# Higher or Lower? It Can Be Complicated

We all remember being told what it means if we’re flying along and we see an airplane, and it’s not moving in our field of vision: trouble, right? RIGHT! Then there’s that part about what it means when that other airplane is level with the horizon. It means it’s at your altitude, right? WRONG! Along with the diagrams that show parcels of air split by a wing and meeting up again at the trailing edge, somehow certain things get oversimplified and propagate through time — even though they’ve become misleading or even dangerous.

HOW IT WORKS
The higher up you go, the more you can see. We could draw a circle and impress the natives with trigonometry, but let’s just use rule-of-thumb calculations to define how far away a horizon is. (Yes, there are finer complications due to possibly uneven terrain, or even the oblateness of the earth. But let’s ignore those.)

Formulas: One says that distance (to the horizon) in Km equals about 3.5 times the square root of your height in meters; another yields a solution in statute miles by multiplying 1.2 times the square root of your height, this time in feet. Take your pick. Now let’s do a little “gedanken” or “thought experiment” … with examples:

• At a 1000-foot pattern altitude, the horizon is over 35 statute miles away.
• At 3500 feet, it’s about 70 miles, and
• at 8500 feet, it’s about 110 away.

Important: The higher up you go, the further you see, sure. The weird thing is that the rate of increase slows down, the higher you go. At 100 feet, the horizon is about 12 miles away — that’s over 600 times your distance above the ground. At 1000 feet, where the horizon is about 35 miles away, the ratio drops to about 200. At 3500 feet, it’s 100 or so, and at 8500 feet, around 70. Translation: The higher you are, the “steeper” the horizon.

WHAT’S ON THE HORIZON?
OK here’s the “thinking” part: What does it mean when something is on your horizon? It means that it falls on the line of sight extending from wherever you are to a point tangential to the earth’s surface … ‘way out there, somewhere.

The Truth: Now let’s say there’s another airplane, and as far as left-right goes, it’s not moving. You estimate it’s still a good three or four miles off. And it’s somewhere on that line extending from your eyeballs down to the horizon. Translation: Any aircraft you see on your horizon is actually at a lower altitude than you are! This can be significant if that aircraft represents converging traffic and you were to descend down into it, thinking you were flying beneath, instead.

The Danger: Let’s say you’re at 3500 feet, and noticed something on the horizon about three or four miles off. Hmmm … looks like an airplane … not moving. (Now let’s also say you hadn’t read this article.) So, to be on the safe side, you drop down a couple hundred feet. Whew! Had you read this article, you would know that when you saw the other aircraft about one twentieth of a horizon away it was therefore about a twentieth of 3500 feet lower than you … exactly the altitude to which you just descended. Congratulations, you’re now set up for a solid mid air. This same thing holds true at pattern altitude, only with a flatter horizon, the typical reaction/recognition distances represent a bigger horizontal “slice” of that horizon slope (about one tenth). But since we tend to be more precise in our altitude control at pattern altitude, a 100 foot “safety zone” (into which one might choose to descend to “avoid” something on the horizon) is just as deadly.

THE BOTTOM LINE: Up at a typical VFR cross-country cruising altitude, another aircraft spotted at three or four miles translates into a smaller percentage of distance to the horizon (it’s about 3% at 8500 feet where the horizon is roughly 70 miles away). But with steeper horizons (a result of the higher altitudes), the altitude difference between you and that aircraft on the horizon increases (about 270 feet) for that same airplane a given distance away. The higher you are, the larger the vertical margin between you and that stationary aircraft on the horizon. When you’re higher, you’re higher. Still, watch out! Understanding what’s going on will help you make the right decision to avoid other traffic. In general if you need to avoid an aircraft on the horizon, climb. If that aircraft is above the horizon, descent may be an option.