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Morphing Wings: Bio-inspiration from Birds.

Wing design for aerospace vehicles is a compromise between stability and performance. Depending on the intended flight regime of operation, design parameters for wings are chosen. Thus, the wing for a particular flight condition will not remain optimal in another flight regime.

However, birds do not conform to these engineering design laws, as they have the capability to change their shapes by ‘morphing’ their wings, tail, and external shape to suit different flying conditions. Birds appear to adapt to flight configurations that are inherently highly unstable and which further require rapid sensory feedback for their flight corrections and stability.

At times, birds glide through the air without even moving their wings and have large endurance. These have interested researchers in fluid, structural, and control mechanics in this multi-disciplinary optimization field to investigate how birds use ‘wing morphing’ to control their flight.

Flights of Future: Bioinspired morphed flight configuration

“Since the Wright Flyer, researchers in the aerospace industry relentlessly strived to develop flight vehicles with morphing wings that can control flight as birds adapt in their flight.”

The art of bird flight would give answers to many problems in the aerospace industry that exist today, viz. maximization of range, endurance; low noise; use of the same vehicle for multi-operation missions; towards a greener air. In fluid mechanics, one of the ways of investigating this phenomenon is by creating Computational Fluid Dynamics (CFD) models based on these morphing geometries. These models can further be used to study the aerodynamic behavior and stability of different wing configurations adopted by birds and look at how changes in geometry are used for control. Validation of the results and actual realization of the ‘morphing wing’ also needs to be considered from a practical point of view.

“PigeonBot ” feathered drone; Image Courtesy: Stanford University

The Art of Flight

The reason for the noise in aircraft is not only due to the jet engines but also because of the behavior of the air as it travels over the wing and the fuselage surfaces. This is astonishing when we compare this to a bird flying over our head gliding almost
silently. The secret lies in how it manipulates the airflow over their wings. It does so by using the little serrations in their feathers.

Studies have been taken up to investigate the separation concept. This has been put in turbine blades and wing geometries. This has shown to augment the aerodynamic efficiency. The nature of airflow from the front to rear and the top and bottom surface is modified. An analogy can be drawn at this stage if we consider the air as if it’s a quiet ocean rushing up over a beach. The waves which are more smaller creates lesser sound and similarly, due to these serrations, the noise is further reduced in an aircraft.

Airbus is exploring the serration technology for developing a silent aircraft. Efforts are also underway to use honeycomb as a structural material as it is tremendously sturdy for its mass and has been employed in reducing the weight of aircraft.

Bats use a form of stretchable wing which is extremely strong on the stretch axis. Research groups has identified this tremendously powerful enabling technology where the wing can be used in its compressed state and expanded state at the same time, it, the adaptable wing can be used for both agile and highly efficient cruise configuration. NASA has been working on a morphing wing aircraft and the breakthroughs with honeycomb structure is likely going to accelerate concepts like these into reality.

The dragonfly wing uses a distribution of vanes and the types of hinges interconnecting them to give them immense flexibility in flight. Genetic algorithm backed optimisation technique on the computer generated wing configuration to bring out the shape of the wing has also been proposed. The genetic algorithms been employed into. Boeing has a concept of blended wing body and it’s benefited from the genetic algorithms in reducing the weight of the aircraft by optimizing the skin of the wing itself.

So, nature has conquered the concept of flight in a vast variety of forms. We, as humans are striving to achieve the same. There are hidden patterns and signals from nature to strive further in the effort to perfect the art of flight in the future to come.

*‘I think nature’s imagination is so much greater than man’s, she’s never gonna let us relax.’ – Richard Feynmann*

The Future of Wings

If we could fly…how would that be! There has been a relentless effort by human civilisation in improving the aerodynamics of flight in last 100 years. As we progress into a new decade, there has been a renewed interest in in mastering the bird flight, though seems to be far away. This is the natural progression on mastering the art of flight. There has been continuous effort in both academia and aerospace industry in particular with the help of the enabling technologies to improve the flight vehicle.

The early pioneers of aviation sought solution by observing bird flight where inspiration were drawn for the aerodynamics and control aspects of the flight. The Wright Brothers, in 1903, brought concepts of wing warping but the concepts of a continuously shape changing wing like that of the birds was really beyond the technologies of that day.

In essence what evolved out of our capabilities were rigid, with a set of flaps connected using standard hinges and pivots. This is what we have used successfully for the vast majority of commercial and military aircraft to this day.

With this background and template, there is now a standard procedure in aerospace industry at making wings and we can believe that we have nearly perfected the wing design. But this template has been a historic and the wings designed from it does not do justice to what Nature has achieved when considering a bird flight.

Many factors need to be considered in the design of a wing; the twist, sweep, taper, camber, aspect ratio and the entire range of aerodynamic parameters. These parameters are considered static and are fixed in present wing design. For the operation of flaps, we use some pneumatic or hydraulic mechanism to move the rigid surface. For the last 100 years, we’ve been building these wings to generate lift while sustaining the aerodynamic loads.

In nature, wings adapt to conform to loading while varying these parameters and this is called ‘Wing Morphing’.

If we could design a flight vehicle to fulfill the role of many while doing a better job each of the states then the overall efficiency would improve. There has been concern on the greener skies and so so not only we would have aircraft consuming less fuel but there would be less of them around as a single vehicle would be able to serve for many purpose. The families of aircraft would be condensed into a multi-purpose vehicles, from a hawk in a high-speed agile configuration to a low speed highly efficient cruise configuration.

Researchers all across the globe are embracing biomimetics concepts into the development of ‘wing morphing’, which are revolutionary in design incorporating incorporating bio-inspired design into real-world giving greener, fuel saving applications.

Optimal LQR Control – Notes on Selection of Q & R

LQR control design is recently becoming quiet popular in aerospace vehicle design. While there are several literature available in LQR theory and applications, little is talked about the selection of the Q & R weights in the design phase…and thus this article. LQR design method mainly concerns stabilizing and controlling a dynamic system,viz, fighter aircraft,rocket at minimum cost.

As a starting point, we can consider R=1 and Q=1/τ ^2*ld (τ has the dimension of a time).
If τ is small, the closed-loop system gets faster, but at the expense of a large control effort.
If τ is large, it’s the other way round.
There are many other, and possibly better, ways to chose Q.
For instance, you can use the partial Controllability Gramian.

Choosing LQR weights:

One of the critical design step in LQR methodology is choosing the weights of Q and R. Apriori knowledge of the system open-loop response is required and the performance objectives to choose specific values for the cost function weight Q and R.

One of the method is to choose diagonal weights as presented below.

For the choice of Q and R, the individual diagonal elements would describe how much each state and input (squared) should contribute to the overall cost function.

Hence, we can consider states that should remain small and attach higher weight values to them. Similarly, we can penalize an input versus the states and other inputs through choice of the corresponding input weight ρj.

Choose qi and ρj as the inverse of the square of the maximum value for the corresponding xi or uj;
Modify the elements to obtain a trade-off between response time, damping and control effort. This second step can be performed by trial and error.

Some additional points:

The main idea in LQR control design is to minimize the quadratic cost function of int(x^TQx + u^TRu)dt.
It turns out that regardless of the values of Q and R, the cost function has a unique minimum that can be obtained by solving the Algebraic Riccati Equation(ARE).
The parameters Q and R are the design parameters to penalize the state variables(x) and the control signals(u).
The larger these values are, the more you penalize these signals.
Choosing a large value for R means to try to stabilize the system with less (weighted) energy. This is often called expensive control strategy.
Choosing a small value for R means you don’t want to penalize the control signal, often referred as cheap control strategy.
Similarly, choosing a large value for Q means to try stabilize the system with the least possible changes in the states and large Q implies less concern about the changes in the states.
Since there is a trade-off between the two, we keep Q as I (identity matrix) and only alter R.
A large R can be chosen if there is a limit on the control output signal, viz. large control signals introduce sensor noise / cause actuator’s saturation.
Quiet often, in tactical missile system design, required power may not be adequately available from the system due to stringent constraints in power, space and volume requirements.

SpaceX Booster Landing | Pic Courtesy : https://julienpascal.github.io

SB | Nov 22, 2020