What is Energy?

Energy is the capacity to do work. Scientifically, there are two main categories of energy: potential energy and kinetic energy. Potential energy is the energy you get from the mass of the object and height. The higher you go, the more potential energy you have. Likewise, the heavier an object, the more energy it carries. For example, if you drop a rock on your foot from 6 inches, it wont hurt that bad. But if you drop it from 6 feet, you will probably break your foot. This is because the 6 foot rock had more energy to break your foot. What about when we move? This is what kinetic energy is: the energy from moving. If a car hits you going 1 mile per hour, you can probably walk away just fine. However, if that same car hits you going 100 miles per hour, you will probably die. Likewise, heavier moving objects also carry more energy. If I throw a pebble at a window, it probably wont break. If I throw a heavy rock at it at the same speed, it will probably break.

For something to get to space, it has to sit on top of a rocket. This rocket will of course end up traveling very fast at thousands of miles per hour very high in space. Of course, this means that we would have to use a lot of energy to get anything to space. Depending on how you calculate it, getting 1kg into low earth orbit(LEO) takes about 100MJ of energy. To compare, this is about $3 of electricity. But wait, if it only takes $3 worth of energy to put 1kg in LEO, why does space travel still cost millions of dollars? This is because the have to launch the weight of the rocket itself, which is extremely heavy. Typically, what makes it to orbit is less than 10% of the weight of the rocket!

September 8, 2015September 8, 2015 by russellphd Categories: LearningTags: energy, rocket science Leave a comment

The Perfect Rocket (Calculus based)

Over 100 years ago, Konstantin Tsiolkovsky, father of modern rocketry, derived an equation that would help lift humanity into the heavens. This is his famous rocket equation.

Newtons second law is F=ma. This can also be written intFdt=ma=dp/dt. The final speed of the rocket will be determined by the initial mass of the rocket and fuel, final mass of the rocket, the exhaust velocity, and the gravitational losses.

We will write Newtons second law as -mg=mdv/dt+vedm/dt where m is the instantaneous mass of the rocket, ve is the exaust velocity, dv/dt is the acceleration. and dm/dt is the rate of consumption of fuel. We can now divide by m on each side and multiply by dt on each side. This will result in -gdt=dv-(ve/m)dm. Now set the bounds and integrate dt from 0 to tf, dv from v0 to tf, and dm from m0 to df. This will result in -gtf=deltav +veln(mf/m0) which we can re-arrange to deltav=-veln(mf/m0)-gtf.

Lets examine this. deltav will be the change in velocity, which should be positive. Since mf/m0 is a fraction less than 1, the ln of it will be negative. Multiplying a negative by -ve will yield a positive, which is what we want. Now we take this number and subtract the velocity losses from gravity, which is gtf. This is known as the ideal rocket equation which states that the change in velocity depends on the burn time, exhaust velocity, and mass ratio of an empty to fully fueled rocket. It is called ideal because it assumes no drag and that the rocket doesn’t change direction.

September 6, 2015September 6, 2015 by russellphd Categories: LearningTags: rocket science Leave a comment

Staging: Diet for Rockets

If you have ever watched a rocket launch either in person or online, then you have witnessed rocket staging. Staging is the only way to get the payload into orbit. Why? Even though rockets can generate millions of pounds of thrust, they also weigh millions of pounds. Our current rockets aren’t powerful enough to make it to space in one piece. Staging is really just stacking rockets on top of each other. Once the first stage uses up all its fuel, it just becomes extra weight. And when a rocket is usually a few hundred feet tall, that is a lot of weight. After the first stage separates, it falls back to Earth and the second stage ignites. This is advantageous because the upper stages already start out at a few thousand miles per hour. That’s all it is. Staging is just simply a way to get rid of extra weight.

August 26, 2015August 28, 2015 by russellphd Categories: LearningTags: rocket science, rockets Leave a comment