Exercises from "Fundamentals of Astrodynamics" Part 1

Over the coming months, years, decades, no one really knows, I will be working through the exercises from “Fundamentals of Astrodynamics” by Bate, Mueller, and White. The intent is to not only provide myself with a refresher, but to provide a resource for enterprising students.

Exercise 1.1 The position, , and velocity, , of a satellite at a given instant in canonical units: Distance Units (DU) and Distance Units per Time Unit (TU), respectively, are described by

Find the specific angular momentum, , and specific mechanical energy, , of the system.

Solution:

Equation for specific angular momentum:

An easy way to set up the crossproduct is using Sarrus’ scheme:

sarrus' scheme

This yields:

Equation for specific mechanical energy:

Since we’re using canonical units, let :

Why are we still doing weight and power by hand?

Weight and power if you’ve never heard of it, or in other parlance, weight and balance is a crucial set of calculations for safety of flight. Having the numbers wrong could be the difference between life or death. Where I work, it involves interpreting various charts and tables and hand jamming numbers into a calculator and penciling in over fifty blanks on a paper form. It takes anywhere from 10 to 15 mins on average to do depending on experience. Time that can be better spent with other aspects of flight planning. So why do we have humans do the calculations when a computer can do it faster and more accurately?

The explanation you’re likely to hear is that it’s because “we’ve always done it that way” or “it’s important to know how to do the calculations.” I’d only begin to accept the later, but it’s still a bad explanation. Sure there’s some merit to knowing how to do it by hand. After all, you may have to do it on the fly or somewhere you don’t have a computer. But the reality is, these situations are far from the norm.

A good solution would be to have one day out of the week for pilots to do it by hand and the rest of the week the computer does it. Sure the software would have to be written, but it’d be close to trivial. Let’s do the math. On average, we schedule 4 flights a day. Let’s go with the low end of 10 minutes to hand jam the numbers. Spread that over 5 days a week and 50 fly weeks a year, that’s 167 hrs. If you go with the high end of 15 min, that’s 250 hrs. Pilots get paid on average $60/hr. That comes out to $10,000 to $15,000/yr of human capital wasted on an easily automated task. I’d write the software myself for far less. It’s 2019, let’s start acting like it.

Starting out your day filling out a redundant useless form

Many of my days at work start with checking out a helmet from a small office for FOD (foreign object debris) walk-down. Just imagine making a line and walking an area to pick up “trash” like the Boy Scouts do to a campsite. But while that may sound frustrating to do day in and day out, it’s not the frustrating part. The frustrating part is the checkout. There is a form that you must fill out with the checkout date and time, your name, your signature, and the helmet (actually “your helmet” because everyone has their own). Then of course, you also have to sign back in with the time and date, your name, and your signature. What’s more? The same people do this everyday at the same time. It’s not like you don’t know the majority of who’s going to show up. Now imagine around 20+ people all trying to checkout their helmets at the same time in this small office. You can barely get in or out of the door. It’s a classic process bottleneck. One day I walked in and there was a refreshing sign of improvement. The lady working in the office, who’s almost never busy at this time, had pre-filled out the date and time since it’s more or less the same for everyone. Checkout speed doubled. But how long did this last? Less than a week. There’s got to be a better way. Of course, technology offers many attractive solutions. My favorite is RFID. The helmets would have a small RFID antenna and when they pass through the door, they get scanned. Simple. Elegant. No one would have to fill out anything. But alas, that would take an act of congress. But what could be done, and what I’m proposing next week is that we make a new form because we can’t not have a form. But this form will be different. It will just require two signatures. One when you check out and one when you check in. All the rest of the information will be pre-printed on the form because it isn’t variable enough to not be. If it flies, it’s a stupid simple improvement. But then again, those types of improvements tend to be the best. Keep it simple stupid.

Copying from a copy...

…works until what comes out of the machine is on the verge of unreadable. So take the time to make a copy of the original if the original still exists. Better yet, make a new original and ask how it can be done better this time around.

Hello World!

In true nerd fashion, here’s my hello world post. It’s been my goal for a long time to start a blog. So here it is. Welcome to my world.

I hope it moves you.