Law of Cosines in Life

I’m a pilot.  I’m fascinated by airplanes, helicopters, gliders, blimps, and anything else that flies.  When I’m not actually flying (which is too often), then I’m reading books or magazines about it.  It’s fun, and it’s my distraction from everything else.  In fact, I should be working on something else at this very moment, but flying is more interesting…and blogging is more interesting…and it’s 3am anyway, so what the heck right?

I remember reading an article in a magazine a few years ago, that I’ll credit it to Barry Schiff in AOPA Pilot magazine, though I’m not 100% sure that’s accurate.  The article was about the law of cosines (oh yeah, did I mention that I like math almost as much as flying?), and how when it comes to planning a flight, the best distance between 2 points may not be a straight line.

For example:

Let’s take someone who wants to fly from point A to point B.  Pilots know that it’s generally safer to have someplace to land at all times during the flight (just in case).  So it may be “better” to fly straight, how much would it cost to take a minor detour in your course to fly near an alternate airport?  Graphically, it would look something like this:

The question he posed is, just how inefficient is it to take a detour? Even without doing any math, it’s pretty easy draw a couple of things from the picture:
     1)  If the angle that you deviate from the straight line course is little, then the distances shouldn’t be much
     2)  If the angle that you deviate from the straight line course is large, then the total distance you fly will be larger

(everybody say “duh” now)

Just for examples though, let’s look at some real numbers.  Let’s take this typical small plane flight distance of 300 miles at an average speed of 120mph.  And let’s figure out just how much further you’d have to go, and how long it would take, if you flew out at 10, 15, 20, and 30 degrees off course.  We’ll also do the baseline, of 0 degrees, or going straight from A to B.

Angle From Straight	Total Distance (miles)	Total Time (min)	% Increase
0	300	150	0%
10	305	152	2%
15	311	155	4%
20	319	160	6%
30	346	173	15%

 

Huh…  not nearly as big as what you might have thought?

For those that are really curious, remember that Cosine is the adjacent side (in this case 150 miles), divided by hypotenuse (which we want to find).  Since we’re simplifying things by having the two halves be equal, we can just use:  300 / Cos(a) to get the total distance flown.  Take the total distance flown, divided by 120 mph, to get the total hours (times 60 for minutes).

 

Well holy cow!  That was sure a lot of work to get to a point which doesn’t actually involve either math, or flying.

 

What I realized, and try to occasionally remind myself, is that there are times in life when you have a goal, and you can see the straight path to get where you want to be.  And then, “life happens”…  Or as some people may describe, you have to “take an unexpected detour”.  These unexpected detours can seem frustrating, and make you feel like you’re completely “off track”, or “spinning your wheels”, or generally way off course from where you want to be going.

 

When that happens, I try to stop and remember…  that just because you’re off track…even if you’re off track by what seems like a huge amount (30 degrees is a huge course change!) – It doesn’t necessarily cause a huge change in how far you need to go to achieve your goals (or in our pilots case, how long it takes to get there)

 

One last random note:  When you’re at the furthest distance “off course”, just before you get to turn back towards your goals…  If this were the plane that took a detour of 30 degrees (the max), how far away from his straight line path would he get (the distance from the peak of the triangle back down to the straight line course)?  86 miles!  When you look at it that way, he’s nearly 90 miles “off course” when he only should have gone 150 miles total.  That’s one heck of a detour, but when he turns back towards his objective, by the time he gets there it only added about 15%… 

 

Maybe those detours in life aren’t that bad after all?

Catalyst

Tomorrow I’ll be heading down to San Diego for Burton Group Catalyst conference.  I’m looking forward to the chance at "attending" a conference, rather than "presenting/working" at one.  Especially after spending many hours in the booth at TechEd in Orlando a couple weeks ago.

So if you’re in San Dawg, let me know.  I’d love to say hi to old friends, and meet new ones.

Comparing TripIt vs. Dopplr – TripIt Wins

Seems like the minute that someone has a good idea, along come a bunch of other people with the same idea.  Now, I have no idea which site for travel came first, TripIt or Dopplr, but they both came into my world at darn near the same time.  First, I was reading a blog post talking about how great TripIt is for frequent travelers.  Then within a day, I received an invitation from Pamela inviting me to use Dopplr.  So of course, a side-by-side comparison was required.

Dopplr

Proving yet again that we’ve entered the MySpace [1] age of the internet, the point of Dopplr was to let users manage their travel itineraries while mostly focusing on letting you share you schedule with your list of Dopplr-Friends.  Because I travel quite a bit, it’s pretty cool to me to find out (before hand) whether I’m going to be in the same place as friends.  Unfortunately, you have to manually add your trips.

TripIT

TripIt is built for consolidating travel schedules into a single, easy to read place.  Very important for the frequent traveller, who is trying to keep hotel, car, train, and airline reservations straight for multiple trips at a time.  The primary benefit of tripit, is it’s continually evolving ability to interpret the e-mails which the various reservation systems send out, and automagically import those into it’s system.  For example, you take your itinerary as sent to you by the airline, and simply forward it to plans@tripit.com and it’s automatically added.  Unfortunately, it’s only “your” trips, and you can’t correlate with your friends.

 

I’m sure many others have as well, but many months back I submitted feeback to both sites, praising the design of the other and hoping for a merger (or at least poaching) of technologies.  Well, I’m happy to announce that TripIt has the friends options which will allow me to reconcile travel plans with any other friends who use their system.

Now, can I convince Pam to join TripIt?  (Oh yeah, and I love the fact, that to “join”, simply involves forwarding your first itinerary to plans@tripit.com.  If your e-mail addy wasn’t previously registered – ie. first time users – then they provision an account and reply back to you with a verification link.  Now THAT’s the way to go)

 

 

[1] – BTW, I believe that MySpace was created when the demon spawn of Satan dipped their bitbucket into the black river of dead HTML, and splashed the contents across a web farm.

3 ounces huh?

Ever tried to bring a liquid or gel that was more than 3.4 ounces (hooray for the metric system! blah…) through security at the airport and had it confiscated?  A while back, I had the nice TSA person explain to me that a 5.0 ounce container was actually larger than 3.4 ounces (oops, my bad), and I was going to have to either go back and ship it home (HA!) or let her confiscate it.  Fair enough, wasn’t that big a deal, have at it.  So, she took the bottle, turned, and tossed it – no, literally, underhanded toss – it into a large trash can which is presumably filled with other large bottles.

Since the justification for the rule by the TSA, is that more than 3.4 ounces of liquid could be sufficient explosives to do bad things to an airplane.  Then is it at all ironic, that airports around the country have trash cans filled with very large amounts of “presumed high explosives” in the middle of their security checkpoints?

(Note to the TSA:  Please, please, please do not put me on the no-fly list for this post…)

Copy of my invoice please

Ok, how hard is it for a hotel to send a copy of the invoice for a stay to an e-mail address?  I would actually UNDERSTAND if they said that they couldn’t do it at all, but I just got off the phone with the Sheraton in London where I stayed recently, and the conversation went like this:

Agent:  Ok I see here where we have your invoice Mr. Puhl.  And it looks like we have your e-mail address as well in the system.

Me:  Thanks, can you verify the e-mail address you have?

Agent:  Yes, we have brian.puhl-at-microsoft.com

Me:  Perfect, if you can send that e-mail I’d appreciate it.

Agent:  No problem, I’ll get that sent off for you within the next two hours

Two hours?  I’m sure I’m not the only customer she’s dealing with (although it’s 1am over there), but seriously – a 2 hour SLA for an e-mail? 

On the one hand, I’m glad that the hotel industry is embracing cutting edge technologies such as e-mail.  Not long ago, they would have asked for my fax number.

On the other hand, it will be nice when the day comes that – with the invoice on their screen – the agent at the front desk can hit “send” and be done with it.

Airline Customer Feedback Program

Have you ever sent an e-mail to a co-worker (and probably their manager) because they helped you out, went over and above, or were just plain good when you needed them to be?  What about doing the same thing for an employee at your favorite restaurant, store, or mega-corporation that’s helped you out?  Sometimes, this can be downright hard to do!

Well, I’ve been traveling a lot this year, enough to get the MVP Gold benefits for Alaska Airlines.  Like many other points/rewards programs, when you reach one of their special levels, they send you a welcome packet in the mail with your membership card, etc…

I was really surprised when I got the package from Alaska Airlines, and there were 10 cards for Alaska’s Employee Recognition program.  The idea was simple, but struck me as brilliant:  Since you’ve reached this level, you must fly a lot, so you probably have a better opinion than most of what’s good and bad, so who better than you to let our employee’s know when they are doing a good job?  Simple, yet effective. 

Now, I don’t know what’s in it for the employee’s, but even if it’s just a little gold foil star on their next performance review I’m sure it means something to them.  After all, who doesn’t like being recognized for doing a good job.

Alaska Airlines – Good job!