For the purposes of discussion, let me start with a square loop. There is a 20kt wind from left to right and I start from the left at 20kts and pull straight up directly iin front of me. I maintain a straight line and slow to 20 kts at the top where I turn into the wind, lose 5 kts and continue at 15 kts plus the added wind speed of 20kt for an air speed of 35kts. I proceed to the down ward turn and dive straight down while chopping the throttle to a speed of 20kts. At the bottom of the leg I pull level, lose 0kts because gravity helped in keeping the speed up in the turn and proceed at 20kts minus the wind speed of 20kts coming from behind for a net air speed of 0kts and hope I can accelerate to a flying air speed before Ihit the ground. Reverse the flying direction and Istart from the right at 20kts and pull up maintaining a straight line and slow to a speed of 20 kts and at the top I turn with the wind, lose 5kts in the turn and end up at 15kts minus the wind speed of 20kts resulting in an air speed of -5kts and hope I can gain enough speed on the way down to avoid hitting the ground.

Rounding up a loop can result in similar results.

Comments

Sorry Larry, I got lost just before the downline.

Could you explain the loop and the changes of velocities for me.

.........and very important, what is the point of references for those velocities?

Thanks

Assuming steady wind the only thing that will change, from no wind, is on your up-line and down-line will need to be flown with the nose heading a into the wind some. The transition from the up or down-line will be either more or less than 90 degs due to the slight nose into the wind attitude. Wind does not change airspeed when you change heading, only ground speed. Otherwise a square "loop" is very possible with or without wind, provided you have an aircraft capable of the maneuver.

P.S. This will only work if you have more air speed then the wind otherwise you will only have a straight vertical then a hover then a descent.

The figures you quote don't add up only because you are changing your point of reference for speed.<div>
</div><div>If you are starting from the left at 20kts in a 20kt wind then your ground speed will be 40kts.</div><div>So your square loop, to remain at constant  visual speed from the ground would need to be </div><div>
</div><div>from left 20kts IAS (40 kts ground speed) </div><div>up accelerate to 40kts IAS</div><div>from right at top accelerate to 60kts IAS (40kts ground speed</div><div>down decelerate to 40kts IAS</div><div>level exit decelrate to 20kts IAS (40kts ground speed)</div><div>
</div><div>and that should add up right.</div><div>
</div><div>
</div>

Edit to correct wording...

The wind speed and direction of travel will only effect your ground speed it will not change airspeed.
When climbing or diving vertically your ground speed is zero, into the wind subtract the wind speed from your airspeed, with the wind add the wind speed to your airspeed and you will have your ground speed.
None of this however effects your aircraft's performance, as the only thing the plane will see is it airspeed (how fast it is moving in the air).

Now you see why in Control Line Precision Aerobatics, we fly the square loops (and other maneuvers) on the down wind side of the circle.

All of the speeds were intended to be air speeds but I was not exactly clear on one speed, the final leg, level with the ground.
The approach you have is 40kts ground speed which I describe as 20kts air speed. The first vertical you have is 40kts AS (not exactly as some speed will be lost in the turn) that slows to 20kts AS at the top turn. Enter the top line at 15 kts (lost some speed in the turn) into the wind speed of 20kts for an AS of 35kts (change your 15 to 35 for AS). Next downline, where you question mark is, will be at 15kts AS (not traveling into the wind) and reaching an AS of 20kts. Final turn is at an airpeed of 20 kts that will effectively be 0kts with a tail wind of 20kts.
Throttle management will be required for some portions of the manuver.

You don't add wind speed to air speed ever. Wind speed only effects ground speed. That is unless the wind speed or direction changes in flight.

Yep, the figure you gave are nonsense because you're mixing air, wind and ground speeds up in a salad of confusion. None of your numbers add up to anything that makes sense.

You said-"There is a 20kt wind from left to right and I start from the left at 20kts "

That implies that you are approching the square loop with a tailwind of 20 kts plus a forward airspeed of 20 knots because you're flying downwind for a total ground speed of 40 kts.

You then said- "(I) pull straight up directly iin front of me. I maintain a straight line and slow to 20 kts at the top where I turn into the wind"

Well, since you were already doing 20 kts AIRSPEED when you were flying downwind to enter into the square loop you can't very well slow down in the vetical line to 20 kts. This is the start of the confusion. But forget that for the moment. So the airplane flew along at 20kt airspeed and pulled vertical and maintained a 20kt airspeed up the line (perhaps thanks to adding power?). That's fine. As it did so the wind hitting the top of the model along with it's momentum from the 40kt ground speed kept it drifting belly first downwind at 20 kts all while the model was heading up at 20kts.

Now you turn the next corner to inverted to fly back into the wind where you said- "...at the top where I turn into the wind, lose 5 kts and continue at 15 kts plus the added wind speed of 20kt for an air speed of 35kts."

So why is this corner costing you 5 kts where the other one didn't? Let's skip any drag related speed losses in the corners for now even though they certainly occur. So the model flips inverted from the 20kt upline to flying at 20 kts of AIRSPEED into the 20kt headwind that is still coming from the left as per your original statement where both the model AND the wind are coming from the left at 20kts each. So you see where our and your confusion is coming from? So anyway, our model has just rotated to inverted and heading back the way it entered and facing the 20 kt wind from that direction. So it sits in the air upside down at zero ground speed apparently defying gravity but is actually very happy because it is still plowing through the passing air at its happy speed of 20 knts.

So from here you pull the last corner for the downline where you said- "I proceed to the down ward turn and dive straight down while chopping the throttle to a speed of 20kts. At the bottom of the leg I pull level, lose 0kts because gravity helped in keeping the speed up in the turn and proceed at 20kts minus the wind speed of 20kts coming from behind for a net air speed of 0kts and hope I can accelerate to a flying air speed before I hit the ground."

Nope, not the case at all. The model does come down at 20 kts like you say but it also is now being pushed by the drift so by the time you get to the bottom line where you pull back to level the model is being pushed canopy first "upwards" at 20 kts. Also it maintains it's speed through the corners because we're ignoring the drag losses in the turns so it pulls out with both 20 kts of airspeed PLUS the 20kts of wind speed from the tail and is immediately flying at 40 kts with out any sign of sag towards the ground.

OK, now let's try it with a 5kt loss per corner.

You are flying downwind at 20kts airspeed and 40 kts ground speed. You turn the corner and fly the upline at 15 kts. Power needs to be added to get back up to 20 kts before you go inverted or the model WILL appear to drift downwind tail first. So you turn the top corner but slow to 15kts momentarily until the airspeed gets back up to 20 kts. So it only seems to do a funny wobbly corner before it seemingly hovers in mid air. If you want to cover enough ground to make it actually look sort of square you'll need to throttle up to 40 kts just to produce a 20 kt ground speed and make some headway upwind. So you turn onto the downline with 35 kts of airspeed because you lost 5 in the turn. You throttle back so the prop can slow you down and turn the bottom corner at 20 knots AIRSPEED and then fly away at 35 kts GROUNDSPEED and 15 kts AIRSPEED due to losing a bit in the last turn. And if you're sharp on the controls you'll quickly speed back up to regain the 5 kts so the model doesn't feel sluggish due to the low AIRSPEED even though it's ripping along at what seems like 0.8 Mach.

Your statement about having to speed up to avoid crashing is due to you forgetting that speed in the downline will be retained as you turn the corner. You also did not allow for the wind pushing the model's wing in the up and downlines so that it actually looks like it's moving on a 45 degree angle in the vertical lines.

<span style="color: rgb(255, 0, 0);">Comments in red.</span>

Thanks, Larry.

I have modified the schematic; see the attachment.

It seems that your square loop cannot be performed properly with those velocities, because it will look like a bump to you.

Note the values in magenta that I have modified.

I know that it is confusing; I recommend trying the loop in calm conditions to have all the velocities correct, and then add wind velocity to see what happens.

I will be back on this tomorrow.

<span style="color: rgb(255, 0, 0);">Comments in red.</span>

Let's consider this as an object moving thru space at an absolute speed and direction, lets not talk about airspeed yet. In your diagram the plane is moving up at a speed of 20 kts and has a certain amount of energy from it's motion, it is then directed to the left, loses 5kts and a portion of it's energy in the turn, and then proceeds to the left at 15kts with the remaining energy. To say otherwise is to say that it somehow instantly lost the energy that it has. Now we consider air speed. Moving to the left at 15kts it encounters air moving to the right at 20kts. The result is that air is moving over the plane at 35kts. If we can agree on this we can continue to analyze the rest of the scenario.

_____________________________________
Edited to insert quote codes in correct spots- bcm

Original BMatthews post in black

<span style="color: rgb(255,0,0)">Flythesky Comments in red.

</span><span style="color: #339966">Bmatthews comments in green
__________________________________________________ __
</span>Yep, the figure you gave are nonsense because you're mixing air, wind and ground speeds up in a salad of confusion. None of your numbers add up to anything that makes sense.

You said-"There is a 20kt wind from left to right and I start from the left at 20kts "

That implies that you are approching the square loop with a tailwind of 20 kts plus a forward airspeed of 20 knots because you're flying downwind for a total ground speed of 40 kts.

You then said- "(I) pull straight up directly iin front of me. I maintain a straight line and slow to 20 kts at the top where I turn into the wind"

Well, since you were already doing 20 kts AIRSPEED when you were flying downwind to enter into the square loop you can't very well slow down in the vetical line to 20 kts. <span style="color: rgb(255,0,0)">I was going 40 kts ground speed, did I somehow lose all of this speed when I pulled up?</span> <span style="color: rgb(255,0,0)">The air (wind) is staionary in respect to the plane now.<span style="color: #339966">Like we've been saying you can't use GROUNDspeed for any of this. T</span><span style="color: #339966">he model only sees and works with AIRspeed. Inthe case of your scenario itcarriesits20 knots of airspeed around the corner less something for drag in the turn. The momentum from the tailwind along with the windhitting the top of the model pushes it downwind at20 knts while the model is climbing. That part of the 40 knots stays horizontal and continues toblowthe model downwind at a constant 20 knots. The actual ground speed of the model can be shown from the vector addition of the air and wind speeds for any point around the loop. You picked an extreme scenario with the wind and flying speed being the same. No one with half a shred of concern for their model would normally flyunder such nasty conditions so you very likely havenotseen how such a wind can affect the vertical lineof a model in flight. But in the case of this scenario if you turn the model so the fuselage isverticaland fly with a 20 kt upward speed in a 20 knot wind the model'sflight path will actuallybe a 45 degree angle upwards and inclinedin the downwind direction. It is no different from theskew of a ground track when flying horizontal in the wind. If you flew your 20 kt model cross wind then it would appear to be crabbing throughthe air at a 45degree yaw angle from the ground when you pass overhead. The crab angle in the square loop just happens tobe upward in this scenario.To actuallytravel in avertical trackas seen from the ground you would have to pitch the modelpast verticalto a 135 degree angle so it crabbed upwind in a true vertical line as seen from the ground but the fuselage of the model would be at a 45degree angle pointed backinto the wind. I took more time to dwell on this first point because it's the root of all the misunderstanding in the rest of the scenario. </span></span> This is the start of the confusion. But forget that for the moment. So the airplane flew along at 20kt airspeed and pulled vertical and maintained a 20kt airspeed up the line (perhaps thanks to adding power?). <span style="color: rgb(255,0,0)">Throttle management is to understood but not defined.<span style="color: #339966">Fair enough.</span></span>That's fine. As it did so the wind hitting the top of the model along with it's momentum from the 40kt ground speed kept it drifting belly first downwind at 20 kts all while the model was heading up at 20kts. <span style="color: rgb(255,0,0)">I do not understand why you would think that this is happening. By definition a vertical line has no ground speed.<span style="color: #339966">We need to consider who's frame of reference isseeing the vertical line. There's no "definition" about it. Forthe model flying along inthe moving river of air at it's happy 20 kts it turns through a 90 degree angle and proceeds upward just fine from ITSframe of reference. Butit is doing this in a moving body of air. You on the ground wouldsee the model crabbing upward and downwind on a45 degree upward track as described above. Pattern flyers in competition deal with this issue all the time in winds. They have to use rudder and elevator to cant the model into the wind so that theupward track LOOKS verticalto the judges.But they deal with up to maybe 15mph winds while flying a model that is moving along atmaybe more like 60 to 70 mph. So the amount they have to cant thefuselage over into the wind to produce a vertical track isn't anything like what we are looking at in your scenario.</span></span>

Now you turn the next corner to inverted to fly back into the wind where you said- "...at the top where I turn into the wind, lose 5 kts and continue at 15 kts plus the added wind speed of 20kt for an air speed of 35kts."

So why is this corner costing you 5 kts where the other one didn't? <span style="color: rgb(255,0,0)">The speed loss was not specified but you can see by my previous statement that the plane is slowing down. <span style="color: #339966">Then to be consistent it should be described as slowing down in all the corners since that is the more realistic scenario. </span></span>Let's skip any drag related speed losses in the corners for now even though they certainly occur. So the model flips inverted from the 20kt upline to flying at 20 kts of AIRSPEED into the 20kt headwind that is still coming from the left as per your original statement where both the model AND the wind are coming from the left at 20kts each. <span style="color: rgb(255,0,0)">The plane is traveling up at 20kts when it turned inverted and lost 5kts. This speed is in relation to the ground now<span style="color: #339966">- no itisn't, the model does notknow there is any ground down there other than the effect of gravity on it. You can only consider airspeed since that is all that the model can feel Andif the model entered the cornerwith 20 kts it'll come out of the turn with 20 kts or 15 if we are allowing for somespeed loss in the corners-</span>and is flying into a 20kt wind. The speed of the air over the plane is now 35kts.<span style="color: #339966">- Again, no it isn't. The modelwas climbing at 20 kts,but was also being blowndownwind at 20 knotsat the same timeand the resulting upward track ends up being a45 degree inclined path.When it turns from vertical to inverted and ifit loses 5 kts fromturning the corner it isnow flying at 15 kts of airspeed. And since this is occuring in a 20 kt wind it would actually appear to the pilot on the ground to be going backwards at 5 kts.But if the model isn'tstalling it'll continue tofly up there in the air just fine.Thewind cannot add actual flying speed to the model and raise it to the 35kts you suggest. That just won't happen. Given that we agree that throttle control will be used to hold the model at 20 kts and that we lose 5 kts in the turns the model's AIRspeed will never drop lower than 15 kts or rise to higher than 20 kts. It can't since the wind speed cannot suddenly add to the model's speed at any time.. </span></span>So you see where our and your confusion is coming from?<span style="color: rgb(255,0,0)"> I am not confused by my scenario. </span>So anyway, our model has just rotated to inverted and heading back the way it entered and facing the 20 kt wind from that direction. So it sits in the air upside down at zero ground speed apparently defying gravity but is actually very happy because it is still plowing through the passing air at its happy speed of 20 knts.

<span style="color: rgb(255,0,0)">You are saying that the upward speed has somehow disappered? Underlying this discussion you seem to be saying that the momentum of a plane continues to move a plane in it's original direction after turning in a new direction. If you dive to the ground and level out do you continue to descend toward the ground at the original diving speed?</span> <span style="color: #339966">The model's FLYINGspeed stays with it as it goes around the corners. But we're dealing with the model doing this in a fast moving river of air with us standing on the stationary bank. You chose to use a square loop as your example.But let's try a slightly different scenario. A radio control glider is winched up and moves upwind from the release point. It's a blustery day with a wind of 15 mph and the model is an old floater that flies best at 15 mph. The pilot feels like he found a thermal so he turns and then sets the trims to hold the model in asteadycirclethat stays in the thermal. The model drifts back overhead. What will the flight path look like from the ground? It won't be a circle. It'll be look like a series of half circle C shapes joined at the points. The points being where the model is pointed directly into the wind and sitting up there with zero ground speed. As it turns off the wind it'll crab to the side and downwind.

Now let's do a square turn overhead with this same glider to bring the horizontal example into line with your looping example. The model comes off the winch and sits there pointed into the wind because it's flying at 15 mph airspeed into a 15 mph wind. The pilot turns the model so the fuselage is pointed 90 degrees to the right. But due to the wind the ground track seen by the pilot from below for this sideways straight leg will be coming back towards him and to the right at a 45 degree line. So far so good? It's simple ground track calculation for wind. So then he turns another 90 degrees to fly dead downwind at the same 15mph of AIRSPEED. But from the ground we see what appears to be 30 kts due to the wind passing by and carrying the model with it. Note that the model doesn't care a bit about this. It is still only seeing 15 mph of air passing by. It is us on the ground that are lead astray due to the model flying in the body of air that is also passing by. Now he again turns 90 to the right from downwind so he's actually headed to the left. Again the model appears to be flying crabbed at a 45 degree yaw angle due to our perspective . And finally we turn back into the wind where the model again comes to a halt as seen from the ground as it is again flying in a 15 mph headwind. The final shape of our "square" as seen from the ground ends up being a trapezoid with two angled sides, a closed short side and an open long side since the model was not able to get any headway back upwind.

Simlarly your 20 kt square loop ASSEENFROMTHEGROUNDwhen started from a path that included a 20 kt tailwind but where the pilot only rotates the model using 90 degree turns will be a fast low line to a 45 degree downwind climb to a stationary inverted hang at the top then a 45 degree down and downwind line to the recovery that continues downwind. The final shape would be a path that looks like ____/\____ The inverted part taking place at the peak of the /\ part. Because of the wind if you want to make the line truly vertical your first rotation would have to be 135 degrees so the model climbs pointed into the wind at a 45 degree angle. At the top you rotate 45 degrees to inverted and just sit therebecause of the wind and flying speed being the same but pointedagainst each other.Andthen to come back down you would only rotate byanother45 so it crabs down on a vertical track as seen from the ground but the fuselage is at a 45 pointed into the wind. And finally to return to level you rotate it through another 135 degrees. All of this would make your square loop look like this ______|______ because there's no actual ground speed while at the top of the loop.

</span>So from here you pull the last corner for the downline where you said- "I proceed to the down ward turn and dive straight down while chopping the throttle to a speed of 20kts. At the bottom of the leg I pull level, lose 0kts because gravity helped in keeping the speed up in the turn and proceed at 20kts minus the wind speed of 20kts coming from behind for a net air speed of 0kts and hope I can accelerate to a flying air speed before I hit the ground."

Nope, not the case at all. The model does come down at 20 kts like you say but it also is now being pushed by the drift so by the time you get to the bottom line where you pull back to level the model is being pushed canopy first "upwards" at 20 kts. <span style="color: rgb(255,0,0)">Again, Ican't understand why you think this. You are saying that a plane can't fly in a vertical line in a wind. Ithink it can because Ido it when Ifly.<span style="color: #339966">In calmer winds where the model's airspeed is much faster than the wind theangle of cant required to produce a track that appears vertical from the ground isn't much. Same as the drift isn't much and it can be missed by a sport flyer. But get someone in your club that has flown or judged pattern competition events and ask them to watch your verticals for signs oftrack pushing due tothe wind. They'll have the experience to seeit or to see that you've got your model canted intothe wind to counter the effect. Or try flying your model on a day where you'd ratherjust stay on the ground due to the high wind conditions. Go off to the side rather than directly up or downwindso you'll see the wind's effect.Then try toturn the model through a 90 degreecorner and go verticalas if you're doing a reallyaccurate wingoverand see the effect. The downwind drift will become very apparent. Try it again and see how far over you have to yaw or pitch the model to actually achieve a ground percieved truly vertical track. I think the angle will shock you.. Even onwindy but tolerabledays if you do this off to the sideof the wind where the effect is morenoticable to you instead of directly upwind or downwindyou'llsee how thewind pushes the actual flight trackl over at an angle while the model is pointed directly up.</span></span>Also it maintains it's speed through the corners because we're ignoring the drag losses in the turns so it pulls out with both 20 kts of airspeed PLUS the 20kts of wind speed from the tail and is immediately flying at 40 kts with out any sign of sag towards the ground.

Either the OP is a joke of some sort or the poster is incapable of understanding even the most basic aerodynamics. Someone who says you can point a plane's nose straight up in a 20 kt wind and have it fly straight up without being carried downwind by the wind "because I've done it" is not someone who can be reasoned with. The "groundspeed is 40 kts so it will zoom up at 40 kts when you turn it 90 degrees" is revealing, too. A plane flying in a moving mass of air is still in that moving mass of air when it changes direction. Until one can grasp that it's pointless to throw numbers around.

Is it possible to do a square loop in a 20knot wind? Yes it is. You can do one that looks square with a model that'll do more than 20 knots, and also do one that doesn't look square with one can't do 20 flat out in calm. You might not be able to land back at the runway, but it's possible to do.

Is it possible for model pilots to judge the speed their model is flying closely enough to fly it at an exact 20 knots ? or any chosen airspeed? Not really.

Basically it's not possible for the vast majority of us to actually do what is described. Because the description includes things not possible to know, such as actual airspeeds as stated. And it's not possible for anyone who has actually flown a square looking loop in a wind to have known the wind speeds encountered along the path nor the airspeeds or the ground speeds.

Got a better description of the impossible feat?

Larry,

We cannot agree on that.
This morning, I was thinking that one problem with the example is that the speed of the airplane does not match with the speed of the wind in real life.
Any plane being able of fying so slow as 15~20 knots without stalling must have a very low wingload.
I don't know of planes with low wingload that can perform compensated aerobatic maneuvers in winds of 20 knots.

I suggest reducing the wind speed or increasing the minimum speed of the airplane in your example.

So many people cannot be wrong.
It seems that we have been talking different concepts so far.

Could you define airspeed and groundspeed for all of us trying to discuss this?

I agree with these definitions shown in Wikipedia:

http://en.wikipedia.org/wiki/Airspeed:

"Airspeed is the speed of an aircraft relative to the air.
.....
The measurement and indication of airspeed is ordinarily accomplished on board an aircraft by an airspeed indicator ("ASI") connected to a pitot-static system. The pitot-static system comprises one or more pitot probes (or tubes) facing the on-coming air flow to measure pitot pressure (also called stagnation, total or ram pressure) and one or more static ports to measure the static pressure in the air flow. These two pressures are compared by the ASI to give an IAS reading."

Note that a sensor located in the leading edge of the wing is needed to measure the airspeed; hence, the LE is the point of reference for such measurement.

http://en.wikipedia.org/wiki/Groundspeed

"Ground speed is the speed of an aircraft relative to the ground. Information displayed to passengers through the entertainment system often gives the aircraft groundspeed rather than airspeed.

Ground speed can be determined by the vector sum of the aircraft's true airspeed minus the current wind speed and direction; a headwind subtracts from the ground speed, while a tailwind adds to it. Winds at other angles to the heading will have components of either headwind or tailwind as well as a crosswind component.

An airspeed indicator can only indicate the aircraft's speed relative to the air mass. The air mass as a whole may be moving over the ground due to wind, and therefore some additional means to provide position over the ground is required. This might be through navigation using landmarks, radio aided position location, inertial navigation system, or GPS. When more advanced technology is unavailable, an E6B flight computer is often used to calculate groundspeed.

Ground speed is quite different from airspeed. When an aircraft is airborne the ground speed does not determine when the aircraft will stall, and it doesn't influence the actual aircraft performance such as rate of climb."

Note that a sensor located on the ground is needed to measure the ground speed; hence, the ground is the point of reference for such measurement.

Again, these concepts are confusing for many pilots; I recommend trying the loop in calm conditions to have all the velocities correct, and then add wind velocity to see what happens.

Even better, let's try the example of the hot air balloon that has been used in other similar threads:

Imagine that you are in the basket of a hot air baloon, while you are flying your RC plane in a normal circular pattern around that balloon.
The wind is making the balloon drift in one direction, but you don't know what is the speed of the wind and the balloon.
However, you are able to keep the circular pattern of your plane around the balloon.

An an observer on the ground will see deformed shape of the loop that you are seeing from the balloon.
If there is a strong wind, both persons cannot see the same shape.

If there is zero wind, an observer on the ground will see the same shape of the loop that you are seeing from the balloon.

Can you explain how that happens?

I think this quotation provides a perfect illustration of the OP's confusion. A plane does not fly "at 15kts [airspeed]" and then "encounter" air moving toward it. The plane is flying in the moving air, not toward it. A plane flying at a 15 kts airspeed has that airspeed whether it is flying toward, away from, or across the direction in which the wind is blowing relative to the ground.

Many beginners think that a plane turning into the wind will have its airspeed increased as a result of that turn and that a plane turning toward downwind will lose airspeed as a result of the turn, just as a car would. Understanding why these effects do not occur is an essential first step in understanding how an airplane behaves in the wind. Arguing at length that these effects do occur is just a waste of everybody's time. (In principle, this is just another version of the "plane on a treadmill" puzzle: the people who insist that the plane on the treadmill won't be able to take off are mostly the same people who think a plane turning into the wind has its airspeed boosted because of the turn. They are so used to thinking about vehicles moving on the ground that they can't get their heads around the notion that a flying plane has no connection to the ground save gravity (or ground effect when very low).)

Square loops are judged by the shape of the manuver.
The orientation of the airplane is discounted.
That's in the judging guide.
The pitch angle of the plane has to changed from pointing straight up, as it would be in a calm wind, to something that provides thrust to offset the effect of the wind moving the plane downwind.
Only the inexperienced attempt these with the first leg up while flying downwind.
The plane would be on its back going up.
And in a inverted dive on the down leg, all the time pointing into the wind to maintain a constant position relative to the flyer/judge.

The bolded part seems to be at the root of your difficulty. As mentioned by someone else already the model doesn't "encounter" wind and add it to the airspeed as you suggest. In a steady wind the model flies at a steady speed when flying in a straight line with its 15 knots of wind passing over the wings. And in actual fact a 15 kt flying speed into a 20 kt wind would result in the model drifting backwards at -5kts ground speed.

Wow, what a discussion!

It may be the OP's fault to put his question the way he did, but that "possible?" is still a perfectly valid question for me. Actually, it's a question about kinetic energy, its conversion and conservation. Why don't you just imagine an aerobatic glider trying that square loop as a pattern fixed to the ground, not to the moving air. Adding a decent wind shear, you might even invent a new DS pattern.

Wow, so many people to thank. Special thanks to BMatthews and Lnewqban who clearly took quite a bit of time trying to explain where I was wrong in my thinking. Thanks to cfircav8r, mboland, iron eagel, da Rock, Top Gunn, and Tall Paul for their contributions to my education.

I finally get it. One big step in understanding what is happening to my planes up in the air.

Not one erg of energy is unaccounted for. It's all a matter of perspective.