October 5, 2004

Cirrus Three-Four-Golf, traffic 10 o'clock, five miles, 1,000 below your altitude."

"New York...looking...no joy...Three-Four-Golf."

"Cirrus Three-Four-Golf, traffic is now two miles, 10 o'clock."

"New York...no contact, Three-Four-Golf."

"Cirrus Three-Four-Golf, clear of traffic."

"New York, we never saw traffic, Three-Four-Golf, roger."

We all have difficulty identifying potential conflicting traffic. During some flights we may never see half the traffic called by controllers. My experience with traffic-avoidance systems has not proven proportionately better. While a fish finder identifies more traffic than I ever knew was out there, the percentage of traffic I find visually has not improved much.

Some traffic cannot be seen because of poor lighting or because it is hidden from view by parts of the aircraft — only a small sector of sky is visible out the windows. Another factor is wind-correction angle. Air traffic controllers know your track across the ground but not your heading, so they call traffic relative to track. If you have a large crab angle, traffic called at 12 o'clock may really be at 1 o'clock.

Poor distance vision is also a factor. Many of us get reading glasses when we cannot read the small print on aviation charts, but we are more tolerant of poor distance vision. Thus, we may avoid wearing glasses to correct for distance vision longer than reasonable. If you need glasses to fly you are in good company — more than half of pilots over the age of 40 require glasses.

Physiology also plays a role. When we do not have a distant object on which to set our focus, our eyes settle into a resting focus that is perhaps 20 feet in the distance. This is called empty field myopia. As with a camera focused too close, objects in the distance are blurred, and small objects such as an airplane may not be seen at all.

I don't have any particular brand preference — Evian, Poland Spring, Arrowhead — but I look for a water bottle with close to an 11-to-1 height-to-neck ratio. That will be a rather tall bottle with a small cap. I began preparing water bottle clinometers using a pocket knife to cut out the soft bottoms. This is the preferred method if you are preparing one or two. However, when I was faced with manufacturing about 150 bottles for my talk at the AOPA Fly-In and Open House in June, a knife was impractical. So here is the method I developed: Using a hot soldering iron I created a dimple in the center of the bottom of each plastic bottle. I used this as a centering point so a drill would not wander. A quarter-inch drill then makes a pivot hole. Finally, a two-inch-diameter circular saw with a centering axle placed through the pivot hole prepares the final sighting opening. Attempts to short cut this procedure using only the saw were unsuccessful, as the power drill stalled and the hot plastic cutout bottom jammed in the saw. — *IBF*

However, perhaps the most correctable problem is not looking for traffic in the right place. Most of us are taught to look for traffic on the horizon, because that is where the greatest threats are. Yet we tend to desperately hunt all over the sky to find closing traffic when, in fact, most conflicting traffic appears within a very narrow strip of sky. To find just how small that area is, let's do a few simple calculations.

Richard "Dog" Brenneman taught me what I call the Brenneman Triangle and an easy mental way to calculate small angles. Now a retired Air Force pilot, he developed a system of mental aviation mathematics while in the Hanoi Hilton, where he spent more than five years as a prisoner of war after his F-4 was shot down over Vietnam. As a 1-degree right triangle has a base of 1 nautical mile and has a height of 100 feet, he proposed a simple formula for small angles: The angle equals hundreds of feet divided by nautical miles. (Angle equals hundreds of feet/nautical miles, or A=hundreds of feet/nm.)

Conflicting traffic is typically 500 or 1,000 feet above or below our altitude (or at our altitude). Thus, Brenneman's formula reduces to angle=5/nm or angle=10/nm.

Let's put this to use. Assume traffic is at 10 nm and plus or minus 1,000 feet. Using Brenneman's formula, we see that the angle is only 1 degree, meaning that traffic is only 1 degree above or below the horizontal (A=10 hundreds of feet/10 nm, or A=1 degree). As traffic approaches and is 5 nm away, it is only 2 degrees above or below the horizontal (A=10/5). Now let's consider some very close traffic, 500 feet low and only 1 nm distant. That traffic is only 5 degrees below the horizontal (A=5/1). Once traffic is within 1 nm and separated by 500 feet or more in altitude, it is generally no longer a factor. The speed of closure makes it unlikely the conflicting aircraft will have the performance to climb or descend fast enough to cause a midair collision. Thus, we can assume all closing traffic will be within a band 5 degrees above and 5 degrees below the horizontal.

Unfortunately, humans have difficulty estimating small angles. We can accurately estimate a right angle (90 degrees) and a 45-degree angle, and some of us can fairly accurately draw .a 30-degree angle. However, most of us can neither estimate nor draw an angle of 1 or even 5 degrees with accuracy.

Foresters and surveyors use clinometers to measure small angles accurately. However, they cost $100 and up, and may not be in a pilot's budget.

However, a simple substitute I call the water bottle clinometer will suffice.

Take a typical 500-milliliter or one-pint plastic water bottle, cut out the bottom, and throw away the cap. Measure the inside diameter of the top opening and the height of the bottle. Divide the height by the diameter of the opening. (The math is easier with a metric ruler.) The result should be compared with this table for an approximation of the angle.

**Bottle height divided by inside neck diameter= 11 is equivalent to 5 degrees 10 is equivalent to 6 degrees 8 is equivalent to 7 degrees 7 is equivalent to 8 degrees 5.6 is equivalent to 10 degrees**

The bottle I use has a 2-centimeter opening, and is 21.5 cm tall (after the bottom is removed); 21.5 divided by 2 is close to 11. Therefore, the bottle projects an approximately 5-degree circle.

To use this homemade clinometer, hold the open base of the bottle against your eyebrow. Keeping both eyes open has the effect of projecting a circle (the bottle neck opening) against the distant sky. The circle is of a known diameter in degrees. If you use a bottle with a 10-degree circle, all traffic called by ATC should appear within this circle if it is centered on the horizontal. This is an excellent training device. While I can't suggest that you use it every time traffic is called, it will train you to scan a very small slice of the sky and increase the likelihood that you'll actually see the traffic.

So far I have not discussed traffic at the same altitude, and have used the word horizontal and not horizon. Assume ATC calls traffic at our altitude and 2 o'clock. Where is traffic relative to the horizon? Is the traffic on the horizon, above the horizon, or below the horizon?

Traffic at the same altitude is always above the horizon. This is because anytime we are above the ground, the surface of the Earth curves away from us and to see the horizon we must look slightly downward. Therefore, any traffic at our altitude is projected above the horizon. This is because traffic is relatively close compared with the horizon. For example, at 13,000 feet the horizon is about 120 nm in the distance. Traffic is so much closer that the Earth's curvature is not a significant factor.

The next question is how many degrees above the horizon is the traffic? That depends upon altitude. The higher you are flying, the higher traffic appears in relation to the horizon. Here is a simple table of approximations:

**Depression of the horizon (and distance to the horizon) At 3,000 feet=1 degree (60 nm) At 13,000 feet=2 degrees (120 nm) At Flight Level 290=3 degrees (180 nm) At FL510=4 degrees (240 nm)**

Thus, while flying at 13,000 feet, traffic at the same altitude appears to be 2 degrees above the horizon.

The calculations used here are approximations. Basic trigonometry provides more accuracy, but such precision is not likely useful while in flight. And for those of us who are not mathematicians, using this easily memorized table (those with higher-performance airplanes require larger brains) and the water bottle clinometer gives us the tools we need to know where to look for traffic.

*Ian Blair Fries, M.D., sits on the board of visitors of the AOPA Air Safety Foundation.*