How is the efficiency of a rocket launch calculated when the weight keeps changing with fuel being spent + stages detaching?

Question

I assume it has to be a really complex calculation, how is the weight accounted for when the target number keeps changing constantly so dramatically?

In: 5

Answer 1

Let’s simplify to an an easier problem first. If you drive the car at constant speed, and you know the speed of the car and time you spent driving, how to you calculate the distance you traveled?

Easy. Distance = speed × time

But, what if you’re speeding up, i.e. your speed is changing just like the rocket weight is constantly changing?

Let’s say the [red line in this graph](http://calcprojectpo.weebly.com/uploads/2/9/7/4/29745541/2512833_orig.gif) is your speed graph. You can’t just multiply speed with time because speed is changing. But you can take smaller chunks of time (let’s say, 0.5 seconds) and make an approximation by saying that your speed was constant during that small chunk of time because that’s not enough time for your speed to significantly change. Those are the green rectangles in the image.

Now that you’ve taken a small chunk and assumed the speed is constant during that chunk, you can multiply distance = speed × time. So, your distance traveled during the first chunk would be, say, 5 km/h × 0.5 s; your distance traveled during the second chunk would be 5.2 km/h × 0.5 s, third chunk 5.4 km/h × 0.5 s. As you add up, say 100 chunks, you can know how far you’ve traveled during 50 seconds of your ride.

The smaller the chunks, the more accurate your result because your approximation more closely resembles the actual situation.

Similarly, a rocket scientist would take a mass of the rocket at a certain small chunk of time, assume that weight and speed are constant during that chunk of time, and make his calculations easier for that particular chunk. Then you add up all the chunks and you’ve got your result.

That’s called calculus. It’s basically a branch of math that, among other things, deals with quantities that change with other quantities (i.e. speed that changes with time, rocket acceleration that changes with mass, altitude, air resistance, …).