Rocket Science — Basics — Part 1🚀🧑🚀
Rocket science have grown leaps and bounds in the 21st century with many private players like SpaceX and public players like NASA, ISRO compete to reach and explore other planets, moon and even space tourism (Blue Origin)😇.
It is a very fascinating and super cool field and with the advent of AI and Robotics, it is soon going to be a trillion dollars industry. People even talk about nuking the mars atmosphere and make people move to mars.
A century ago, no one would have thought about having a space station, sending robots to mars (Mars Rover), sending miniature satellites, sending man to space, sending even a dog and even a car to space.
In this series, we will start going deep into some basic physics concepts and then slowly move towards complex ideas that make up the rocket science. Let’s start this wonderful journey.
Position — Location of a vehicle in a particular reference frame. Let’s say that we have a lane following robot in a frame of 100 meters. Now, position of the robot is at starting point (say 0m). If the robot moves 10 meters, the position will then be 10m point.
Velocity — The rate of change of position with respect to time. If the robot’s position changes from zero to 10 meters in 1 minute, then the velocity of the robot is 0.166 m/sec (10/60). Velocity is obtained by taking first derivative of position with respect to time. The unit of velocity is m / sec.
Acceleration — The rate of change of velocity with respect to time. Say we are climbing a mountain in a car during uphill the acceleration needs to be high which is also called as positive acceleration (e.g., high velocity in normal bends and low velocity in hair pin bends). Acceleration is obtained by taking the derivative of velocity or second order derivative of position with respect to time. The unit of acceleration is m / sec².
Vector — Vector is a two dimensional entity (magnitude and direction). Consider two points A and B at a certain distance of 25 miles. When a vehicle moves from point A to B, we say vehicle is moving in east direction or west direction to reach a distance of 25 miles. Here east or west is the directions of the vector and magnitude is 25 miles.
In the above diagram, we can tail and head are the end points. They are at a certain distance (magnitude). They have a direction and you can go from tail to head or head to tail. Above depicted one shows 2D vector in which directions are North, South, East and west. We live in a 3D world and rocket science uses another vector direction as ‘UP’ also known as vertical direction. Even gravity is a vector that has vertical direction.
Let us analyze the three sections above.
- The person is at start of the reference frame. This is position A. He starts moving towards end of the reference frame. This is position B. The distance he covers at in a specified time frame while moving in a direction is velocity. He starts to move quickly from the position A and B. This change in velocity over time is acceleration. This is also called as positive acceleration.
- In the second section, the person moves slowly from position A to B. This is called as deceleration. The velocity is positive and acceleration is negative.
- This third section is interesting. We knew that velocity is a vector that means even if the bee in the picture moves at a constant velocity, it is again accelerating because of change in direction.
Now, you should have thought like, what is the difference between speed and velocity? 🤔The answer is velocity is distance traveled per second in a particular direction and speed is just distance traveled per second. So, we can say that velocity is a vector and speed is a scalar (only magnitude and no direction).
Ballistic Motion — We saw that gravity is also a vector acting in vertical direction. Imagine this scenario, A shot put athlete throws the iron ball into the air. If you could watch closely, he wouldn’t have thrown the ball in horizontal or vertical direction but at an angle to get the distance. There are two phases here. First, the athlete gives enough acceleration to the ball thrown from his hand. Once the ball is in the air, this phase is called as Ballistic Motion because, the only force acting on it is gravity. In the horizontal axis, the velocity would remain the same but the vertical axis will be controlled by the gravity. Also, for the fact that airplanes and parachutes does not follow ballistic motion because of the lift from the wings balances the airplane from gravity to maintain at the same horizontal direction.
Same for parachutes, the drag makes the chute to come down in a slow pace.
Below is a simple depiction of ballistic motion. Here the bullet from battle tank is analogous to shot put.
Sometimes, rockets also follow Ballistic motion not entirely but in phases. The first phase is not ballistic. It is the acceleration / thrust given by the engine to make the rocket go in upward direction. Once the rocket reaches the upper atmosphere, the engine will be dropped and there is only force acting on the rocket is gravity. This phase is ballistic. The last phase resist the high speed fall due to gravity by using the drag from the parachutes and makes it not ballistic.
Newton’s First Law — You may have had question, how do acceleration works? It is because of force applied to the vehicle. Newton’s 1st law says An object at rest remains at rest and an object at motion remains at motion unless acted upon by an unbalanced force.` . This law is also called as law of inertia. What Newton says is, vehicle will not move unless a force is acted upon it. Also, when a vehicle is in motion in a straight line, it will not stop and move at a constant velocity unless again a force is acted upon it, for e.g., driver changing the direction through steering. The resistance to these changes is called as inertia.
Newton’s Second Law — Newton’s second law states that the acceleration depends upon mass of the object and the force acting upon it. Almost every one in their higher studies would have learnt the famous equation f = m * a`. We can see from the equation that force is directly proportional to mass and acceleration.
We shall explain it with an example. In the picture, you can see that the force applied ‘F’ is similar to both vehicle. You see that the acceleration is slow for heavier vehicle with high mass than the one with low mass. The same thing applies to rocket science. Rockets carrying only small satellites tend to be lighter than the ones that carry people to space.
Newton’s Third Law — When an object exerts force on another object, the second object will exert same and opposite force on the first object.
Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. Since forces result from mutual interactions, the air must also be pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards).
From the above figure, we can see how thrust works on rockets that helps the rocket to propel upwards during the ignition. The stuff coming out of the rocket during ignition makes the rocket to go in opposite direction.
Momentum — Momentum is product of velocity and mass. We know that velocity is a vector (speed with direction) and mass is a scalar. So, their product is also a vector. People often use mass and weight interchangeably. Weight = mass * gravity. You can say change in momentum is force. You can ask a question like ‘why momentum is useful? we have force right?’. To answer that question, consider a car and heavy truck moving at the same velocity of 100 mph. Their momentum is very different because of their mass. If they both collide on to rock force exerted by them will be very different. We also say, small things moving fast will have same momentum as a big things moving slow. It makes the object to continue moving. Also, force (gravitational force) exists for a stationary object but not momentum. Force is an external stimuli or action on an object that makes push or pull. Momentum is what makes the object in motion to move.
Relativity — Some some facts,
We all know that earth rotates itself and around sun’s orbit in our solar system. The earth rotates itself in about 23.933 hours. We may feel that we are not rotating as the earth rotates. But from the center of earth, we are rotating. But the question is with relative to what? The radius of earth is 6371 km in equator from the center of earth. Since, we are on the surface of earth, treat it like we are rotating around the circle. We know that the circumference of the circle is 2*pi (3.14) *radius / time (23.933). So, we will be rotating at the speed of 1,672 km/hour from the equator. So, if you are living above or below the equator and want to know how fast are you moving relative to center of earth, the radius of earth would be different because the circumference of the earth above and below the equator would vary. For to get the speed of how fast are you moving from your location, you need to multiply 1,672 km/hour * cosine (your latitude).
Thrust — We now know that force is change in momentum. Thrust is a force that makes the object move forward and it is opposite to drag. Thrust is used to overcome the drag of an airplane, and to overcome the weight of a rocket. In rockets, it is a mechanical force generated by the propulsion system in the engines by producing a mass of gas making the rocket to move upwards. The equation of thrust is T = (mass flow rate) * (exhaust velocity). In rockets, in order to take more load, they tend to increase more exhaust velocity by adding more engines. For example, SpaceX’s falcon-9 have 9 engines and falcon-heavy contains more than 20 engines.
In the next part, we will dive deep into more of thrust and rocket equation.
Thanks for reading!!!
