Rocket science

The basics of rocket science are not difficult to understand and might be relevant to your business

Rocket science can indeed become very complex and difficult depending on how much you want to get into it. But, like all good science, it begins with simple ideas and some of the principles can be extended to other scenarios. The factors that make the rocket go faster might be similar to those that make your business more profitable.

A rocket is, by definition, completely self-sufficient. With careful planning, it will at the outset have all the fuel it needs to reach it’s destination. Without any external sources for its propulsion it can even get you to the moon!

The ideal rocket equation

“Ideal” means in the absence of any forces other than the rocket’s propulsion (which operates perfectly) which would make things more complicated. In theory a rocket in space far from the influences of planets or stars would qualify.

The equation was first derived in 1813 by British mathematician William Moore and then again, independently, in 1903 by Russian physicist Konstantin Tsiolkovsky after whom it is also named.

A rocket converts some of its mass (fuel) into high energy exhaust and blasts it out of a nozzle. The ideal rocket equation comes from Newton’s laws of motion and calculates the maximum increase in velocity in terms of the velocity of the exhaust and the relative amount of mass ejected:

$\text{Δ}v={v}_{e}·\text{ln}\left(\frac{{m}_{o}}{{m}_{f}}\right)$

Where Δv (“delta-vee”) is the change in velocity of the rocket, ve is the exhaust velocity, mo is the original mass and mf is the final mass.

It’s not difficult to understand. The only thing that might be unfamiliar is the behavior of the natural log, ln. Basically, since the final mass of the rocket mf (after fuel has been burnt) is going to be less than the starting mass mo then mo/mf will always be greater than 1 and it’ll be larger if more fuel is burnt. The natural log gets larger too but not in a straight line - it tails off like this:

The equation shows us two ways to make the rocket go faster:

1. Faster exhaust: ve is larger
2. Eject more mass: ln(mo/mf) is larger

Burning off more mass gives us a diminishing return because of the curve of the natural log but faster exhaust give us a better return because is directly proportional.

Well, OK, this is a bit of a stretch but essentially we can use the idea in business as follows:

1. Analyze the business and develop a simple ("ideal") model
2. Identify how the components affect the model (profitability)
3. Focus on the components that produce the greatest results

Rough example: Sales = Advertising × f(Price) where we find that sales increase in relation to the amount of advertising we do and how cheap the product is, except that they increase in direct proportion to advertising whereas the effectiveness of making the product cheaper tails off. So we limit how much effort we put into making the product cheaper and concentrate on advertising.

Do you like this? I thought it was fun. I studied Boron chemistry to a limited extent, largely because it had held potential as a high energy rocket fuel. I later switched from chemistry to business, so there’s another connection.

Caveats

The simplistic approach so far presented does not include other possible effects, such as gravity or atmospheric drag. When these factors are taken into account we discover something called “the tyranny of the rocket equation” in which launching a heavier rocket requires more fuel... which makes the rocket heavier.

utexas.edu has a derivation of the ideal rocket equation with some notes about how the final velocity of a chemical rocket can never significantly exceed the speed of ejection of the exhaust, mit.edu introduces the effect of gravity (-gt) for a launch scenario and ucr.edu considers a relativistic rocket (yes, Einstein’s relativity).

John Walker has a good overview at fourmilab.ch and rocket equations applied to model rockets (ones you can actually use) can be found at rocketmime.com.

Admittedly, “it isn’t rocket science” applies to many businesses, however SpaceX (founded by Elon Musk), Blue Origin (founded by Jeff Bezos) and Virgin Galactic (founded by Richard Branson) are definitely about rocket science.

Of course, knowing rocket science improves your status at parties.