Blog

For Best Experience, View on Desktop/Laptop

String Pulley Constraints are very commonly used in high school physics and mainly comes under Newton’s Laws of motion (NLM). This concepts are frequently asked in exams such as JEE Mains and even JEE Advanced !! 

Time becomes an important factor in such competitive examinations, especially JEE Mains. 

Index : 

1. How to apply the trick
2. Easy examples
3. Moderate-Difficult Examples

1. How to apply ?

Remember the rules :

• Only one string at a time

 

• On the string –> ‘minus’ sign (Recall the -ve charge sign on ions from chemical bonding because that’s how I kept it in my mind)

 

• Away from the string –> ‘plus’ sign

How to use it in problems ? (Have patience…Lot of things will get easier for you)

Steps :

1.  Mark the points on the string such that whole string is covered (starting to end)
2. For pulleys, mark for the points- where the string first comes in contact with the pulley (pt 2) and where the string leaves the contact with pulley (pt 3)
3. Now start from one end,( say pt1) . The relation will be as follows :

                                    -Va + 0 + 0 +Vb 

Why ?

-Va because Va is going on the string

+0 because pt2 is connected to pulley and pulley is at rest

+0 pt3 is connected to pulley and pulley is at rest

+Vb because pt4 is connected to block B and Vb is going away from the string

      4.  Finally equate everything to zero

                                    -Va + 0 + 0 +Vb = 0

                                        Va  = Vb

2. Easy Examples :

Q.1 Write down the constraint relation between velocities of block A and block B by referring the image of setup alongside.

Solution :

Constraint relation can be written as : (Applying trick, starting from block A)

Q.2 Write down the constraint relation between velocities of block A and block B by referring the image of setup alongside.

Solution :

We start from block A (Just move along the string one-by-one) :

Q.3 Write down the constraint relation between velocities of block A and block B by referring the image of setup alongside.

Solution : Let’s start from block A

Moderate to Difficult Examples :

Solution : Part(a) –

 (Lets start from the point near the rigid support)

Part (b) :  Again we start from the point attached to the rigid end 

(Note that the derivative of velocity wrt time is acceleration. So once you get the velocity constraint relation, just taking its derivative wrt time will give you the constraint relation for accelerations)

Q. Give the constraint relations between block A and block B in the setup shown in image alongside 

Solution:

Recall that this trick can only be applied to one string at a time !

So, we take velocity of pulley X as Vx as shown in figure below and we start applying trick from block A end

But, we need relations between Vb and Va

Q. Next Example :

Solution : 

As we discussed, only the velocity component along the string are to be considered

Starting from star (*) mark

Same approach, mark all the points  on the string first

But, we know that the value of Vb (RHS) from the above expression is always going to be positive since 

So, the assumed direction of Vb (upwards) is also correct !

Conclusion :

So, over here, we end this article. Do practice some more string pulley constraint problems using this trick. But also don’t miss out on the actual procedure. Tricks should always be your secondary option !!

We will keep coming up with more such articles to help you in your preparation !! Thank you for your time.

All the very Best !!

For Best Experience, View on Desktop/Laptop

#RC Airplane Series – 4

Now, we enter into the electronics side of the RC Airplane . In this article, we discuss about ‘How shall we exactly choose a motor for our RC Airplane ?’. This is one of the very crucial step because your electric motor and propeller combination in RC Airplane does the work similar to the fan engines in real RC aircrafts. This motor + propeller combination is responsible to provide the necessary ‘thrust’ required.

Topics Covered :

• Electronic Components in RC Airplane
• Deciding the type of flight
• Choosing the motor – Motor Terminologies & Procedure 
• Choosing the appropriate Propeller
• Example for Better Understanding

Just to clarify !

I am sure, you will have a question that, if in last article I asked you to refer a plan from online sources, then why not copy their electronic components as well. 

There’s a problem in that !!

Many students/hobbyists aim to participate in various aeromodelling competitions. And when there’s a competition, there are some rules/constraints which we need to follow. Basically, this is where, it’s important to know how to exactly model the aircraft (design part + electronics part) OR else if there were no rules, there are so many resources about ‘How to make an rc airplane ?’. So , everyone would just copy them !!

And apart from this, the joy and the interest which u generate in the field of aeromodelling once you try to understand these concepts is unmatchable !!

1. Electronic Components for RC Airplane

• Motor + Propeller combination
• ESC (Electronic Speed Controller)
• Battery
• Servo motors
• Receiver
• Connectors

Here, we are just naming the electronics needed to drive an RC plane. We cover the motor and propeller selection in this post. In the upcoming articles, we start discussing each one in detail. We are going to keep everything to the point but discuss the important and necessary things in detail.

2. Deciding the Type of Flight

In order to select motor, We need to first decide the type of flying which we need from our plane. 

And based on that, we have a term called ‘Thrust-to-weight’ ratio. Also known as ‘TWR’ or ‘T/W’. Based on the type of flying we choose, we need to fix our TWR accordingly. To elaborate,

• So, the first step for motor selection will be to be fix the TWR for your plane.

3. Choosing the motor

We need to follow a specific procedure in order to get therequired motor. Refer to the following flowchart for that :

Step – 1 :

In the previous article, we learnt to calculate the the ‘model weight’ (i.e. only the design part). Now, we need to first assume the electronic components and calculate the ready-to-fly weight. It means that the plane is fully ready (design + electronics) to fly and the weight of the plane at that point of time is called here as ‘ready-to-fly‘ weight. 

Assuming electronic components :

• Most of the components (motors, ESC, battery, etc) have their weight within a fixed range. And note that, you DON’T have to be very specific and exact for this. We need an approximate weight of aircraft. 
• Refer the product’s website and check the specification section to get the weight
• This part will become more clear once you have the knowledge of all the components used in RC plane. I have attached a file below as an example to demonstrate the whole process

Note : If you are using landing gears for your plane instead of hand takeoff, you need to include that weight as well.

Step – 2 :

From previous section, we have fixed our TWR. Use this value to calculate the thrust. This will be the thrust required to achieve the required TWR for aircraft.

Step-3 :

It is advised to use BLDC (Brushless DC motors) due to : 

•  High Efficiency

 

• Longer Life span

 

• Better speed control

 

• Prevents over-heating

 

Q. What is RPM of motor ?

The number of revolutions (one complete circle) that the motor rotates in one minute of time is known as RRM of motor. RPM stands for Revolutions per minute. For e.g. 2500 RPM implies the motor rotates 2500 times in one minute. So basically, RPM is the unit of ‘angular velocity‘ 

Q. What is kV of motor ?

kV rating of a motor gives the idea of : At what RPM will the motor run when a certain voltage is applied. For e.g. If we have a motor of 1000kV and lets say the safe operating voltage range is 5V-12V. So if I am operating the motor at 5V, the motor will run at 5000 RPM , while, if I operate it at 12V, it will run at 12000 RPM. 

Based on this, we can formulate kV rating as :

How to choose kV of motor ?

Recall the type of flying which you chose. 

Now, once the motor kV is fixed, then go to the online electronic stores’ website and search for the motors of the calculated kV which are able to provide the required thrust. A thrust value greater than required is OK !

(Look through the specifications/description section of the product’s page for thrust value)

 

Step – 4 :

The propeller is another very important factor to consider since this fan like thing is the most responsible to generate the thrust required for our airplane. Check the datasheet or the recommended propeller size for the selected motor

4. Choosing Appropriate Propeller :

Working :

The propeller basically ‘pushes’ the air backwards so that the reaction force is acted on the propeller makes it move in forward direction. The working of propeller is a simple application of Newton’s third law.

Dimensions of Propeller

Diameter : The end to end length of the propeller. Mainly responsible for the rotary motion

Pitch : It is the distance covered by propeller in forward direction when one revolution is completed. Pitch is mostly responsible for the translatory motion of aircraft. Pitch is connected to the speed of the aircraft.

Notation : Example : 10×4.5 propeller implies diameter = 10 in & pitch = 4.5 in

How to select a Propeller ?

Again recall the type of flying chosen for your aircraft. Based on that, we need to fix the size of the propeller. 

Consider the below example (pdf file) for better understanding

5. Example :

A problem statement has been given (Like a competition) and based on the constraints, the procedure to select a motor has been given. Go through it thoroughly to get a complete understanding. (We are assuming that we chose some plan and on calculating the model weight of airplane, it came out to be 250 g.

DOWNLOAD

example for motor (1) (1)

Enjoy Learning !!

RC Airplane Series – All Articles  (You are at Part – 4 !)

• Part-5 (Next) : How to choose LiPo Battery ?
• Part-6 : ESC Calculations and Electronics Connection
• Part-3 (Previous) : Designing your Airplane !!
• Part-2 : Understanding the control surfaces !
• Part-1 : What’s in the Wings ?

For Best Experience, View on Desktop/Laptop

#RC Airplane Series-3

In this article, we are going to discuss about designing the plane and after which in the next article (RC Airplane Series – 4), we discuss how shall we exactly select a motor for our RC Airplane. There is proper procedure for motor selection and is one of the important step in RC airplane designing. 

Topic :

• Designing the Airplane

Designing the plane :

This RC Airplane Series is going to be for ‘Beginners’ or for the ones who are not much experienced in this field but just want to know the basics of RC Airplane. Due to this reason, we avoid getting into the details of the analysis. The actual Analysis includes a lot more like: Aerofoil selection through XFLR software, ‘Ansys Fluent’ software for model analysis, etc. 

But for now, we keep it very simple  !!

For beginners, a suggestion would be to use online available plans in order to develop your aircrafts. By readymade plans, I mean that , you can get information with figures about the dimensions of fuselage, rudder, elevator, horizontal stabilizer, vertical stabilizer and all…..

Let’s take an example for now : 

I have considered this below shown plan as an example. You will get a lot of such similar plans online on various youtube channels and website. 

The one which I am using below is from the website :  https://www.rcpano.net/2020/01/28/fpv-airplane-making-rc-airplane/ . I have modified the plan a bit for simplicity ! And also this website does have a lot of more plans. Do check it out !!

• A good website to consider for designing the airplane : https://rcplanes.online/design.htm

DOWNLOAD

Design Plan example final

• As shown in the above flowchart, after selecting a plan, we need to choose the material which we are going to use.

In this case, I decided to go with styrofoam and after which I searched for the density of styrofoam on the internet or you can also get it in the ‘specifications’ section from the website page using which you are going to buy it.

– The density came out to be 60 g/L.

• Then, We calculate the mass of the seperate component using the density formula.

 

•  For this, first calculate the Area first. Area can be calculated by breaking the figure into simple geometric figures (rectangles, triangles, trapezium, etc) . Then, calculate volume and then calculate mass using density formula.

Conclusion:

This was a very short article on the designing of RC Airplane. We will for sure discuss this topic again at an Advanced Level. But for now, for the Beginners stage, lets keep it simple and easy to understand !! After all that’s our main goal.

Enjoy Learning !

RC Airplane Series – All Articles  (You are at Part – 3 !)

• Part-4 (Next) : Motor and Propeller Selection
• Part-5 : How to choose LiPo Battery ?
• Part-6 : ESC Calculations and Electronics Connection
• Part-2 (Previous) : Understanding the control surfaces !
• Part-1 : What’s in the Wings ?

For Best Experience, View on Desktop/Laptop

In this specific article, we are going to learn about the working of GPS. In the upcoming articles, we will be dealing with the interfacing of of GPS module with the Arduino. I feel that it’s important to know the working of the module which we use in our project instead of just learning about ‘how to make the module throw it’s data values at us”…..

GPS stands for Global Positioning System and is mainly used to locate the exact location of the receiver with the help of data which it gives (out of which most important is Longitude and Latitude coordinates)

Working :

– The working of the GPS module is based on the communication between the satellites and the gps receiver module.

   For locating the position of a place on earth, we need several parameters like Longitude and Latitude (2-D) and an extra Altitude (for 

    3-D) 

– To locate the position, in GPS, we have something known as Trilateration.

 In 2-D, 

 we need a total of 2 satellites (say S1 and S2 here). We    are suppose located at point O and we need our location through GPS.

                                                                                   Fig. Determination of position in 2-D

– This implies that, O is somewhere on the region common to circle-1 and circle-2. This means it lies in the points of intersection of circle      1  & 2 (here O and P).

– To decide between O and P, we take into account the circle-3 which is the earth surface itself. All the 3 circles intersect at O (therefore, P is eliminated) and hence we obtain the position of a GPS receiver in 2-D.

In 3-D,

– We need a total of 3 satellites for locating position of GPS receiver

Here, we need to consider just the spheres instead of circle. 

For quick overview,

But, there exists a problem of time delay, since the satellites have accurate atomic clocks while the GPS receivers uses the clocks which are installed in mobile phones.

But since all the satellites use the same specifications for atomic clock, the ‘time offset’ is the same. Even error of microseconds can give an error in kilometers !! Hence we use fourth satellite (S4).

As we discussed earlier, that we need the distance ‘d’ for locating the positions of satellites. 

• But HOW DO WE EXACTLY DETERMINE ‘d’ ?

The ‘radio signal’ which is sent, it carries 2 information mainly :
          – Exact time when it was transmitted (t1)
          – Position of satellite

Now the receiver receives the signal at time t2 (say) :

The below is about What happens inside the GPS receiver (mainly a topic of discussion for our next Article)

Keep Learning !!

For Best Experience, View on Desktop/Laptop

Have a look at question once again : QUESTION

This question is like an ultimate test of comprehension. The Key is to extract the necessary information from the question. This quality is very much essential for the competitive exams like JEE Advanced. 

The Solution is divided into 2 parts : Part(a) solution & Part-(b) solution

In part (a), the explanation to the maximum effort chart is covered. Through this, the velocity-time graphs are explained and various topics like it’s behaviour, how to calculate displacement from v-t graph, etc has been covered. 

In part (b), we try to predict the result of the game based on some time calculations. Also, we try to analyze the Last ball situation in detail

At the very end, we try to highlight the parts in the question which were important to be noted since that information had to be used while solving the problem. And also, not all information given in the question is relevant. Just pick the important ones and Ignore the Rest

Topics Covered :

• velocity-time graphs (Kinematics)
• Time taken by charge in magnetic field
• Nature of the path covered by charged particle in magnetic field
• Use of F = q(v x B) for direction

Solution :

DOWNLOAD

Final-Solution-Cricket-Problem-4 (1)

Keep Learning !

For Best Experience, View on Desktop/Laptop

# RC Airplane Series-2

In the previous part (RC Airplane Series -1) , We learnt about the wings of the aircraft and what is the reason behind the generation of Lift for the airplane. Now that we have learnt to take the airplane into the air, it’s time to control the aircraft. So, in this part, we are going to learn how are the control surfaces used in order to control the aircraft properly.

TOPICS TO BE COVERED :

• What are different control surfaces in aircraft ?
• Different dimensions of movement 
• Aileron
• Elevator
• Rudder
• Flaps

1. Different Control Surfaces

For the controls part, we have them divided into two parts : Primary and Secondary Control Surfaces

• Primary : Ailerons, Rudder, Elevator

           (These are the necessary ones! Like Air, Water and Food for us)

• Secondary : Flaps 

           (These are the extra ones which help in controlling the aircraft more precisely) In the Secondary part, we do have some more surfaces, but for basic RC planes, Flaps are enough 

                                                                          Fig. Positions of Ailerons, Rudder & Elevator

2. Dimensions of Movements :

There are basically 3 axes about which movement of the aircraft happens :

• Longitudinal : It goes from nose to tail of the aircraft
• Lateral : It goes from wingtip to wingtip and is perpendicular to the longitudinal axis
• Vertical : It is mutually perpendicular to both, longitudinal and lateral axis

                                                                               Fig. Movements exhibited by an aircraft

• Pitch : It is the rotational motion of the aircraft about the Lateral Axis (Nose – Up and Down)

• Roll : Rotation about longitudinal axis is Roll. During this, the aircraft tilts its wing up and down

• Yaw : Rotation about vertical axis is Yaw. Basically, moving right and left in the plane itself

                                                                                              Fig. How it exactly happens?

3. Ailerons :

– Ailerons are the control surfaces situated on the wings and are responsible for the ‘Roll’ motion of aircraft.

• There are mainly 2 types of Ailerons (in Trainer Aircraft mostly) : Strip Aileron and Normal Ailerons

           Strip Ailerons are the ones which span over the entire half wing and have a width = 1/8 of chord length

           In normal ones, the length = 1/4 of wingspan and are situated towards wingtip and have a width = 1/4 of chord length

Working of Aileron :

For example, we need our airplane to roll towards right. For this to happen, the Right Wing should get lowered while the Left wing should be lifted up (when viewed from tail)

I will try to explain this in a very simple manner. Just remember that,

                                                                         “Obstruction causes velocity to decrease“

(This is applicable for all control surfaces)

                                                        Fig. Right Aileron is raised up while Left Aileron is lowered down

• Now, we want to Roll our aircraft towards right. So we control the Aileron with the help of transmitter (in case of RC Airplane), steering wheel in case of real aircrafts. 

          On giving the signal, the right Aileron is raised while the left Aileron is lowered down. For the moment, let’s focus on the Right                      Aileron. The control surface here as been moved up & now, this causes Obstruction for the Air !!

• Because of this obstruction, the velocity of air in the upper part decreases and hence Pressure in the upper part increases. (refer RC Airplane Series-1) and this causes the Right wing to go down and left wing goes up and as an overall effect, we get the Roll towards right.

4. Elevator :

Elevator is connected to the horizontal stabilizer. The elevator is responsible to control the pitch of the Aircraft.

Working of Elevator :

Consider an example where we need to pitch up the plane (make the nose up !). In this case, when the signal is given, the elevator is deflected upwards. Now, again the air flow in the upper region feels an obstruction which lowers the velocity of air in upper region. This causes the Pressure in the upper region to get bigger. 

This results in the ‘pressing‘ of the horizontal stabilizer downwards. Due to this the nose of the aircraft (front part) rises up.

(Just consider a pencil and hold it somewhere

                                                                                       Fig. Elevator is deflected upwards

• The process is the same for all, whether its the aileron, elevator or the rudder

Consider an example of pencil. It’s CG (center of gravity) is marked. So when we apply a pressure on the back side (FigP(a)), the front part (part which is ahead of CG) rises up (which we say here as ‘pitch up’) as it rotates about the lateral axis passing through CG (FigP(b))

FigP(a). Pressure is applied at the back end of pencil                                    FigP(b). Result of the application of pressure (Nose Rises) 

5. Rudder :

Rudder is attached to the Vertical stabilizer. It is responsible mainly for the Yaw motion of the aircraft. Basically, Yaw is like moving right and left in your plane itself !

Working of Rudder :

Consider that we need to move shift to left while being in the plane of the aircraft (i.e. just try to give nose a different direction)

• When the signal is given such that you want your nose of airplane to move towards left, then the rudder also deflects towards left. Now the rudder acts as a obstruction to the airflow on that side. Hence velocity decreased. Therefore, pressure increased. The higher pressure causes the front part to move to left (in the geometric plane)

                                                                                                           Fig. Rudder 

6. Flaps :

Flaps are the Secondary Control Surfaces which help the pilot to have a stronger control and stability over the airplane. Flaps are situated besides the Ailerons. Sometimes, the Ailerons itself work as Flaps as well (in case of single servo for each Aileron **). In this case, we call those control surfaces as ‘Flaperons’ (Flaps + Ailerons)

You must have hear pilots saying “FLAPS ON !!” or “FLAPS DOWN”. This tells that the Flaps are to be deflected downwards. 

                                                                                                        Fig. Positioning of Flaps

We are very well aware of the Lift generated because of the Flaps getting deflected downwards. (Same as Ailerons getting deflected downwards) but there is an important factor to consider, which is ‘DRAG’

DRAG :

– There is lift, but there is also DRAG developed due to downward    deflection of flaps. Since, due to this, the contact between the airflow and the surface gets broken.

– This Drag causes the wing speed to decrease

• For Landing, we need the plane to be slow moving since ofcourse it’s easier to handle a slow moving car than an fast one. So the drag component takes care of reducing the speed of aircraft while on the other hand we also have the Lift generated which combinedly gives a slow and controlled descent.

 

• From takeoff point of view, we need Lift to be generated at lower speeds itself and hence Flaps are essential in this case as well.

Note that : “FLAPS UP” implies the retracting of flaps to the original position (no deflection)

The amount of deflection can be controlled based on the need with the help of control stick !!

Conclusion :

Through this article, We discussed about the Controlling of the Aircraft. Go through it slowly and try to visualize by yourself. You will definitely get it. In this Series, we will keep going step by step and gradually make the whole basic RC Airplane model. I hopw you enjoy this Series !!

Keep Learning !!

RC Airplane Series – All Articles  (You are at Part – 2 !)

• Part-3 : Designing your Airplane !!
• Part-4 : Motor and Propeller Selection
• Part-5 : How to choose LiPo Battery ?
• Part-6 : ESC Calculations and Electronics Connection
• Part-1 (Previous) : What’s in the Wings ?

For Best Experience, View on Desktop/Laptop

Commentary: Oh! we are witnessing the most exciting final ever. Just look at the score board mate! The crowd is going crazyyy at the Wankhede stadium. For now, We are having some discussion going on between captain and umpires and seems like they have been given a new ball for the last ball of the match.

 Fig. Scoreboard Situation

Commentary: Till the game resumes back, we show you the stats of the players as well as the info of the Wankhede stadium.

Striker :

• Age : 26
• Right handed batsman
• Average : 25.5
• Highest : 67(36)
• Maximum effort chart: (‘v’ in m/s and ‘t’ in s)

                    – Nature of graph : Straight line

                                                                                  Fig. Maximum effort chart for Striker

Non – Striker :

• Age : 27
• Right handed batsman
• Average : 23.2
• Highest : 56(23)*
• Maximum effort chart: (‘v’ in m/s and ‘t’ in s)

– Nature of graph : Parabolic  (It’s a curve involving some parabolas)

(This tells how a player runs between the wickets when he performs at his maximum potential and it’s a pre-recorded data)

                                                                                      Fig. Maximum Effort Chart for Non-Striker

                                                                                    Fig. Circular Shaped Wankhede Stadium

Commentary : Okay, So after a long wait, we are all ready for the play to begin !

What exactly happened?:

**The half portion of the ground (not containing the striker) is introduced with an magnetic field of upwards direction (seems as if it comes out of the ground) having magnitude 0.54 T (tesla)

                                                                                                 Fig. What exactly happened ?

Regarding the New Ball

• Mass : 160 g
• Charge : 164 mC
• Colour : White

Commentary :  Man, I am just out of words…Just picth the ball towards the batsman, I can’t wait anymore.

 So, here we go Guys !….

Match Resumes !!…It’s the last ball now

Commentary : Oh, what a excellent toe crushing yorker just ahead of the stumps, to which batsman replies with a flick towards the leg side. The ball is running towards the boundary along the ground…………….

Commentary : Both the striker and the non striker have started running with their maximum efforts across the pitch, trying their level best !!

                                                                                                Fig. Final Last Ball Situation

In the figure above,

v is the velocity of the ball just after the impact with the bat and theta is the angle which the ball makes with the center pitch line.

Commentary : Hey, watch out! What’s happening in here, I just can’t believe what’s happening, Also, with me, my co-commentator friends, audience as well as the players themselves are just completely astonished.

---

Question Parts :

(a) Why are there only 3 regions in the Maximum Effort Chart of both, striker and non-striker. Are you able to verify, if the                    velocity-time graphs are correct?

(b) In this scenario, can you predict What’s the result of the match!? Also, if you want, you can give some nice commentary as well to describe the situation completely.

(Assume ball to be point mass; there is no friction between ground and the ball )

---

 Some points from my Side :

I feel that this problem is completely comprehensive based. Hint which I can give is that, Try to Extract the necessary information from the comprehension.  These problems are designed to make you enjoy the subject, enjoy the process while solving. No one is there here to reduce your marks, So solve it without any hesitation !!

“I want you to be in that atmosphere as if you are an spectator seeing this match going on in front of your eyes“

Solution has been uploaded !! – SOLUTION 

All the very Best !!

For Best Experience, View on Desktop/Laptop

https://www.youtube.com/watch?v=SnWEVEGm9ss

# RC Airplane Series – 1

RC Airplanes are fun to make and really a nice beginning step to understand Aeromodelling. This series aims to cover the aspects necessary for the modelling of RC aircraft and this will teach you can you design your own RC airplane based on your constraints/requirements !!

In this article, we are going to discuss about one of the most important aspect of the airplane, i.e. Wings.  

TOPICS TO BE COVERED :

•  What’s the principle behind this ? (Bernoulli’s principle)
• A small experiment with 2 A-4 sheets
• Aerofoil shape explanation (How does it help ?)
• Some Terms (About Wing tip, Aspect Ratio, etc.)
• Wingspan is Everything !

1. What’s the principle behind this ?

So, in order to understand about how the wings help to generate the lift, we need to know about the Bernoulli’s Principle. It states that:

” The sum of the pressure, kinetic energy density & the gravitational potential energy density at a point in streamline remains constant “

The mathematical equation for this looks like :

All this looks a bit complicated, isn’t it !?

But the only thing which we require from this equation, to understand the reasoning is that :

“As pressure increases, velocity in that region decreases & vice versa is also true”

2. A Small Experiment….!!

What do we need ?

• A-4 sheets x2
• A quiet room (FANS OFF please !)

Procedure :

1. Hold the 2 papers vertically with each paper in each hand.
2. Observe that nothing happens here
3. Now, blow air with your mouth into the region B (region between the 2 papers)
4. Observe what happens !!

The step-by-step procedure & it’s result is shown in the figure below  (  !! Not that good at drawing, but pls manage !! :))  )

Fig. A-4 sheets experiment procedure

Why did this exactly happen !?

Note : The region between the 2 sheets is named as ‘B’ while the region except B is called ‘region A’ (i.e. the surroundings to region B)

1.  Initially, the pressure in region B and A is the same since the velocity of air is same everywhere
2. Now, we blow air into the region B (between the sheets). This causes the velocity of air in the region B to increase in comparison to its surroundings (region A)

       3. Now, by Bernoulli’s principle we can derive the conclusion that, 

        4. Because of this, the sheets are pushed towards each other by the surroundings due to the relative higher pressure of the                              surroundings than that of the region B

3. Aerofoil Shape !

Now, to use the above results into an application, we have a shape known as ‘Aerofoil’. We can describe this shape by its upper and the lower surface. The upper surface has a curvature known as ‘Camber’ and the upper surface has larger length as compared to lower surface which is done purposely.

To understand the shape, have a look at the figure below. (I will try improving my drawing skills !!)

Fig. Aerofoil shape explanation

       1. Consider points A and B. At point A, the streamlines diverge to pass over the aerofoil and then meet up again at point B. Now, we                that the flow is streamlined and laminar, the air particles flowing over the upper surface have to keep up with the air particles                      passing under the lower surface.

      2. We already know that the upper surface has greater length as compared to lower one. Hence to meet at B at same instant, the                     velocity of air passing over the upper surface has to be greater since it has to cover more distance in the same time.  

            Hence, 

But, by Bernoulli’s principle we know that, 

This is how lift is generated !! & we can see that the aerofoil shape has a lot of role to play in this.

4. Some terms you will need…

• Leading Edge & Trailing Edge :

               – Leading edge is the foremost edge of the wing. This is the first part of the wing which comes in contact with the air flow. It is                          mostly rounded in order to have a smooth airflow over the wing.

               – Trailing edge is the rearmost edge of wing. This is the portion where the airflow leaves the wing. This edge of the wing includes                    the control surfaces with Ailerons and the Flaps

• Chord :

               – The distance (straight line length) between the leading edge and the trailing edge of the wing is called ‘chord’.

               – It is not always that the wing will be rectangular, so, in that case we consider the ‘mean’ chord length which can be calculated                       based on the shape of the wing.

               – For rectangular wing, the width of the rectangle becomes the chord.

• Vortex Drag :

                 – Now, this is something which comes as a by-product with the ‘Lift’ which we don’t need and hence we must try to atleast                               minimize it as much as possible. 

                  Fig. explanation : When the air flows over the Wings, lift is generated & simultaneously, wing tip vortices are also formed                                                                which we need to minimize since it consumes fuel, hence dropping the fuel efficiency of plane.

                Why does it happen ?

                  – The wing is an finite dimension part and hence it will come to an end at some point. This is the point which we call as

                    ‘Wing tip’. Just at the wing tips, there is still a high pressure region below and a low pressure region above. This pressure                                difference causes the air particles to execute a rotational type of motion which we call ‘vortex’

Now due to this, 1. The air particles exhibit rotational motion (as we see in the figure)

                              2. But from where do these particles get energy to exhibit this rotational motion

                              3. This energy is extracted from the wings (or indirectly, the part of the fuel is getting consumed to overcome this drag)

                              4. Therefore, we conclude that, the induced drag affects the fuel efficiency of airplane

• Aspect Ratio (AR):

                – Aspect Ratio is defined as the ratio of the wingspan to the mean chord length

                – It is one of the most characteristic of the object (here airplane) and AR for an aircraft is determined based on the work it is                            going to be used for. 

 

                For example,

                      – High Aspect Ratio : Used to have more fuel efficiency for aircraft (due to lesser induced drag)

                      – Moderate Aspect Ratio : Used to get the benefits of both : maneuverability & fuel efficiency

                      – Low Aspect Ratio :  Used to get more maneuverability (ability to change direction)

5. Wingspan is everything !

While designing the RC airplane, the first most important thing which you need to fix, is the ‘Wingspan’ of your aircraft. Wingspan is nothing but the length of your wing (including fuselage width). 

Generally, while designing the RC Aircraft, we have a fixed set of ratios defined which tell us what all dimensions should different parts/components of airplane have.

For examples, we take some ratios like: (We fix Wingspan = 1m)

         1. The fuselage length = 75% of wingspan

                                                 = 75 % of 100cm

                                                 = 75 cm

          2. Now for Trainer Aircraft, Aspect Ratio is 5:1

              hence, chord = wingspan/5

                                      = 100/5

                                      = 20cm

          3. Aileron length has to be 1/4th of wingspan

              Aileron length = (1/4) x wingspan

                                        = (1/4) x 100cm

                                        = 25cm

We can clearly see that in all calculations, somehow or the other, ‘Wingspan’ is getting involved.

There are still many dimensions you can calculate directly/indirectly using wingspan…

Conclusion : 

To conclude this post, we learnt about the basic working principles of wings. Just making an RC Airplane is one thing while Understanding the RC Airplane is another thing. We are going to focus on the understanding part first which will surely make our further work much more easier + the additional satisfaction that we know the reasoning behind what we are doing !! 

Till then, Keep Learning & Enjoy the Process !!

RC Airplane Series – All Articles  (You are at Part-1 !)

• Part-2 (Next) : Understanding the control surfaces !
• Part-3 : Designing your Airplane !!
• Part-4 : Motor and Propeller Selection
• Part-5 : How to choose LiPo Battery ?
• Part-6 : ESC Calculations and Electronics Connection

For Best Experience, View on Desktop/Laptop

Have a look at the problem once again if needed : QUESTION 

Here we have the Solution to the problem : Smartwork > Hardwork !!

The level of the problem is EASY in comparison to the previous 2 problems (Chess OR Physics?   &    Bhelpuri Problem). The problem is mainly based on Electrostatics 

• The problem gets it’s name based on the approach you choose to solve the problem & get the answer. The thing which I want to tell from my side is that, Try to read the problem carefully before starting & most importantly, Observe & Analyze the problem. Just one good observation can reduce a lot of work of yours !!

SOLUTION :

DOWNLOAD

Solution to problem - Smartwork vs Hardwork

All the Best !! and Enjoy Reading the solution !!

Keep Learning !

View on Laptop/Desktop for Better Experience

Problem Description :

An arrangement of several ‘charged’ discs is done such that all of them subtend the same solid angle Ω at point A. This arrangement is shown in the figure below. The discs are charged positively and negatively alternately (starting with positive first). Magnitude of surface charge density of charged discs is ‘σ_o’ .

‘x’ is the distance from point A representing the position (used to actually point out the location of discs). It is given as :

                                                                                          x = nx_o          ….(I)

     where,   n belongs to natural numbers

                    x_o is a constant

Also, similarly the surface charge density (σ) can be represented as a function (for clarity) as :

                                                                                 σ = (-1)^{n + 1} σ_o         .…(II)

Question Parts : 

(a)   when x = x_o , the radius of the disc is 2R_o . Find the function of radius of the disc (R) as a function of x using constants x_o , R_o  

 

(b) The radius of the last disc (for greatest n) in this arrangement is 42 R_o . Find the Electric field at point A due to the whole system. 

(c) All these discs are merged together giving rise to a single disc of ‘some’ pattern. A negatively charged black coloured ink is made to be put over this merged disc. Draw down the final presentation of the disc. (Optional)

Hint : ‘n’ represents the disc number in the arrangement shown in the figure

Enjoy Solving !!

Solution has been uploaded  – SOLUTION