high airspeed, or a very low airspeed. The net aerodynamic force generated by the airflow around the aircraft (excluding thrust from the engine if present) will be proportional to the square of whatever airspeed you happen to have when you place the wing at the stall angle-of-attack. L and D will both vary in relation to the square of this airspeed.

We often think of stall speed as being proportional to the square root of the g-loading, at least when weight is fixed. In some previous posts I was suggesting that it is more appropriate to focus on the lift-wise component of the g-loading vector. IF angle-of-attack and Cl and Cd are constant, and L/D is therefore constant, but we have a motor and we are varying the thrust in a powered climb, then the more of the aircraft's weight is carried by thrust, the less is carried by L, and the stall speed goes down in proportion to the square root of the reduction in L. This is what the table I posted on June 16 is showing. It would be equally valid to say that the stall speed goes down in proportion to the square root of the reduction in D. Remember, L/D is constant in this thought experiment--I specified an L/D of 40:1 in the table I posted on June 16. However, the dragwise component of the G-loading vector is also influenced by the Thrust vector, which complicates everything. So in this particular case-- which is certainly not a glider-- the stall speed does in fact vary according to the square root of the liftwise component of the G-loading vector, but not according to the square root of the dragwise component of the G-loading vector, and not according to the total G-loading vector, which in this particular case is always 1G. The reason L has gained this privileged position, is that we are varying the Thrust force, which acts parallel to Drag and purely perpendicular to Lift, at least for this purposes of this simplified discussion. That's the only reason Lift has become a "privileged" force-- because our engine is bolted on in such an orientation as to make thrust that acts parallel to the flight path.

In the table I posted on June 16, I was imagining that angle-of-attack, Cl, and Cd were all staying constant. I should have said that explicitly. It would be equally valid to use some other arbitrary set of axes, but much more complicated, because then T would no longer act parallel to the direction of one of our chosen axes.

Back to the pure glider case-- and the table I posted on June 6. If we are decreasing the L/D, the obvious question is "how?"

Are we increasing Cd while leaving Cl unchanged? If so, the airspeed that will yield a steady-state condition in wings-level flight right at the stall angle-of-attack, will be decreased, especially if we are talking about steep glide angles where the drag vector is supporting much of the aircraft weight. Imagine a gigantic parachute letting the whole glider come nearly straight down.

Or are we deceasing Cl while leaving Cd unchanged? If so, the airspeed that will yield a steady-state condition in wings-level flight right at the stall angle-of-attack, will be increased, especially if we are talking about flat glide angles where the lift vector is supporting nearly all of the aircraft weight. This is usually the scenario we're talking about, when we talk about deploying spoilers.

So I absolutely agree that if we are varying the lift coefficient and/or the drag coefficient, we can't say that the stall speed will vary according to the square root of the lift force, i.e. the square root of the lift-wise component of the G-loading vector. We need more information.

So it really wasn't appropriate for me to suggest that the variable-thrust case described in the table I posted on June 16 had much to do with the glider case described in the table I posted on June 4, if we're interested in how the stall speed varies in each case. The June 4 table doesn't have enough information to tell us how the stall speed varies, while the June 16 table does.

I'm trying to remember exactly how we got on this track. Opening a new browser window and scrolling back through the thread--

See Dan Marotta's question of June 3. Dan was asking about how the increase in G-loading due to banking was different in a descending glide than in horizontal flight. My table of June 4 answered that. I wasn't trying to claim that we could make any deductions about how the stall speed changed as we move up and down in the table (different L/D ratios, different Cl values, different Cd values, different angle-of-attack values). I was just showing that the lift-wise component of G-loading varied DIFFERENTLY as we change the bank angle, when the L/D is high than when the L/D is low. I still stand by that table.

I'm not saying that in the glider case (no thrust), L has a privileged position in determing the stall speed. It would be equally valid to say that stall speed varies according to the square root of the lift-wise component of the G-loading vector, or according to the square root of the lift vector, or according to the square root of the drag-wise component of the G-loading vector, or according to the drag vector, or according to the square root of the net aerodynamic force vector, or according to the square root net G-loading vector. All those things would be true, at least if we are holding angle-of-attack and Cl and Cd all constant. Which is what we should be doing, if we are going to the left or right in any given line on the table I posted on June 6, and intending to learn something about stall speed.

Key point-- KEY POINT-- in the case of an unpowered glider, not only is the lift vector or the lift-wise component of the G-loading vector less in a 60-degree bank with a 1/1 L/D than in a 60-degree bank with a 50/1 L/D -- so too is the NET G-loading vector and NET aerodynamic force vector less in a 60-degree bank with a 1/1 L/D than in a 60-degree bank with a 50/1 L/D. And the same is true of the drag vector. I'm not putting the Lift vector in a privileged position here. The worse the L/D ratio, the more of the aircraft's weight is supported by the drag vector. As a result, a high bank angle makes causes LESS increase in the L vector than it would in horizontal flight or in a flatter glide with a better L/D ratio. Likewise, when the L/D ratio is poor, a high bank angle also makes LESS increase in the net aerodynamic force vector or total G-loading vector than it would in horizontal flight or in a flatter glide with a better L/D ratio.

The extreme case is this: at L/D ratios near zero, we're nearly in a terminal-velocity vertical dive, with nearly all the weight supported by the drag vector, and the bank angle has very little effect on anything. When the flight path is truly vertical, the bank angle becomes undefined, and Lift is zero.

So I still say I answered Dan's question correctly.

Did I ever suggest that simply decreasing the L/D ratio would necessarily decrease the stall speed, due the decrease in the L vector? If so that would be inappropriate due to the reasons given above. But scanning back through my past posts, I don't see that I ever said that. My June 6 post beginning "One could steer this conversation in the direction" specifically referenced changes to the Cl and Cd values-- I was not assuming that stall speed varied in lockstep with changes in the L/D ratio.

OK, I do see that on June 12--DEEP into the discussion and AFTER several folks had already objected to many of my previous posts which I still say were 100% accurate-- I did make a post that said "Key point-- this is the g-loading component that is normally of greatest interest to pilots, because this is the g-loading component that affects the stall speed." That's true in the powered case, where we are varying thrust, as illustrated by the table I posted on June 16. But in the glider case where there is no thrust, if angle-attack is constant and Cl and CD are constant, there's nothing "privileged" about L-- as you have pointed out. That fact in no way invalidates anything I posted before that point, including the table I posted on June 6 in answer to Dan's question. The June 6 table was meant to be a table of G-loading, not stall speed, and the discussion didn't drift over into the topic of stall speed until many days after I posted that table. But the fact is that the June 6 table DOES tell us something about stall speed. Remember again, L/D was meant to be constant, going from left to right on any given line. IF we want to expand our conception of the table to encompass something about stall speed, then we ALSO have to specify that angle-of-attack, and therefore Cl and Cd, are held constant as we go to the left or right on any given line of the table. As long as we agree that that's what we're thinking of, then the table DOES tell us how stall speed varies with bank angle-- but NOT because there is anything uniquely privileged about the L vector. We could come to the same conclusion by looking at the D vector or the Net Aerodynamic Force vector-- they all must vary in exactly the same way.

I want to emphasize once more that the NET G-loading or NET aerodynamic force vector varies in exactly the same way as the lift-wise G-loading or Lift force varies, in the table I posted on June 6, because L/D is constant. The NET G-loading is less in a 60-degree bank with a 1:1 L/D ratio, than in a 60-degree bank with a 50:1 L/D ratio.

You've raised the issue that we can have the same L/D ratio at more than one angle-of-attack. I.e. holding L/D constant doesn't hold angle-of-attack or Cl or Cd constant. That doesn't matter, as far as the concepts illustrated in the table I posted on June 6 are concerned. Again, it wasn't originally meant to say anything about stall speed. IF we want the table to tell us how stall speed varies when we move right or left on any given line of the table, THEN we do have to specify that Cl and Cd are staying constant, on any given line of the table.

In summary-- I erred in saying that in the glider case, the liftwise component of the G-loading vector was uniquely privileged in determining the airspeed at the stall angle-of-attack. In the glider case, the dragwise component of the G-loading vector, or the total G-loading vector (i.e. the net aerodynamic force vector) would serve just as well. But I didn't make this statement into deep into the discussion, and I still stand by my answer to Dan Marotta's original question of June 3.

Sorry for getting a bit carried away in exalting the L-D-W vector triangle.... S

Substitute the words "table of June 4" for "table of June 6", sorry.

S

A bit more concisely now--

See Dan Marotta's question of June 3, and the discussion of whether or not L/D ratio affects "wing loading" in subsequent posts.

My table of June 4 was directly relevant to this discussion.

The take-home message of the table was as follows:

If we are holding L/D constant, then then L, D, and Na (net aerodynamic force) are fixed in proportion to each other.

If we are holding L/D constant and degrading the glide angle by banking, the magnitude of L, D, and Na (net aerodynamic force) must all increase as the bank angle increases, but the increase in these force vectors is much smaller if the L/D ratio is very poor than if the L/D ratio is very high.

Whether you define wing loading as N/W or L/W, there is much less increase in wing loading with increasing bank angle when the L/D ratio is very poor, than when the L/D ratio is very high.

For typical sailplane L/D ratios-- even with spoilers open-- the effect is likely too small to ever be noticed-- as I said to Dan-- but it is a real effect.

If we are not only holding L/D constant, but we are also holding angle-of-attack and Cl and Cd all constant, then we can see that for any given angle-of-attack-- including the stall angle-of-attack-- as we degrade the glide angle by banking, the airspeed must increase, because the airspeed is proportional to the square root of L, or the square root of D, or the square root of Na. (Remember that L and D and Na are fixed in proportion to each other.) The increase in airspeed with increasing bank angle will be much less when the L/D ratio is very poor, than when the L/D ratio is very high.

Again, for typical sailplane L/D ratios we'll probably never notice this, but it is a real effect.

The extreme case of a very poor L/D ratio is a terminal-velocity vertical dive, in which case the bank angle is undefined (or defined to be zero?) and thus has no effect on airspeed, L, D, and Na at all.

Any suggestion that opening the spoilers will reduce the stall speed, by degrading the L/D ratio, was in error-- when we open the spoilers, we change Cl.

We can't draw conclusions about the how stall speed varies as we move vertically (rather than horizontally) in the table I posted on June 4, because we haven't specified why the L/D ratio is changing-- whether due to changes in Cl, Cd, or both. But we can still see how the wing-loading (L/W or Na/W) varies as we move vertically through the table.

Here is the table one more time, but I've modified it to included Na/W (net aerodynamic force / weight) as well as L/W at various bank angles. Take your pick of which one you prefer to call the "G-loading". I could have also added the D/W, but you can easily calculate that from L/W. I've also added a line for the L/D =0 case.

Gliding flight (no thrust.) A table of (lift / weight), followed by (net aerodynamic force / weight), at various bank angles and L/D ratios:

Bank angle, L/W, Na/W:
L/D Infinite--
0 deg 1.000,1.000 30 deg 1.155,1.155 45 deg 1.414,1.414 60 deg 2.000,2.000
L/D 10:1--
0 deg .995,1.00 30 deg 1.147,1.153 45 deg 1.400,1.407 60 deg 1.966,1.976
L/D 5:1--
0 deg .981,1.00 30 deg 1.125,1.147 45 deg 1.361,1.388 60 deg 1.869,1.906
L/D 2:1--
0 deg .894,1.00 30 deg 1.000,1.118 45 deg 1.155,1.291 60 deg 1.414,1.581
L/D 1:1--
0 deg .707,1.00 30 deg 0.756,1.071 45 deg 0.817,1.155 60 deg 0.894,1.264
L/D 0/1
0 deg 1.00,1.00 30 deg 1.00,1.00 45 deg 1.00,1.00 60 deg 1.00,1.00

S

****Re-posted-- the only change is in the last line of the table****

A bit more concisely now--

See Dan Marotta's question of June 3, and the discussion of whether or not L/D ratio affects "wing loading" in subsequent posts.

My table of June 4 was directly relevant to this discussion.

The take-home message of the table was as follows:

If we are holding L/D constant, then then L, D, and Na (net aerodynamic force) are fixed in proportion to each other.

If we are holding L/D constant and degrading the glide angle by banking, the magnitude of L, D, and Na (net aerodynamic force) must all increase as the bank angle increases, but the increase in these force vectors is much smaller if the L/D ratio is very poor than if the L/D ratio is very high.

Whether you define wing loading as N/W or L/W, there is much less increase in wing loading with increasing bank angle when the L/D ratio is very poor, than when the L/D ratio is very high.

For typical sailplane L/D ratios-- even with spoilers open-- the effect is likely too small to ever be noticed-- as I said to Dan-- but it is a real effect.

If we are not only holding L/D constant, but we are also holding angle-of-attack and Cl and Cd all constant, then we can see that for any given angle-of-attack-- including the stall angle-of-attack-- as we degrade the glide angle by banking, the airspeed must increase, because the airspeed is proportional to the square root of L, or the square root of D, or the square root of Na. (Remember that L and D and Na are fixed in proportion to each other.) The increase in airspeed with increasing bank angle will be much less when the L/D ratio is very poor, than when the L/D ratio is very high.

Again, for typical sailplane L/D ratios we'll probably never notice this, but it is a real effect.

The extreme case of a very poor L/D ratio is a terminal-velocity vertical dive, in which case the bank angle is undefined (or defined to be zero?) and thus has no effect on airspeed, L, D, and Na at all.

Any suggestion that opening the spoilers will reduce the stall speed, by degrading the L/D ratio, was in error-- when we open the spoilers, we change Cl.

We can't draw conclusions about the how stall speed varies as we move vertically (rather than horizontally) in the table I posted on June 4, because we haven't specified why the L/D ratio is changing-- whether due to changes in Cl, Cd, or both. But we can still see how the wing-loading (L/W or Na/W) varies as we move vertically through the table.

Here is the table one more time, but I've modified it to included Na/W (net aerodynamic force / weight) as well as L/W at various bank angles. Take your pick of which one you prefer to call the "G-loading". I could have also added the D/W, but you can easily calculate that from L/W. I've also added a line for the L/D =0 case.

Gliding flight (no thrust.) A table of (lift / weight), followed by (net aerodynamic force / weight), at various bank angles and L/D ratios:

Bank angle, L/W, Na/W:
L/D Infinite--
0 deg 1.000,1.000 30 deg 1.155,1.155 45 deg 1.414,1.414 60 deg 2.000,2.000
L/D 10:1--
0 deg .995,1.00 30 deg 1.147,1.153 45 deg 1.400,1.407 60 deg 1.966,1.976
L/D 5:1--
0 deg .981,1.00 30 deg 1.125,1.147 45 deg 1.361,1.388 60 deg 1.869,1.906
L/D 2:1--
0 deg .894,1.00 30 deg 1.000,1.118 45 deg 1.155,1.291 60 deg 1.414,1.581
L/D 1:1--
0 deg .707,1.00 30 deg 0.756,1.071 45 deg 0.817,1.155 60 deg 0.894,1.264
L/D 0:1-- (vertical dive) (bank angle could also be considered to be undefined)
0 deg 0.00,1.00 30 deg 0.00,1.00 45 deg 0.00,1.00 60 deg 0.00,1.00

You cannot take an arbitrary mathematical construct, deal with it in isolation, and draw any momentous (or perhaps even any valid) conclusions.

The great thing about defining L as acting perpendicular to the flight path, and D as acting parallel to the flight path, is that it is so easy to relate the L/D ratio to the glide angle or glide ratio. (Easier when wings-level than when banked, but do-able in either case.) Knowing the glide angle or glide ratio unlocks the door to knowing the actual value of the L vector, the D vector, and the Net Aerodynamic Force vector, assuming coordinated, steady-state flight.

Keep in mind that at very steep bank angles, the glide ratio is much lower than the L/D ratio. The resulting steep glide angle allows the Drag vector to support much more of the aircraft's weight than it does in wings-level flight at the same L/D ratio, so that the Lift vector and the Net Aerodynamic Force vector both end up being smaller than they would at the same bank angle with an infinite L/D ratio. This effect is more pronounced when the L/D is very low than when the L/D is very high.

Even with an L/D of 40:1, we can see that the Net Aerodynamic Force generated at extreme bank angles is slightly less than we'd see if L/D were infinite (i.e. if drag were zero).

Here is the table expanded to cover 40:1 L/D, and also to cover 80 and 85 degrees of bank:

If the L/D ratio given in some particular line of the table happens to correspond to the L/D ratio at the stall angle-of-attack of some particular glider in some particular configuration (flaps, spoilers, landing gear), then the stall speed of that glider in that configuration would be expected to vary with bank angle according to the square root of the L/W or Na/W values given in that line of the table. (For most real-world sailplanes there will be no discernible difference from the way the stall speed varies with bank angle in the infinite L/D case; if we're talking about a glider shaped like the space shuttle (L/D as low as 1:1 at hypersonic speed -- see https://en.wikipedia.org/wiki/Space_Shuttle ), it will be a different story!)

Gliding flight (no thrust.)
A table of (lift / weight), followed by (net aerodynamic force / weight), at various bank angles and L/D ratios:

Bank angle, L/W, Na/W:
L/D Infinite--
0 1.000,1.000 30 1.155,1.155 45 1.414,1.414 60 2.000,2.000, 80 5.759,5.759
85 11.478, 11.478

L/D 40/1
0 1.000,1.000 30 1.154,1.155 45 1.413,1.414 60 1.998,1.998 80 5.700,5.702
85 11.029,11.032

L/D 10:1--
0 0.995,1.000 30 1.147,1.153 45 1.400,1.407 60 1.966,1.976 80 4.990, 5.015
85 deg 7.54,7.58

L/D 5:1--
0 0.981,1.000 30 1.125,1.147 45 1.361,1.388 60 1.869,1.906 80 3.776,3.851
85 4.58,4.67

L/D 2:1--
0 0.894,1.000 30 1.000,1.118 45 1.155,1.291 60 1.414,1.581 80 1.889,2.112
85 1.97,2.20

L/D 1:1--
0 0.707,1.000 30 0.756,1.071 45 0.817,1.155 60 0.894,1.264 80 0.986,1.394
85 0.996,1.409

L/D 0:1-- (vertical dive) (bank angle could also be considered to be undefined)
0 0.00,1.00 30 0.00,1.00 45 0.00,1.00 60 0.00,1.00 80 0.00,1.00
85 0.00, 1.00

Example: According to the POH, a 650kg (1430lbs) Twin Astir stalls at about 90km (49 knots) with spoilers fully deployed. Add a 45 degree bank and the stall speed increases to 126 km/h (68 knots).
This is usually above the normal approach speed flown during circuits so I can conceive that a pilot who is not "ahead of the glider" could possibly fly too slowly during the turn. Throw in an uncoordinated turn and things could go wrong very quickly depending on glider type.

Do you have a source for a stall speed of 68 knots at 45 degrees? PHAK and other sources say the stall speed increases with the square root of the load factor. A 45 degree bank has a load factor of 1.41; the square root of this is 1.189. So a 45 degree bank results in a 19% increase in stall speed, or in this case 58 knots.

Ditto the above question-- unless the L/D ratio is really poor, the stall speed in a 45-degree banked turn ought to be about 1.189* the stall speed in the same configuration in wings-level flight. S

And if the L/D ratio IS really poor, the increase in stall speed with increasing bank angle is even less. S