One Degree of Change

“They always say time changes things, but you actually have to change them yourself.” - Andy Warhol

F-16 Fighting Falcon Ready to Rock! (Photo taken by James)

There are quite a lot of aspects of aviation and flying airplanes that, surprisingly, transfer over seamlessly to real life.  One of the best examples of this is if you're flying an airplane and your heading is off by 1 degree then after 60 miles you will be 1 mile off course.  1 mile off course may not seem like a lot but keep in mind that resulted from your heading only being 1 degree off initially, which is a very miniscule amount.  If you've never had the pleasure of trying to hold a heading to an exact degree while hand flying an airplane that's getting rocked around by changing winds and turbulence, I can tell you with great certainty... it is not easy (but it is really fun).  At the same time, going 60 miles may seem like a fairly large distance but you have to keep in mind, the speed that airplanes travel at vary wildly and airplanes can cover a lot of ground... fast!

A Cessna 152 cruising at 120 miles per hour (mph) will cover 60 miles in only 30 minutes, which is at the slow end for airplanes.  A Cirrus SR-22 cruising at 240 mph will cover 60 miles in 15 minutes.  A Dassault Falcon 50EX corporate jet cruising at 480 mph will cover 60 miles in 7.5 minutes.  A Boeing 737-700 airliner cruising at 520 mph will cover 60 miles in 6.6 minutes.  An F-16 Fighting Falcon going 960 mph will cover 60 miles in 3.75 minutes.  An SR-71 Blackbird going 2,300 mph will cover 60 miles in 1.56 minutes.

Back when I was actively flight instructing (teaching people how to fly airplanes), this was one of my many favorite thought experiments to do with students, usually after their first cross country flight (with me onboard) during which they would always, inevitably, at some point during the flight, stop comparing their heading indicator to the actual magnetic compass (commonly referred to as a wet compass).  The heading indicator gauge is not magnetic, it's a gyroscopic instrument and anything with a gyro in it means it has friction which means it needs to be reset often to keep it on the correct heading.  It needs to be compared to the actual magnetic compass every 15 minutes and adjusted accordingly.  If you forget to do this, after an hour your heading indicator will suddenly be off by about 15 degrees (some airplanes more, some airplanes less).  Which is significantly more than 1 degree off, it's 15 times as much in fact!  This results in you thinking that you're on course but your heading is actually 15 degrees off and each minute that goes by you'll be significantly further off course, in terms of mileage.

With new students learning to fly, you can go over non-stop how important it is to check your heading indicator every 15 minutes, practice this in the airplane, talk about it on the ground time and time again.  No matter how much you do all that, sure enough, on just about every single first cross country flight, normally on the return leg, when they get comfortable and complacent, the student would almost always forget to keep checking their heading indicator and would wind up being pretty far off course, pretty fast.  Once they realized it they were always extremely surprised and it would then take them quite a while to sort out what had actually happened, how they had gotten so far off course and how in the world are they going to get back on course.  Once we got back on the ground we would talk about it in-depth and that's usually when I would pose this thought experiment to really hammer home how important it is to constantly check the heading that you're on, adjust the heading indicator and how these seemingly small changes can compound once you get into higher performance airplanes that fly much, much, much faster.

The thought experiment is to simply look at different airplanes that fly at different speeds and use the rule of if your heading is off by 1 degree then after 60 miles you will be 1 mile off course to see just how fast, and how far, different airplanes would be off course.

A Cessna 152 is a typical airplane that a lot of people learn to fly in, it's a very small airplane (two seats) and has a whopping 110 hp with a cruising speed of roughly 120 mph.  If you are flying at 120 mph and your heading is 1 degree off then after 1 hour you will be 2 miles off course.  Now let's say your heading is 10 degrees off, after 1 hour you will now be 20 miles off course.  Are you starting to see how quickly these small degree changes can compound?

Now lets hop into a Cirrus SR22 TN (TurboNormalizer - don't worry about what that actually is) which is still a single engine airplane but can seat 4 people and has 310 hp.  Now we're cruising at 240 mph and if our heading is 1 degree off then after 1 hour we will be 4 miles off course.  10 degrees off?  1 hour later we're now 40 miles off course.  This is quickly becoming a big problem.

Next we're jumping into a Dassault Falcon 50EX which is a pretty neat corporate jet that can seat 9 people and has 3 engines, each of which have about 4,700 hp.  With more power comes more speed and now we can cruise at about 480 mph.  After being 1 degree off for 1 hour, we are 8 miles off course.  10 degrees off and 1 hour later we are now 80 miles off course.  Holy cow, now the mileage is really building up.

We're not done yet, there are a lot of faster airplanes out there.  Next up is the Boeing 737-700, the most common airliner and usually seats around 130 people.  This aircraft has 2 engines with 37,440 hp each and has a rough cruising speed of about 520 mph.  If our heading is 1 degree off then after 1 hour we are 8.67 miles off course.  Bump that up to 10 degrees off and after 1 hour we are now 86.7 miles off course.

Now we're going to hop into some very neat and mighty military aircraft.  The F-16 Fighting Falcon is an extremely powerful (and extremely cool) jet.  With a single engine of 69,000 horsepower it is basically a giant rocket with a person strapped to it.  Say you're flying along at 960 mph, if your heading is 1 degree off then after 1 hour you are 16 miles off course.  10 degrees off and 1 hour later, now you're 160 miles off course... yikes.

We can take this even further, next up is the mightiest (known) aircraft ever, the SR-71 Blackbird.  Two engines with 196,267 horsepower each means this airplane has a very serious need for speed.  Say you're flying along at 2,300 mph, if your heading is off by 1 degree then after 1 hour you are suddenly 38.33 miles off course.  Bump that up to 10 degrees off and after 1 hour you are now a whopping 383.3 miles off course, which is how wide the entire state of Colorado is (from east to west)... eek... that's probably less than ideal for taking surveillance photos.

The point of all this is small changes add up fast, even if the changes initially seem like they're insignificant and don't matter.  This is not limited to flying an airplane, this can be applied to any and every aspect of life.  It is human nature to view this negatively but this exact same concept is true for positive change.  If you're trying to make positive change in your life or in the world: small and sustained changes... over time... add up.

If you're trying to learn a new musical instrument or learn a new language or kick a bad habit or are dealing with addiction or are working on fitness or are just working on improving your life in general, the actual impact (positive or negative) is over time.  The key is persistent, small changes to make a lasting impact.  The bigger of a change you can make now, then the more impact that change will have over time.

Lets take learning an instrument as an example.  If you pick the instrument up once a week for 15 minutes, it is going to take you a very long time to learn that instrument.  It's a very small heading change with a low amount of speed behind it which means it is going to take a very, very, very, very, very long time before that change has any sort of significant impact on your life.  It can still have a meaningful impact, if given enough time and if that change is sustained.  But if you kick it up a notch and start playing your instrument for 1 hour, every single day, no exceptions - now you have a significantly larger heading change with a lot more speed behind it which means you are going to learn that instrument at an incredibly fast rate (compared to what you had been doing).  This also means you are going to notice the effects of the change faster which should help you with being able to mentally sustain that change in the long run.

It doesn't matter what you're doing in life, small changes add up over time.  What may seem to be insignificant initially, can actually have a very large impact... if given enough time.  If you move faster, those same small changes will suddenly make an even bigger impact over the same amount of time.  The larger the amount of change you're able to make initially, then the bigger the impact will be as time goes on, even if your speed is on the slower end.  It's important to keep in mind that this is a double edged sword and this applies equally to good and bad habits, the laws of the universe don't discriminate.

If you start picking up a small bad habit every now and then.  Over time, you will suddenly find yourself waking up one day and wondering how all of these negativities popped up in your life.  It will seem very sudden, but it's really not.  Conversely, if you make very small, positive changes in your life, they will seem extremely insignificant in the moment but if you consistently make positive change after positive change after positive change, those changes can have an extremely large positive impact on your life... over time.  The faster you go, the faster the impact.  The more changes you make, the larger the impact.  The fact and concept is simple, changes compound quickly.  One other very important factor to point out is the changes do need to be sustained in order to have any impact at all.

Back to our learning an instrument example.  You have the instrument, you have the intention of practicing 1 hour every single day, you have the instruction, you have everything you need.  Say the first day, you successfully practice for one hour then you forget for the rest of the month.  That's a heading change that you quickly reverted back to the original heading, which means, there's not going to be any change at all.  Say you successfully practice every day for a month, then you forget to keep practicing.  Within that month you will have covered some meaningful ground but then you're going back to the original heading so the change is going to stop.  Now lets say you successfully practice every day for a year then stop after that.  Within that year, you're going to have learned a lot but that change stops the second you stop practicing.  Change needs to be sustained, you have to put the work in and this applies to everything in life.  You're not going to learn a new language just by thinking that one day you're going to learn the language and be fluent.  You can have that intention and think about it all you want but you're not going to start learning until you actually decide to put the work in and that work is put in consistently... every single day... with no exceptions.  To sustain the change you need to constantly compare what you're doing with where you want to go and adjust accordingly.  If you don't do this then you'll find yourself drifting off course ever so slowly, even though you'll think you're right on course.  You won't even realize this drift until you're very far off course, making it much harder to correct to get back on course and will result in a lot of frustration.

The trick with all of this is to actually recognize the truth in this concept and how if you harness it correctly, it can (and will) impact your life significantly.  What you do, makes a difference.  It doesn't matter if it's only using one less plastic water bottle a day, reducing plastic usage overall, eating one healthy meal a day, growing a single plant, etc.  Small changes add up and while you can't change where the other airplanes in the sky are flying, once they see where you are going, they might decide that they like that overall destination too and you'll start seeing more and more airplanes changing course and following your lead.

Which bring us to the biggest question of all.  How are you going to harness this in your life (or in the world) to make a lasting impact?  The choice is yours now that you have the knowledge.

Here are the full tables I made showing the various amounts of change based on heading and speed using the various aircraft mentioned:

Cessna 152 – 110 hp - 104 knot cruising speed = 120 mph (Mach .16)

120 mph – 1 degree off for 1 hour = 2 miles off course.

120 mph – 2 degrees off for 1 hour = 4 miles off course.

120 mph – 5 degrees off for 1 hour = 10 miles off course.

120 mph – 10 degrees off for 1 hour = 20 miles off course.

Cirrus SR22 TN - 310 hp - 208 knot cruising speed = 240 mph (Mach .31)

240 mph – 1 degree off for 1 hour = 4 miles off course.

240 mph – 2 degrees off for 1 hour = 8 miles off course.

240 mph – 5 degrees off for 1hour = 20 miles off course.

240 mph – 10 degrees off for 1 hour = 40 miles off course.

Dassault Falcon 50EX – 4,700 hp per engine (3,704 lbs of thrust per engine) – 3 engines - 417 knot cruising speed = 480 mph (Mach .63)

480 mph – 1 degree off for 1 hour = 8 miles off course.

480 mph – 2 degrees off for 1 hour = 16 miles off course.

480 mph – 5 degrees off for 1 hour = 40 miles off course.

480 mph – 10 degrees off for 1 hour = 80 miles off course.

Boeing 737-700 - 37,440 hp per engine (27,000 lbs of thrust per engine) – 2 engines -  452 knot cruising speed = 520 mph (Mach .68 – worth noting that typical cruising speed is actually Mach .78)

520 mph – 1 degree off for 1 hour = 8.67 miles off course.

520 mph – 2 degrees off for 1 hour = 17.34 miles off course.

520 mph – 5 degrees off for 1 hour = 43.35 miles off course.

520 mph – 10 degrees off for 1 hour = 86.7 miles off course.

General Dynamics F-16 Fighting Falcon – 69,000 hp per engine (27,000 lbs of thrust per engine) – 1 engine - 834 knot speed = 960 mph (Mach 1.25)

960 mph – 1 degree off for 1 hour = 16 miles off course.

960 mph – 2 degrees off for 1 hour = 32 miles off course.

960 mph – 5 degrees off for 1 hour = 80 miles off course.

960 mph – 10 degrees off for 1 hour = 160 miles off course.

Lockheed SR-71 Blackbird – 196,267 hp per engine (32,000 lbs of thrust per engine) – 2 engines – 2,000 knot speed = 2,300 mph (Mach 3.00)

2,300 mph – 1 degree off for 1 hour = 38.33 miles off course.

2,300 mph – 2 degrees off for 1 hour = 76.66 miles off course.

2,300 mph – 5 degrees off for 1 hour = 191.65 miles off course.

2,300 mph – 10 degrees off for 1 hour = 383.3 miles off course.

Semi-Important Notes: Trying to compare these different types of airplanes to each other is a bit like comparing apples to oranges.  Airplanes with reciprocating engines have power measured in actual horsepower, just like your car.  Airplanes with jet engines have power measured in pounds of thrust and that doesn't necessarily translate into horsepower... easily.  Converting engine pounds (lbs) of thrust to horsepower (hp) is dependent on the speed (velocity) in miles per hour (mph) of the aircraft.  So it’s not a straight forward conversion and is why even though the lbs of thrust of the 737 and F-16 are roughly equivalent the horsepowers are drastically different.  Velocity makes a difference!  The general conversion for this is:  HP = (Thrust x Velocity) / 375.  Thrust = lbs of thrust.  Velocity = mph.  The airspeeds of the different airplanes also don't necessarily translate... easily.  Small airplanes that fly at lower altitudes, such as the Cessna 152 do in fact measure their airspeed in knots.  You will never hear a Cessna 152 pilot refer to their airspeed as Mach .16... although that would be hilarious.  They certainly could, but it would be a ridiculous amount of mental math to figure out what their real Mach number actually is and it would be a lot more trouble than its worth.  Airplanes that fly fast and at high altitudes, actually fly at specific Mach numbers (not knots).  There are a lot of factors that actually effect a Mach number such as the temperature of the air, altitude, density of the air, humidity of the air, etc. all of which are constantly changing.  So if you're trying to think of the speed of sound as a specific number in terms of knots or mph, that number is actually constantly changing based on all of those environment factors, which is why the speed of sound is expressed in terms of a Mach number and not in knots or mph.  Long story short, Mach numbers don't easily translate into knots or mph which makes it hard to compare the speeds of the various aircraft listed above.  Lastly, for speed in aviation, knots are always used, not mph.  But if you're not in aviation (or the marine world) you're not going to know what in the world a knot is or how it translates to mph and since everyone in the US is used to mph, mph are used in this article for ease of use and understanding.  For the purposes of this article, none of this really matters since we're talking in extremely general terms and none of that has any effect on the overall concept of this article.  However, if any pilots or anyone interested in aviation happen to read this article, these are going to be the very first things they think about so it's important to acknowledge this and make note of it.