Piloting Part 4, Distance Off

In Part 3 we discussed getting the answer to “Where am I?” and introduced a couple of ways to measure distance off… distance from a visible object that is also on the chart. In this post, we’ll show additional techniques to measure distance off.

More Preparation

 In the post on "Preparation", we suggested you print charts of the area you intend to cruise in. There is some additional preparation of those charts which can be very helpful when piloting the area.

• Mark a scale on the chart for distance in miles or kilometers. For example, if the chart is scaled 1 inch to the mile, draw a line  4 inches long, with tick marks at 0, 1, 2 and 3 miles, then divide the last inch into eighth inches. Then it will be easy to measure distance on the chart.
  
  
• Annotate major land marks such as water towers, bridges, light houses with heights, widths, colors, etc. If you do a Google search for the object, you can often find the required information. For example, when I did a search for Mantoloking Bridge , I found the center span vertical clearance is 30 feet and the horizontal opening is 80 feet. Published nautical charts typically provide this information.
  
  
• Pre-measure and mark on the chart distances between points that will be obvious from the water. For example, the distance between two jetties protecting an inlet... distance between two small islands... distance between two shorelines that mark the edges of a narrow channel. You'll see in the discussion below how having these measures at hand will help you.
  
  

Using Object Size to Estimate Distance Off

We can estimate distance by noting what we can see at various distances. For example…

• At 5 miles (8 km), we can see houses (but no detail), ships, water towers, light houses 
  
  
• At 2 miles (3.2 km), we can see large trees and windows in the houses 
  
  
• At 1 mile (1.6 km), we can see big branches in trees, large buoys
  
  
• At 1/2 mile (0.8 km), we can see people as dots or sticks, small buoys 
  
  
• At 1/4 mile (0.4 km), we see people's arms & legs, detail on boats, such as an outboard 
  
  
• And at 1/8 mile (0.2 km), we can see faces, registration numbers. 
  
  

Using Small Triangle to Find Distance Off 

Doing this is illustrated in the diagram below:

Let's make this easier by simplifying the 'mathematics' we have to do.

How to Create the 'Small Triangle' Using a Kamal

To make the mathematics easier, we need to make a 'kamal', an Arabic device that was originally used to measure the altitude of the North Star so that sailors were able to sail east and west (along a given latitude) between Africa and India out of sight of land for weeks at a time.

Here's one way to make a kamal: Use a 6" (15cm) plastic ruler and at least a meter (40+ inches) of heavy (durable) string. Tie one end of the string to a (carefully) drilled hole in the center of the ruler. Tie a second knot exactly 57 cm from the ruler. Leave the rest of the string, we'll use that for the second technique for creating the 'Small Triangle'.  

A small triangle 57 cm high with a base of 1 cm subtends 1°. So what? The general equation for  using a 'small triangle' for measuring distance off is shown in the illustration above. By introducing degrees into the equation and simplifying it, we can create a formula that is easier and more flexible in use:

                                     60 times Width of the target (in miles)
Distance off (miles) = ------------------------------------------------------

                                    Target angle in degrees as viewed on the kamal

Mnemonic: Sixty miles [per hour] over degrees.

Example: Looking at the chart, I see that the distance between a water tower and a building on top of a hill is 2.3 miles. I grab the 57 cm knot of the kamal with my teeth, keeping the kamal extended and perpendicular to the string, I align the 0 mm mark on the water tower and note that the hill-top building is at 5 cm (which is 5 degrees).

                                                 60 times 2.3

So the Distance off in miles = ------------------

                                                         5

60 divided by 5 is 12. 12 times 2.3 is 2 times 12 (= 24), plus 0.3 times 12 (= 3.6) for a Distance off of 27.6 miles. 

This formula above works when the target Width is expressed in miles. Let's modify the formula so that it works with a target Width expressed in feet.

                                    Target Width in feet
Distance off (miles) = --------------------------------------------------------------------

                                    100 times target angle in degrees as viewed on the kamal

Mnemonic: My feet are over a hundred degrees.

Example: I'm heading for Mantaloking Bridge which has a vertical clearance of 30 feet.  Using my kamal, but holding it vertically, I align the 0 mm mark with the water and note that the bottom edge of the bridge itself is at 0.5° (5 mm).

                                     30                  30

Distance off (miles) = ---------------  = -----  I'm approximately 3/5ths of a mile from the bridge.

                                    100 times .5   50

How to Measure Distance Off with a 'Wink'

In the discussion above, the base of the 'small triangle' is the kamal (a 15 cm ruler) and height of the triangle is 57 mm. What if we use the distance between our eyes as the base of the triangle and 10 times that distance as the height of the triangle? 

If we do, we can hold up a pointer (finger, pencil, kamal...) at a distance of 10 times our eye 'span', sight on an object (e.g., a bridge from shore to shore) with one eye and then (without moving), sight with the other eye, the pointer will seem to 'jump' across the bridge. The length of the 'jump', measured on the object, is Width in the formula in the illustration below. 

If the 'jump' crosses the bridge in one jump, then the 'distance off' is 10 times the known width of the bridge. If it takes 4 'jumps' to cross the bridge, then 'distance off' is 10 times 1/4th of the known width of the bridge. If it the 'jump' spans 3 times the width of the bridge, then 'distance off' is 10 times 3 widths of the bridge.

The average ratio of eye span to arm length is 10:1. To make the 'winking technique more accurate, do the following:

• Measure the distance between your pupils by looking into a mirror with a metric ruler aligned just below your pupils. My eye span is 61mm.
  
  
• On the string attached to my kamal, I tied another knot at 61cm (10 times MY eye span) from the kamal.
  
  
• When using the 'winking' technique, I just hold the 61cm knot in my teeth and stretch out the string and use the kamal on edge as the pointer. 
  
  

The beauty of the 'winking' technique for measuring distance off is that all you need is the 'width' of the object, be it the horizontal opening of a bridge... the distance between two jetties... size of a large building. The calculations are easy: Distance off = 10 times the estimated width of one 'jump' (on the object). The answer will be the same measure as the measure of the object width, i.e., feet to feet, meters to meters, miles to miles. 

Example: I'm rowing south of Mantaloking Bridge, where the horizontal opening is 24 m (from my notes I wrote on my chart during my preparation work). I align the pointer with the left side of the opening using my right eye. When I close my right eye and use my left eye (a wink), the pointer 'jumps' to twice the width of the horizontal clearance. So the width of the jump is 48 m on the object. Therefore the distance off is 480 m or 0.48 km. 

Summary

Below is a summary of the key formula and factors (room to personalize it for yourself) for the piloting materials we covered so far. I've personalized my copy, water 'proofed' it with clear spray and glued it to the back of the map holder I made for myself... see Part 2 for the map holder. (Click on the image below to enlarge it.)

The Fine Print

I’m not a professional pilot. I try to be accurate and I check my information, but I’m not perfect. This post is for information purposes and is intended to be only a starting point for learning the skills of piloting. As with any activity with a small boat, there is always the opportunity for ugly surprises. Practice the skills under ideal circumstances and you’ll increase the probability of being able to use the skills during an ugly surprise to keep you and your boat safe.