Most spacecrafts use chemical rocket engines to propel themselves around in space. Spacecrafts use chemical rockets because they produce a high impulse, which is the change in momentum produced in a given amount of time. Therefore, these engines don’t have to run for long, since they can generate the needed force to move quite quickly. The energy produced from the chemical combustion is great, but the time the reaction goes on is relatively short.

As an athlete who has played a variety of sports (hockey, soccer, basketball, badminton, cross-country, road racing, tennis), I’ve found that there’s one trait in particular that separates the great players from the good ones. It’s more applicable in racquet or ball sports, but every sport can make use of this trait in some small way. While I’m only going to focus on sports for today, it’s actually applicable to nearly any kind of game.

If you’ve ever had a calculus class, you may remember that the idea of an integral is to calculate the area under the curve of a function. The way this is done is by taking the sum of the infinitesimal “rectangles” that are under the curve. Each rectangle is effectively a line, but by adding them up you can create the area under a function.

For those motivated with their training, it can seem as if time stretches out. We are meticulous with our warm ups, our stretching and strength work, and everything else that goes into being a great athlete. However, I want you to think about a different idea: efficiency. What would happen if the time you had to train was cut in half? For those who enjoy running around ten hours a week (plus let’s say two hours of work outside of running), that’s twelve hours of training per week. What if that time was cut in half? If you only had six hours a week to train, what would you do?