The ideal glider wings are neither overly stiff nor too flexible. Wings that are too stiff are heavier and vibrate, creating drag that slows down the glider. If the wings are too flexible, like the paper that is too thin, the wings will fold and will flutter, causing the glider to crash. The best wings are made from materials with properties similar to thin stiff paper. When using this material, the wings will bend to form a better streamline profile which is more efficient for airfoil, thereby increasing the distance the glider will fly. This is similar to the behavior of the wings of commercial airplanes which are designed to flex to form airfoils.

Basics of Glider Aerodynamics 1a What keeps a glider moving comes down to managing how fast it loses height. Without motors, these planes rely entirely on altitude they start with to fight drag - the pull that slows them through the air. When airflow rushes faster over the top of the curved wing compared to underneath, lower pressure forms above, lifting the craft up into thinner sky. This effect ties directly to glide performance: distance covered per unit of drop shows exactly how efficiently motion trades for descent. Flying farther across while falling slowly means better numbers here - less sinking happens when efficiency climbs high.

Basics of Aeroelasticity and Passive Shape Change 1b Wings on planes usually stay stiff, built that way for steady flight. Now though, engineers are leaning into bend - watching how air pushes while materials push back. Elastic reactions mix with airflow in ways once avoided, now explored. Shape shifts mid-sky used to mean trouble, today it's part of the plan. Firmness gave control, but flexibility may offer gains. What resisted motion before now dances with wind pressure. Designs once locked in place now respond, twist, adapt. When air pushes against it, the wing bends on its own - no motors needed. This shift happens quietly, shaped by airflow instead of gears. Flexibility lets form follow force, changing mid-flight without commands. Movement comes from pressure, not parts. The structure gives way gently, adapting as conditions change. Wings that bend tend to curve more along their shape - this added roundness helps them grab extra lift when flying slow. Because of this change, flexible wings might keep a glider up in the air longer compared to rigid ones stuck in place. How much they twist and swell matters - subtle shifts in form open room for staying aloft without rushing forward.

Material Science: Youngs Modulus and Flex Ratio 1c How stiff something is comes down to its Young’s Modulus. Wings bend based on that stiffness level. What changes here depends directly on the wing material’s value. When the number runs high - meaning very rigid - the example used is three layers of poster board. Even with stiffness from three layers, poster boards resist bending well. Still, their rigidity keeps them from adjusting to shifting air forces. One layer of paper bends easily, showing low resistance. A special test applies two grams on the wing tip to check how much it dips. This number gives the Flex Ratio, guiding choices. Finding balance matters - too stiff and it cracks, too soft and it folds. Just right means it moves without breaking.

Aerodynamic Risks From Flutter and Turbulence 1d A sudden wobble can grow when a wing becomes too flexible. This motion steals power from the airflow around it, feeding itself into wild oscillations. Wings that bend more easily might start to rock uncontrollably under certain conditions. Instead of calming down, the movement gets stronger as air pushes back unevenly. Laminar flow keeps flights steady, air sliding in neat sheets along the surface. When wings bend too much, that smooth motion breaks apart. Instead of gliding, the airflow tumbles into chaos. Smooth layers give way to messy swirls. Stability fades once flexibility interferes. Turbulence takes over where order once ruled. Because turbulence creates lots of extra resistance - often called parasite drag - gliders lose lift quickly, sometimes stopping altogether. That’s why during testing, ultra-flexible materials tend to fail compared to those with stiffness near that of cardboard.

Design Iteration through Horizontal Stabilizers and Pitch Stability 1e Not just the wings decide how well a glider performs - the whole frame must sit evenly in flight. Early trials revealed dives happened unless 3D-printed bodies had their mass placed just right. To fight unwanted nose drops from bendy wings, scientists enlarged the tail's flat parts instead. When everything lines up properly, shape shifts that happen on their own turn airflow into forward motion.

Biomimicry and Environmental Impact 1f Wings that bend follow nature’s lead - birds and bugs mastered them long before humans arrived. Look ahead. Big names such as Boeing, flying the 787 Dreamliner, along with NASA, now test these shifting wings to cut down on heavy parts and strain. Efficiency climbs when wings reshape themselves without added power. Planes then sip less fuel instead of guzzling it. Fewer emissions come out behind. That quiet shift could matter deeply in slowing global warming. Research into pliant wings won’t shout - but its role may grow where it counts.

Bench Test Methodology Measuring 1g Flex One way to make sense of how flexible something feels - like calling a wing “bendy” - is by using the Flex Ratio. Based on an old idea called Euler-Bernoulli Beam Theory, it shows what happens when force bends a structure. When testing stillness, the wing acts like a beam clamped at one tip. At the open end, exactly 2 grams - a bit more than a dime - gets added. What matters most is how far that point moves down compared to the full span. That number comes from dividing deflection by length. So Fr equals Δy divided by L. This number lets you compare how different materials - like paper and cardstock - behave even when wing sizes aren’t exactly the same. Bending resistance matters in design work, where stiffness defines performance under load.

Flight Dynamics and Efficiency Metrics 1h Phase 3 testing measures how well potential energy turns into motion, along with how far something travels. Figuring out efficiency means finding two key numbers tied to air movement. One is Glide Ratio (D/L), which compares Lift (L) to Drag (D); during real tests, it shows up as Horizontal Distance divided by Launch Height. When this number climbs, it hints the wing uses "Passive Morphing" effectively - staying aloft while fighting minimal resistance. The second measure? Sink Rate - that's just how fast the glider drops straight down. A wing that resists bending too much might fall faster because it fails to generate enough upward force. When built too loosely, vibrations can take over, dragging the descent even steeper. What works best comes down to a middle ground - subtle give without wobbling apart - slowing the drop just enough to stay airborne longer.

The Raindrop Fuselage Design 1i Starting mid-sentence, shape matters when air pushes back. A glider took its form from droplets falling through sky. Because nature solves problems first, engineers copied how water tightens while dropping. Streamlined like that, less pressure builds up front. Built with plastic layers stacked by machine, the frame follows flow found in storms. When objects move fast, edges that taper beat flat fronts every time. A smooth airflow sticks close to the shape thanks to the blunt front and narrow rear. When air stays attached, it avoids forming a dragging vacuum at the back. Sharp edges would trip the flow, but curves guide it along gently. Without early separation, pressure stays balanced across the surface. That quiet zone behind doesn’t get pulled apart by turbulence. One shape fits all wings - keeping the fuselage unchanged means differences in how far it flies come only from wing bend, not body shifts. What you see flying farther? Blame the flex, not the frame. Same tube, different twist. Flight path tweaks trace back to one thing: how much the wings give. Not the shell. Never the nose cone. Just the way they curve midair.

Stability and Surface Controls 1j When wings bend during flight, the spot where lift acts moves around. Studies found that floppy wings make this shift hard to predict. Because of how they flex, pressure location jumps instead of staying put. A bigger horizontal stabilizer got added to fix that problem. Because of it, the tail section keeps things steady in flight. That setup stops the glider from tilting upward too much - something flimsy paper wings often do. Without this balance, it might just nosedive instead. Long-term wobbling gets canceled out by smarter shaping behind the main wing. Wings bend under pressure, yet tails resist that motion - keeping things level demands careful adjustment. Flight stays smooth only when both parts respond just right, not too stiff, not too loose. One shifts, the other follows, each affecting how the plane holds its course. Balance emerges through subtle opposition, never perfect, always shifting.

Variable Control and Environmental Consistency 1k Finding solid answers means noticing how outside factors can shape results. Flying took place inside a closed space so gusts and rough air could not interfere. Flexible wings needed calm conditions to deliver clear results. Without walls around, shifting winds might twist the readings off track. From one trial to the next, the drop point stays fixed. A steady toss angle means airflow effects stand out clearly. Only what the object is made of changes each time. That change shows how flexibility shapes flight. Watching how far or long each one goes reveals patterns. Each test checks just one thing at a time. Results link directly to how stiff or bendy the item happens to be. Measurements track distance and timing alike. The setup keeps everything else locked down. What flies best becomes obvious under these rules.

Experimental Variables 

• Independent Variable (The Cause): The flex ratio (flexibility) of the wing material. We are trying this with 3 different materials. 
• Dependent Variable (The Effect): Collected glider efficiency data. In the logbook we stated that we want to include other performance metrics such as lift-to-drag (L/D) ratio, glide distance, and sink rate, but ultimately we are trying to find the “optimal flexibility”. 

Controlled Variables (The Constants) 

• In order to conduct a fair test, we have controlled a number of variables. 
• Main Body (Fuselage): We will use a 3D printed frame for all the tests, so that the base is the same in all the frames. 
• Wing Dimensions: The wings will ALL be of the SAME dimensions & shape (surface area S) regardless of the material. 
• Attachment Method: We will use the same position & orientation to attach each wing to the body.
• Launching: Even though the human arm cannot replicate and exact the amount of pressure every time, the height and position will be the exact same. Minimizing the difference in the outcome, however this can also be quantified as a confounding variable. 

Confounding Variables

• These are factors that are not obvious but could unintentionally impact our results if not controlled carefully.
• Wing Weight: Unfortunately, not every material has the same amount of weight. It is a variable that cannot be controlled but we chose dimensions over weight. This is because dimensions matter more on how wind flies around the material rather than just more mass.
• Surface Texture (Skin Friction): We spoke about “surface texture and drag” as a previous thought. Each of your 10 materials (eg. wax paper vs. foam sheets) is different, so the change in “parasite drag” could simply be due to the roughness of the material.
• Laminar vs. Turbulent Flow: At large enough flexibilities (e.g., normal paper), the wing may undergo “Aeroelastic Flutter”. This leads to turbulence and an aerodynamic stall, potentially complicating the assessment of the pure effect of flexibility versus the effect of structural failure.
• Humidity/Environmental Factors: Since many of our materials are paper (coffee filter, cardstock, construction paper), they may gain moisture from the air during the experiment and change in weight or stiffness.
• Launch Consistency: If not using a mechanical launcher, the initial glide velocity and angle of attack will differ for each glide, affecting the Lift Equation. However it will be repeated a number of times to minimize the difference in outcome.

Procedure:

Materials list:

• Group 1 (Ultra-Light): 1 layer, 2 layers, and 3 layers of regular a4 paper. 
• Group 2 (Mid-weight): 1 layer, 2 layers, and 3 layers of thin cardstock. 
• Group 3 (Heavy-Duty): 1 layer, 2 layers, and 3 layers of thin poster board.
• The Hybrid: 3 different wings of different layer combination of each material

Phase 1: Wing Standarization

1. Template (Using a template, we can make the surface area 

constant). This template will be 30cm x 3cm.

1. Cutting the wings will leave us with a finished ready to use product.
2. Measuring each and every wing to put into a graph demonstrating the weight penalty, even if it is a confounding variable.
3. Attachment Setup: Using a 3cm slit we can slide the wing in, allowing us to start the experiment. If there is space between the wing and the hole making it loose, we will add a little small piece of crumbled paper, ensuring basically no weight change and wing misalignment.

Phase 2: The Bench Test 

1. Rest 15 cm of the wing to the edge of a flat elevated space(ex. table), making sure the wing sticks out horizontally
2. Measure the edge of the wing to the floor(y1).
3. Apply a weight (10 cent coin/2 grams) to the edge of the wing. Measure the new height [38-39].
4. Calculate the change in deflection which is second height subtracted by first height(y2-y1=Δy).
5. Now apply it into the formula Fr = Δy/L (where L is the length of the wing).
6. Use the formula EI = PL^3/3Δy [40-44]
7. It allows us to also verify our formula and ensure a more accurate way of measuring flexibility. 
8. Repeat this for all the different materials and layers and record their flexibility.

Phase 3: The Flight Test

1. The plane will be thrown indoors especially to minimize all wind and other external factors.
2. The glider will be released by hand at a constant height and position. 
3. Distance and time will be measured for each material.
4. It will be conducted 10 times per material [45-46]. 
5. Any observation will be recorded. Ex. Aerolastic Flutter

Phase 4: Data Analysis

1. Sink Rate will be calculated. Sinkrate = h/t [47-48].
2. Glide Ratio will be calculated. Glide Ratio = distance/height [47-48].
3. Any other variable we decide will be calculated.
4. Comparing the flex ratio on the x-axis and the glide distance on the y-axis to find the best spot.
5. The sink rate will also be plotted on the graph (secondary y-axis). 
6. The weight penalty will be plotted on the graph on each data point on the axis (overlay).
7. A separate graph will be created using all these variables, however we will replace our formula, with the more known and engineer use formula [49-50].

1. Performance Leaders

• The best performer based on the chart can be seen as hybrid 1.
• It achieved the best distance and glide ratio.
• Hybrid 1 was able to achieve the highest average distance of 478.2 cm and the highest glide ratio of 2.89:1.
• Standard paper performed the worst in distance averaging 278.4cm.

2. Material Behavior & Weight Thresholds

• An important observation is that when more layers were added to paper and poster board it would generally improve the Glide ratio.
• However for cardstock, when 1 layer was used it gave the best results.
• This could translate back to the fact that sometimes more materials or added weight is not always the best.
• The observation of sometimes added layers or weight is not the best can be supported by the results in trials of cardstock.
• For adding more layers to cardstock wings, specifically from 1 layer to 2 layers, the average distance dropped from 379.9cm to 363.8 cm.
• This also confirms the observation and theory that added weight was almost a drawback and the stiffness was just not able to overcome the added weight.

3. Stiffness vs. Stability

• The wings made of 3 layers of cardstock had the lowest sink rate of 170.45 cm/s.
• This means that the wing was able to stay in the air the longest relative to the drop, which is most likely due to the fact that it had just the right amount of stiffness as the poster board was much stiffer.
• In theory since more layers of cardstock layers would make the wings stiffer and fly smoother you would expect cardstock 2 and 3 to perform the best.
• However the opposite happened, cardstock 1 achieved a flight distance of 430 the farthest for cardstock wings.
• Unlike cardstock, poster board had its best distance of 542cm and best average of 421.5cm when it was at its heaviest, which was 3 layers.
• This could suggest that unlike cardstock and other materials, poster board requires more mass and layers to stabilize itself.
• Something interesting to note is that poster board at 1 layer is already the stiffest material, but it needs all the 3 layers to become even stiffer so it can fly the best it can.

Even though the hybrid 1 gave the best results, just looking at the results individually tells another story of how reliable each design was. Cardstock 1 showed very close results between each trial with the trials being between 0.65s and 0.78s. This shows its reliability and its resistance to slight alterations that could happen between or during throws. Hybrid 3 had the widest range of results having a very high distance throw of 647 cm but also several throws in the 400 cm range. This showed how this wing design had the most potential, but the difficulty in achieving and replicating the same launch perfectly every single time can have big effects on it.

Design Specification Describe the status of this specification: unmet, partially met, or fully met?

The glider must produce a stable glide ratio of at least 2:1. Fully Met.

This was surpassed by our Hybrid 1 design, which achieved a 2.89:1 ratio. This shows that with the optimization of the Babbar-Anabathula Flex Ratio (Fr), we developed a wing that is significantly more efficient than a standard rigid wing.

The wings must show evidence of ‘Aeroelastic Tailoring’ and not fail structurally. Fully Met.

Although the 1-layer paper wings suffered from ‘Aeroelastic Flutter’ (unmet), our final Hybrid 1 and 3-Layer Cardstock designs were able to successfully change shape due to an increase in water pressure to enhance lift without structural failure or stalling, and thus, successfully demonstrated the concept of passive morphing.

The fuselage has to be 3D printed. Partially Met.

Our 3D printed raindrop fuselage was made with PLA filament. This material is light and strong. The tapered tail we designed assists in drag reduction. This means the variable wing materials can be the most contributing factor in the flight. Prototypes need to be made with cheap and easy to use materials. Fully Met. We were able to use cheap materials such as Cardstock, Poster Board, and Paper to easily prototype. This made the expense of each wing very low allowing us to scale our range of research and testing.

The glider needs to be designed to ensure a low sink rate to maximize time spent gliding. Fully Met.

We achieved a sink rate of 170.45 cm/s with the 3-layer cardstock wing. This meant we achieved our target and created a wing that would enable long flight times. This is important to the efficiency of gliders in the real world.

Aerospace startups, drone enthusiasts, and schools can make use of my 3D-printed glider and wing designs. The proprietary wing 'Hybrid' designs show that there is no need for heavy mechanical flaps to create deformable wings, and that we can use materials science. For large scale or commercially usable wings, we will shift from hobbyist materials to aerospace-grade materials, based on our findings.

• Hybrid 1 (Our Best Design) → Carbon Fiber Laminates: Like our Hybrid 1, which seeks a "sweet spot," layered materials, real aircraft such as the Boeing 787 Dreamliner use carbon fibers that are \"laid up\" in specific directional patterns. This allows the wing to bend upwards during flight to reduce drag just like our Hybrid 1 model.
• 3-Layer Cardstock (Lowest Sink Rate) → Fibreglass/Kevlar Composites: This material gives the best "stiffness-to-weight" ratio. In real life, this corresponds to the materials used in high-performance competition gliders (Sailplanes) as they are stiff enough to maintain a laminar flow shape but flexible enough to cope with turbulent flow.
• 1-Layer Paper (High Flexibility) → Ripstop Nylon/Dacron: While this was too flexible for a fixed wing, it mimics the materials used in paragliders or solar-powered high-altitude drones (HAPS). These types of aircraft use very thin flexible membranes that are so light that they can remain airborne for weeks at a time with a very low energy consumption.

We could use STL files of the 3D-printed fuselage and sell them on Cults3D or MyMiniFactory. Prices could range from $10 to $20. We could also collaborate with drone manufacturers for the industrial side of the business to incorporate our Babbar-Anabathula Flex Ratio calculations into their wing-stress testing software. This would allow engineers to accurately determine how much a wing would “flutter” prior to construction, which could save millions of dollars in testing.

The objective of our experiment was to learn and analyze how wing flexibility affects glider efficiency by using sink rate and glide ratio. Our research was able to lead us to the best flexibility for wings in aeroelastic tailoring; which is about how a material is flexible to change shape under air pressure but stiff enough to maintain structural integrity.

Our hypothesis was right that wings with moderate flexibility performed the best beating very stiff and very flexible wings. The Hybrid 1 wing was able to achieve the highest efficiency with an average of 478.2 cm and a glide ratio of 2.89:1. It successfully utilized passive morphing to maximize lift. Materials that were too flexible did not perform good due to aeroelastic flutter, where the wing became unstable

In conclusion, this investigation into the Effect of Wing Flexibility on Glider Efficiency successfully demonstrated that a glider’s performance is not solely dependent on rigid structural integrity, but rather on a calculated balance of flexibility a concept known as Aeroelasticity.

To sum up, this study on the Effect of Wing Flexibility on Glider Efficiency showed that a glider’s performance doesn’t just rely on having a stiff structure. Instead, it depends on finding the right balance of flexibility, which is called Aeroelasticity.Our research went through four different testing phases, and here are the main results we found:1. Our Phase 2 bench tests showed a clear link between the material makeup and the Flex Ratio. Regular paper with one to three layers was quite flexible, but it couldn’t hold its shape well enough to keep a steady airfoil form. On the other hand, three layers of poster board turned out to be too stiff and didn’t bend well with the airflow. The "sweet spot" was found in the Hybrid 1 (H1) design, which mixed a stiff front edge with a flexible back surface, letting it change shape on its own.The flight data from Phase 3 and 4 showed that the Hybrid 1 wing had the best Glide Ratio (D/L) and the lowest Sink Rate. When the wing bends a bit under the wind's pressure, the glider boosts its lift-to-drag ratio. Wings that were too stiff ended up with more parasite drag, and on the other hand, wings that were too flexible ran into Aeroelastic Flutter, making them wobble uncontrollably and lose altitude fast.The Raindrop Fuselage design and a bigger Horizontal Stabilizer turned out to be really important for the plane's stability. We found out that when wings bend, the center of pressure moves. If the stabilized tail wasn't there to balance things out, the flexible wings would have made the craft pitch all over the place without control. This shows that for flexible wing technology to work, the whole shape of the aircraft needs to be matched to how the wing moves.Our results reflect where the aerospace industry is heading right now. Companies like Boeing and NASA are looking at how nature works through Biomimicry to develop "morphing wings."Our project shows, even on a small scale, that these designs can make flights more efficient. If airlines started using flexible wings on a larger scale, it could cut down fuel use and carbon emissions quite a bit in commercial flights.In the end, our idea was partly right: some flexibility does help with efficiency, but if there's too much, it causes problems like turbulence and flutter that can make the structure fail. The best glider is one that’s stiff enough to keep its shape but still flexible enough to move with the wind.Finding the right balance is what will drive the future of aerospace engineering.

Innovations in Commercial Aviation Efficiency

Fuel Saving: New age models like the Boeing 787 Dreamliner have wings designed to bend/flex by 26 feet during flight. This natural bending allows for the wings to change their shape during flight reducing the need for heavy mechanical systems to achieve the same purpose. This change directly results in the use of reduced amounts of fuel. Emission Reduction: The wings of the Boeing 787 Dreamliner help in reducing thecarbon footprint of the aircraft as the wings help in the aircraft "sipping" the fuel.

Biomimicry and Cutting Edge Design

Passive morphing of wings: As merger and acquisition activities in the airline industry continue, financial analysts predict that the triad of high volume traffic, low operational costs, and quality airline service will be achieved by the newly formed airline. This "passive morphing" will help a wing be pushed into an optimal curve that will be needed during flight to create a higher degree of lift without the use of complex mechanical systems that are present.

Aircraft Structures and Management of Stress Safety and Stress

As aircraft wings are designed to be flexed, the structure of the aircraft will be able to absorb the stress and turbulence instead of merely breaking it which will significantly increase the life of the aircraft and the overall safety. The process of "aeroelastic tailoring" helps to achieve the perfect balance in wing construction.

Future Aerospace Technology

NASA research: NASA and other large aerospace companies are now testing such bending, flexible wings to reduce the burden of heavy mechanical components.

Unmanned Aerial Vehicles (UAV): The principles you apply in your small-scale models—including discovery of the optimal Flex Ratio—apply to design of high-efficiency gliders and drones who need to maximize airtime at low energy usage.

Sources of Error

1. Varied Launch Force (Human error) The largest source of error in our testing was the manual launch of the glider. Although we tried to keep the thrust constant\, there could be variation in the force and launch angle. - Impacts: This is most likely the cause of differences in distance for the three trials of each wing type. - Future Improvements: To improve this in future iterations\, we would use a mechanical launcher (like a rubber-band catapult) to ensure the launch velocity and angle ($0^circ$ pitch) is consistent.

2. Consistency of Wing Shape (Structural error) The wings were made of materials like cardstock and poster board and were affixed together manually\, so there could have been slight imperfections in the "camber" of the wing. If one wing had a slight twist or asymmetrical bend\, the result would be that the glider would bank or roll instead of flying in a straight line. - Impacts: This increased the parasite drag and decreased the glide distance measured.

3.Environmental Factors (External Error) Tests were carried out in one of the indoor hallways to eliminate the possible influence of wind on the Sink Rate. Nevertheless, i\the building's HVAC system could influence the Sink Rate. - Impact: An updraft or downdraft as small as a few centimeters could cause the glider to remain airborne for multiple milliseconds.

4. Measurement Precision (Systematic Error) For distance\, we used a regular measuring tape\, and for time\, a manual stopwatch. - Impact: The reaction time of a human (usually in the order of pm 0.2seconds) leads to an error in the calculation of the Sink Rate. For a 2 second flight\, a 0.2 second error lies in the 10% range of error.

5. Material Fatigue (Physical Error) During trials\, the 1-layer Paper wing became fatigued and showed signs of creasing and softening at the attachment point to the 3D printed fuselage. - Impact: The Flex Ratio (Fr) is assumed to have increased slightly during the trials because the material lost its solid structural memory\, leading to a greater form of Aeroelastic Flutter in the later trials.

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Images:

• Wikipedia contributors. (2024, February 12). Glider (sailplane). In Wikipedia, The Free Encyclopedia. Retrieved fromhttps://en.wikipedia.org/wiki/Glider_(sailplane

Ms. Judy Fan (Grade 9 Science & Math Teacher / CYSF Coordinator, FFCA NHS) We thank Ms. Fan, our first mentor, and the most important one, for guiding us through the Calgary Youth Science Fair. Ms. Fan's experience with the scientific method helped us focus on our experimental variables and keep us on track with our analyses.

Ms Fan. Ms. Regan Inkster (Art & Design Studies Teacher, FFCA NHS) Ms. Inkster, thank you for the access to the specific supplies and equipment needed to build our wing prototypes. The ability to utilize the resources in the Design Studies department was key in the production of our precise models for the wind and glide testing.

Mr. Ryan Smitham (Art & Design Studies Teacher, FFCA NHS) Thank you Mr. Smitham for your assistance and for providing us with access to the lab and equipment. Your knowledge of the materials and structural design had a major impact on our ability to address problems we were encountering in our flexible wing models.