How Dead Reckoning Works

Basic Elements of Dead Reckoning

The two basic elements of DR are:

  • Direction

and

  • Distance

As a navigator, you should already know the supposed direction you're traveling in.

To dead reckon, all you must do then is to compute the distance you've traveled in your given direction. There are two ways to compute distance:

  • By formula: Distance = Speed x Time traveled. Distance is the speed you travel times the amount of time you travel. Given the right information and using this basic formula, you can figure out how far you've traveled, the speed at which you traveled, and the amount of time you traveled.

or

  • By pace count: Count the number of paces you take, and use that to figure out how far you've walked.

1. Dead Reckoning by Formula

Let's look now at dead reckoning by formula. Recall the basic formula given above:

Solving for Distance

Distance = Speed x Time traveled

For our purposes, distance will be stated in kilometers (klicks, for short) to the nearest 1/10th of a kilometer, speed will be stated in kilometers per hour to the nearest 1/10, and time will be stated in minutes to the nearest whole minute.

To correctly use in the same calculation one variable stated on a per-hour basis and the other stated in minutes, we'll have to divide by 60 at some point. Here, then, is our basic dead reckoning equation for land navigation purposes:

Distance = Speed x Time/60

The abbreviated form is:

D = S x T/60

Example -- Let's say you normally walk through the woods at a speed of 3 klicks per hour. In 60 minutes of walking, you'll cover 3 klicks, as follows:

D = S x T/60
D = 3.0 x 60/60
D = 180/60
D = 3.0

Example --  In 30 minutes you'll cover 1.5 kilometers, as follows:

D = S x T/60
D = 3.0 x 30/60
D = 90/60

D = 1.5

Example -- In 28 minutes you'll cover 1.4 kilometers, as follows:

D = S x T/60
D = 3.0 x 28/60
D = 84/60

D = 1.4

Solving for Time

As you leave one checkpoint for another, you may wish to know how much time it will take you to travel a given distance. If you're traveling by DR, for example, from one baseline to another, it's helpful to have a good idea how much time it should take you to reach it. If it's going to take, say about half an hour, then you should start anticipating the next baseline as the half-hour mark approaches.  

The formula for time is derived algebraically from the formula for distance (I hope you paid attention to old Mr. Kahle in high-school algebra class. He tried to tell you'd one day use this stuff.):

D = S x T/60 (The Basic DR formula)
60D = S x T (multiply both sides of the equation by 60)
60D/S = T (divide both sides by T)
T = 60D/S (re-order the variables)

Let's say you just left a forest road walking at your normal speed of 3.0 klicks per hour, and your next catching feature is the shore of a large lake lying 2.2 klicks to the west. How long should it take you to walk to that shore? Compute your answer as follows:

T = 60D/S
T= 60 x 2.2 /3.0
T= 132 /3.0
T = 44

Traveling a your normal 3.0 klicks-per-hour pace, it should take you about 44 minutes to walk to the lake.

Solving for Speed

It's always helpful to know your speed over a given type of terrain, and under varying conditions. You'll walk faster, for example, over dry prairie with no backpack than you will loaded down with gear through a swamp. Having an accurate idea of your speed improves your dead reckoning accuracy.

The formula for speed also comes from the basic formula for distance.:

D = S x T/60 (The Basic DR formula)
60D = S x T (multiply both sides of the equation by 60)
60D/T = S (divide both sides by T)
S = 60D/T (re-order the variables)

Let's say you decide to time your walking speed through thick woods to know what speed variable to use for future dead reckoning calculations. Your map shows that an east-west road lies 1.4 klicks to the south of your current position. Timing yourself, you find that it took you 36 minutes to walk to the road. Compute your speed as follows:

S = 60D / T
S = 60 x 1.4 / 36
S = 84 / 36
S = 2.3

Given that time and distance, your speed was 2.3 klicks per hour.

How to Keep Up with Time Traveled

Use the stopwatch feature on a digital wristwatch. Reset the stopwatch as you begin any leg of your trip. If you cease making forward progress along that leg, pause the stopwatch but don't reset it. Pause the stopwatch, for example, when you stop to rest or when you're bypassing an obstacle and not going forward along your intended course. When you resume forward progress, un-pause the stopwatch. If you're careful, the accumulated time on the stopwatch provides an accurate count of travel time.

2. Dead Reckoning by Pace Count

In lieu of keeping up with time traveled, you can count paces. You'll want to count paces when you don't expect your travel speed to remain constant. Or, you'll need to count paces if you have no watch.

For our purposes, count as one pace each time your left foot (or right foot, it doesn't matter which) hits the ground. You don't count each individual step because that would involve twice as much counting.

While on foot, counting paces is usually the most accurate way to measure distance traveled.

Your Personal Pace Count

But how do paces translate into distance? To know the answer, you'll need to find out how many normal paces you walk in 100 meters.

To do this, go to a 400-meter running track. Maybe a nearby high-school has one they'll let you use. Walk in a normal fashion for one revolution around the track, counting paces as you go. Don't "pace it out," taking exaggerated steps. Just walk naturally.

When you finish, take the number of paces you walked, divide by four, and get the average number of paces it takes you to walk 100 meters. In my case, it's 61, meaning every time I walk 61 paces over even, level ground, I cover 100 meters. If the ground is rough, or is uphill or downhill, I'll surely take fewer or more paces in 100 meters, but 61 is still plenty close enough for most land navigation purposes.

Things That Affect Your Pace Count

Different things can affect your pace count. 

Uphill or Downhill?

Walking uphill increases your pace count--downhill reduces it.

Wind in Your Face or at Your Back?

Walking into a wind increases your pace count. A wind at your back reduces it.

Heavy load?

A heavy load increases your pace count.

Night navigation?

Navigating at night increases your pace count. You can't see as well, and will likely take more steps to cover a certain distance.

Rough Terrain?

Your "standard" pace count was taken over a smooth and level track. Rough terrain--swamp, thick brush, soft sand, for examples--increases your pace count.

Running?

Running reduces your pace count. Serious orienteers, who run just about everywhere while navigating, know this full well. Run around a track, then get an average of your running pace count. Use that when necessary.

Maintaining an Accurate Pace Count

To keep up with total distance walked, put 10 items such as pebbles, pennies, bits of twig in one pocket. Every time you walk 100 meters, remove one item from that pocket and put it in another pocket. When all the items in the pocket have been transferred to the other pocket, you've walked 1,000 meters, or one kilometer. 

Then, transfer all the items back to the original pocket and start all over again to measure off another kilometer. Always work from the same pocket. If you switch up pockets, you're liable to forget which way you're working, and foul up your distance calculation.

For counting paces, you might like a set of "Ranger beads," a few beads on a string especially made for maintaining a pace count. U.S. Army soldiers use these, and they work very well. Ranger beads will help you keep count up to five klicks, and then you start all over.

Don't count paces while you're bypassing obstacles, meaning you're walking more or less perpendicular to your azimuth. Count only those paces that contribute to your forward progress. Remember, the purpose of your pace count is to estimate as closely as reasonably possible your actual forward distance traveled.


Noting Your Position

Mariners mark their DR positions on their charts every half-hour or so. We land navigators could learn from this, and do the same, although you might want to mark your DR position even more frequently--say every 15 minutes or so.

A DR position is only a theoretical position. Its accuracy depends on how well you keep track of distance traveled, and how well you maintain the direction of your intended course.

If you're reasonably accurate in keeping up with both of these, your DR position will be pretty close to where you actually are. It likely won't be exact, however. DR positions are seldom exact. The idea in plotting a DR position on your map is to gain some reasonable idea of your current position. Although you'll identify your position with a penciled dot (don't use a pen on your map), your true position is likely to be not exactly at that dot, but somewhere within a circle of precision surrounding that dot. The longer you go without a definite position fix (most likely either with terrain association or GPS), the greater will be your probably accrued navigation error, meaning your exact position will become increasingly uncertain, and that presumed circle of precision will become ever larger.

Having enough checkpoints spaced not too far apart helps keep accrued navigation error to a minimum. Whenever you arrive at any checkpoint, you can fix your position by terrain associaton, and all accrued navigation error evaporates, since you know exactly where you are.

Of course, you can fix your position almost any time with a GPS. The question then becomes "If I can use a GPS, why do I need to dead reckon?" The short answer: A good navigator never likes to rely on any one source of navigational information. GPSes can and do stop working now and then. Maybe, for example, you're in the mountains and can't get a good signal. With dead reckoning, you at least have backup navigational data, and can continue on with confidence.

Traveling cross country, unless you can use terrain association the entire way, you'll often go from a fixed position at any given checkpoint to several dead reckoning positions in between any two checkpoints, then backed to a fixed position at a subsequent checkpoint. In this manner, you can cross great stretches of terrain keeping navigation error to a minimum by using numerous checkpoints along the way.

Return from How DR Works to Intro to DR

Return from How Dead Reckoning Works to Pathfinding

Return from How Dead Reckoning Works to Home